Showing 1–50 of 77 results for all: Peter rohde

Quantum conditional mutual information of W state in non-inertial frames

Authors: H Saveetha, Peter P. Rohde, R Chandrashekar

Abstract: Quantum conditional mutual information (QCMI) is a versatile information theoretic measure. It is used to find the amount of correlations between two qubits from the perspective of a third qubit. In this work we characterise the QCMI of tripartite W-states when some of the qubits are under accelerated motion. Here for our investigations we consider a massless fermionic field in the single mode app… ▽ More Quantum conditional mutual information (QCMI) is a versatile information theoretic measure. It is used to find the amount of correlations between two qubits from the perspective of a third qubit. In this work we characterise the QCMI of tripartite W-states when some of the qubits are under accelerated motion. Here for our investigations we consider a massless fermionic field in the single mode approximation. We consider all possible situations with respect to acceleration of the qubits. From our results we observe that QCMI can either increase or decrease depending on the role of the qubit being accelerated. Finally we discuss the connection between QCMI and correlations by studying the biseparable and separable states. △ Less

Submitted 23 November, 2023; originally announced November 2023.

Comments: 22 pages, 6 figures

Journal ref: Phys. Scr. 99, 025106, 2024

Improving Continuous-variable Quantum Channels with Unitary Averaging

Authors: S. Nibedita Swain, Ryan J. Marshman, Peter P. Rohde, Austin P. Lund, Alexander S. Solntsev, Timothy C. Ralph

Abstract: A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel and so reducing the channels capacity. We present a scheme of passive linear optical unitary averaging for protecting unknown Gaussian states transmitted through… ▽ More A significant hurdle for quantum information and processing using bosonic systems is stochastic phase errors which occur as the photons propagate through a channel. These errors will reduce the purity of states passing through the channel and so reducing the channels capacity. We present a scheme of passive linear optical unitary averaging for protecting unknown Gaussian states transmitted through an optical channel. The scheme reduces the effect of phase noise on purity, squeezing and entanglement, thereby enhancing the channel via probabilistic error correcting protocol. The scheme is robust to loss and typically succeeds with high probability. We provide both numerical simulations and analytical approximations tailored for relevant parameters with the improvement of practical and current technology. We also show the asymptotic nature of the protocol, highlighting both current and future relevance. △ Less

Submitted 9 May, 2024; v1 submitted 17 November, 2023; originally announced November 2023.

Comments: 10 pages, 6 figures, 1 table

Shapes of infinite conformally balanced trees

Authors: Oleg Ivrii, Peter Lin, Steffen Rohde, Emanuel Sygal

Abstract: Numerical experiments by Werness, Lee and the third author suggested that dessin d'enfants associated to large trivalent trees approximate the developed deltoid introduced by Lee, Lyubich, Makarov and Mukherjee. In this paper, we confirm this conjecture. As a side product of our techniques, we give a new proof of a theorem of Bishop which says that ``true trees are dense.'' We also exhibit a seque… ▽ More Numerical experiments by Werness, Lee and the third author suggested that dessin d'enfants associated to large trivalent trees approximate the developed deltoid introduced by Lee, Lyubich, Makarov and Mukherjee. In this paper, we confirm this conjecture. As a side product of our techniques, we give a new proof of a theorem of Bishop which says that ``true trees are dense.'' We also exhibit a sequence of trees whose conformally natural shapes converge to the cauliflower, the Julia set of $z\mapsto z^2+1/4$. △ Less

Submitted 31 October, 2023; originally announced October 2023.

Comments: 48 pages, 12 figures

Proof-of-work consensus by quantum sampling

Authors: Deepesh Singh, Gopikrishnan Muraleedharan, Boxiang Fu, Chen-Mou Cheng, Nicolas Roussy Newton, Peter P. Rohde, Gavin K. Brennen

Abstract: Since its advent in 2011, boson-sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson-sampling using input states that depe… ▽ More Since its advent in 2011, boson-sampling has been a preferred candidate for demonstrating quantum advantage because of its simplicity and near-term requirements compared to other quantum algorithms. We propose to use a variant, called coarse-grained boson-sampling (CGBS), as a quantum Proof-of-Work (PoW) scheme for blockchain consensus. The users perform boson-sampling using input states that depend on the current block information, and commit their samples to the network. Afterward, CGBS strategies are determined which can be used to both validate samples and to reward successful miners. By combining rewards to miners committing honest samples together with penalties to miners committing dishonest samples, a Nash equilibrium is found that incentivizes honest nodes. The scheme works for both Fock state boson sampling and Gaussian boson sampling and provides dramatic speedup and energy savings relative to computation by classical hardware. △ Less

Submitted 11 January, 2024; v1 submitted 31 May, 2023; originally announced May 2023.

Comments: 21 pages, 6 figures (v2 fixes typos, add references)

Optical cluster-state generation with unitary averaging

Authors: Deepesh Singh, Austin P. Lund, Peter P. Rohde

Abstract: Cluster states are the essential resource used in the implementation of Fusion-based quantum computation (FBQC). We introduce a method to generate high-fidelity optical cluster states by utilising the concept of unitary averaging. This error averaging technique is entirely passive and can be readily incorporated into the proposed PsiQuantum's FBQC architecture. Using postselection and the redundan… ▽ More Cluster states are the essential resource used in the implementation of Fusion-based quantum computation (FBQC). We introduce a method to generate high-fidelity optical cluster states by utilising the concept of unitary averaging. This error averaging technique is entirely passive and can be readily incorporated into the proposed PsiQuantum's FBQC architecture. Using postselection and the redundant encoding of Fusion gates, we observe an enhancement in the average fidelity of the output cluster state. We also show an improvement in the linear optical Bell-state measurement (BSM) success probability when the BSM is imperfect. △ Less

Submitted 30 September, 2022; originally announced September 2022.

Compilation of algorithm-specific graph states for quantum circuits

Authors: Madhav Krishnan Vijayan, Alexandru Paler, Jason Gavriel, Casey R. Myers, Peter P. Rohde, Simon J. Devitt

Abstract: We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli measurements on this graph state. By compiling the graph state directly instead of starting with a standard lattice cluster state and preparing it over the course of th… ▽ More We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages, such as Cirq and Q#. The computation can then be implemented using a series of non-Pauli measurements on this graph state. By compiling the graph state directly instead of starting with a standard lattice cluster state and preparing it over the course of the computation, we are able to better understand the resource costs involved and eliminate wasteful Pauli measurements on the actual quantum device. Access to this algorithm-specific graph state also allows for optimisation over locally equivalent graph states to implement the same quantum circuit. The compiler presented here finds ready application in measurement based quantum computing, NISQ devices and logical level compilation for fault tolereant implementations. △ Less

Submitted 8 December, 2022; v1 submitted 15 September, 2022; originally announced September 2022.

Journal ref: 2024 Quantum Sci. Technol. 9 025005

Upper Bounds for the Clock Speeds of Fault-Tolerant Distributed Quantum Computation using Satellites to Supply Entangled Photon Pairs

Authors: Hudson Leone, S Srikara, Peter P. Rohde, Simon Devitt

Abstract: Despite recent advances in quantum repeater networks, entanglement distribution on a continental scale remains prohibitively difficult and resource intensive. Using satellites to distribute maximally entangled photons (Bell pairs) between distant stations is an intriguing alternative. Quantum satellite networks are known to be viable for quantum key distribution, but the question of if such a netw… ▽ More Despite recent advances in quantum repeater networks, entanglement distribution on a continental scale remains prohibitively difficult and resource intensive. Using satellites to distribute maximally entangled photons (Bell pairs) between distant stations is an intriguing alternative. Quantum satellite networks are known to be viable for quantum key distribution, but the question of if such a network is feasible for fault tolerant distributed quantum computation (FTDQC) has so far been unaddressed. In this paper we determine a closed form expression for the rate at which logical Bell pairs can be produced between distant fault-tolerant qubits using a satellite network to supply imperfect physical Bell pairs. With generous parameter assumptions, our results show that FTDQC with satellite networks over statewide distances (500-999 km) is possible for a collective clock rate on the order of 1 MHz while continental (1000-4999 km) and transcontinental (5000+ km) distances run on the order of 10 kHz and 100 Hz respectively. △ Less

Submitted 15 February, 2024; v1 submitted 31 August, 2022; originally announced September 2022.

Comments: 11 pages, 5 figures

Integrated Photonic Platforms for Quantum Technology: A Review

Authors: Rohit K Ramakrishnan, Aravinth Balaji Ravichandran, Arpita Mishra, Archana Kaushalram, Gopalkrishna Hegde, Srinivas Talabattula, Peter P Rohde

Abstract: Quantum information processing has conceptually changed the way we process and transmit information. Quantum physics, which explains the strange behaviour of matter at the microscopic dimensions, has matured into a quantum technology that can harness this strange behaviour for technological applications with far-reaching consequences, which uses quantum bits (qubits) for information processing. Ex… ▽ More Quantum information processing has conceptually changed the way we process and transmit information. Quantum physics, which explains the strange behaviour of matter at the microscopic dimensions, has matured into a quantum technology that can harness this strange behaviour for technological applications with far-reaching consequences, which uses quantum bits (qubits) for information processing. Experiments suggest that photons are the most successful candidates for realising qubits, which indicates that integrated photonic platforms will play a crucial role in realising quantum technology. This paper surveys the various photonic platforms based on different materials for quantum information processing. The future of this technology depends on the successful materials that can be used to universally realise quantum devices, similar to silicon, which shaped the industry towards the end of the last century. Though a prediction is implausible at this point, we provide an overview of the current status of research on the platforms based on various materials. △ Less

Submitted 30 June, 2022; originally announced June 2022.

Comments: 48 pages, 3 figures

The Quantum Internet: A Hardware Review

Authors: Rohit K. Ramakrishnan, Aravinth Balaji Ravichandran, Ishwar Kaushik, Gopalkrishna Hegde, Srinivas Talabattula, Peter P. Rohde

Abstract: In the century following its discovery, applications for quantum physics are opening a new world of technological possibilities. With the current decade witnessing quantum supremacy, quantum technologies are already starting to change the ways information is generated, transmitted, stored and processed. The next major milestone in quantum technology is already rapidly emerging -- the quantum inter… ▽ More In the century following its discovery, applications for quantum physics are opening a new world of technological possibilities. With the current decade witnessing quantum supremacy, quantum technologies are already starting to change the ways information is generated, transmitted, stored and processed. The next major milestone in quantum technology is already rapidly emerging -- the quantum internet. Since light is the most logical candidate for quantum communication, quantum photonics is a critical enabling technology. This paper reviews the hardware aspects of the quantum internet, mainly from a photonics perspective. Though a plethora of quantum technologies and devices have emerged in recent years, we are more focused on devices or components that may enable the quantum internet. Our approach is primarily qualitative, providing a broad overview of the necessary technologies for a large-scale quantum internet. △ Less

Submitted 1 June, 2023; v1 submitted 30 June, 2022; originally announced June 2022.

Comments: 38 pages, 1 table

A general framework for the composition of quantum homomorphic encryption \& quantum error correction

Authors: Yingkai Ouyang, Peter P. Rohde

Abstract: Two essential primitives for universal, cloud-based quantum computation with security based on the laws of quantum mechanics, are quantum homomorphic encryption with information-theoretic security and quantum error correction. The former enables information-theoretic security of outsourced quantum computation, while the latter allows reliable and scalable quantum computations in the presence of er… ▽ More Two essential primitives for universal, cloud-based quantum computation with security based on the laws of quantum mechanics, are quantum homomorphic encryption with information-theoretic security and quantum error correction. The former enables information-theoretic security of outsourced quantum computation, while the latter allows reliable and scalable quantum computations in the presence of errors. Previously these ingredients have been considered in isolation from one another. By establishing group-theoretic requirements that these two ingredients must satisfy, we provide a general framework for composing them. Namely, a quantum homomorphic encryption scheme enhanced with quantum error correction can directly inherit its properties from its constituent quantum homomorphic encryption and quantum error correction schemes. We apply our framework to both discrete- and continuous-variable models for quantum computation, such as Pauli-key and permutation-key encryptions in the qubit model, and displacement-key encryptions in a continuous-variable model based on Gottesman-Kitaev-Preskill codes. △ Less

Submitted 21 April, 2022; originally announced April 2022.

Comments: 13 pages, Two columns

A central limit theorem concerning uncertainty in estimates of individual admixture

Authors: Peter Pfaffelhuber, Angelika Rohde

Abstract: The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\ allele frequ… ▽ More The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from $K$ ancestral populations. Each copy of each allele has the same chance $q_k$ to originate from population $k$, and together with the allele frequencies $p$ in all populations at all $M$ markers, comprises the admixture model. Here, we assume a supervised scheme, i.e.\ allele frequencies $p$ are given through a reference database of size $N$, and $q$ is estimated via maximum likelihood for a single sample. We study laws of large numbers and central limit theorems describing effects of finiteness of both, $M$ and $N$, on the estimate of $q$. We recall results for the effect of finite $M$, and provide a central limit theorem for the effect of finite $N$, introduce a new way to express the uncertainty in estimates in standard barplots, give simulation results, and discuss applications in forensic genetics. △ Less

Submitted 29 July, 2022; v1 submitted 15 October, 2021; originally announced October 2021.

Comments: 25 pages, 7 figures

Accessible and inaccessible quantum coherence in relativistic quantum systems

Authors: Saveetha Harikrishnan, Segar Jambulingam, Peter P. Rohde, Chandrashekar Radhakrishnan

Abstract: The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence and the entire analysis has been carried out in the single-mode approximation. First we investiga… ▽ More The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence and the entire analysis has been carried out in the single-mode approximation. First we investigate tripartite systems, considering both GHZ and W-states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a non-zero value. These results hold for both single- and two-qubit acceleration. In the GHZ and W-states the coherence is distributed as correlations between the qubits and is known as global coherence. But quantum coherence can also exist due to the superposition within a qubit, the local coherence. To study the properties of local coherence we investigate separable state. The GHZ state, W-state and separable states contain only one type of coherence. Next we consider the $W \bar{W}$ and star states in which both local and global coherences coexist. We find that under uniform acceleration both local and global coherence show similar qualitative behaviour. Finally we derive analytic expressions for the quantum coherence of N-partite GHZ and W-states for n < N accelerating qubits. We find that the quantum coherence of a multipartite GHZ state falls exponentially with the number of accelerated qubits, whereas for multipartite W-states the quantum coherence decreases only polynomially. We conclude that W-states are more robust to Unruh decoherence and discuss some potential applications in satellite-based quantum communication and black hole physics. △ Less

Submitted 5 May, 2022; v1 submitted 6 July, 2021; originally announced July 2021.

Comments: 19 pages https://link.aps.org/doi/10.1103/PhysRevA.105.052403

Journal ref: Physical Review A 105, 052403 (2022)

QuNet: Cost vector analysis & multi-path entanglement routing in quantum networks

Authors: Hudson Leone, Nathaniel R. Miller, Deepesh Singh, Nathan K. Langford, Peter P. Rohde

Abstract: Entanglement distribution will form the backbone of many future distributed quantum technologies, especially the quantum internet. The act of purifying multiple noisy entangled states into a single one of higher quality has no analogue in classical networking and as such, this transforms the way in which we will consider future algorithms for routing entanglement. We outline the differences that a… ▽ More Entanglement distribution will form the backbone of many future distributed quantum technologies, especially the quantum internet. The act of purifying multiple noisy entangled states into a single one of higher quality has no analogue in classical networking and as such, this transforms the way in which we will consider future algorithms for routing entanglement. We outline the differences that arise because of this, demonstrate some elementary formalisms for `multi-path entanglement routing', and discuss the philosophical differences that arise when comparing this regime to conventional digital network theory. We also present a software package, QuNet, that uses novel `quantum cost-vector analysis' to simulate and benchmark routing in multi-user entanglement networks in a way that is is highly scalable in network size and the number of competing users. Our software accommodates both ground- and space-based networks, and implements efficient multi-user time-optimisation for mitigating congestion when quantum memories are available. △ Less

Submitted 19 December, 2021; v1 submitted 2 May, 2021; originally announced May 2021.

Comments: 28 pages, 28 figures

Comment on "Relativity of Quantum States in Entanglement Swapping: Violation of Bell's Inequality with no Entanglement"

Authors: Luiz Carlos Ryff

Abstract: In a recent interesting article Chris Nagele, Ebubechukwu O. IloOkeke, Peter P. Rohde, Jonathan P. Dowling, and Tim Byrnes discuss an entanglement swapping experiment using a setup where it is possible to switch the time ordering of measurements. I would like to draw your attention to the fact that the very same idea w… ▽ More In a recent interesting article Chris Nagele, Ebubechukwu O. IloOkeke, Peter P. Rohde, Jonathan P. Dowling, and Tim Byrnes discuss an entanglement swapping experiment using a setup where it is possible to switch the time ordering of measurements. I would like to draw your attention to the fact that the very same idea was introduced in two previous papers, and briefly address some important points related to the subject. △ Less

Submitted 7 February, 2021; originally announced February 2021.

Comments: 3 pages, no figures

Quantum crypto-economics: Blockchain prediction markets for the evolution of quantum technology

Authors: Peter P. Rohde, Vijay Mohan, Sinclair Davidson, Chris Berg, Darcy Allen, Gavin K. Brennen, Jason Potts

Abstract: Two of the most important technological advancements currently underway are the advent of quantum technologies, and the transitioning of global financial systems towards cryptographic assets, notably blockchain-based cryptocurrencies and smart contracts. There is, however, an important interplay between the two, given that, in due course, quantum technology will have the ability to directly compro… ▽ More Two of the most important technological advancements currently underway are the advent of quantum technologies, and the transitioning of global financial systems towards cryptographic assets, notably blockchain-based cryptocurrencies and smart contracts. There is, however, an important interplay between the two, given that, in due course, quantum technology will have the ability to directly compromise the cryptographic foundations of blockchain. We explore this complex interplay by building financial models for quantum failure in various scenarios, including pricing quantum risk premiums. We call this quantum crypto-economics. △ Less

Submitted 1 February, 2021; originally announced February 2021.

Comments: 12 pages, 1 figure

A robust W-state encoding for linear quantum optics

Authors: Madhav Krishnan Vijayan, Austin P. Lund, Peter P. Rohde

Abstract: Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of ph… ▽ More Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest in passive linear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems are passive by definition. In usual scenarios, error detection and correction techniques are inherently active, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit. We present our scheme in the context of a single photonic qubit passing through a noisy communication or quantum memory channel, which has not been generalised to the more general context of full quantum computation. △ Less

Submitted 12 July, 2020; v1 submitted 7 October, 2019; originally announced October 2019.

Comments: Updated draft to accepted version in Quantum

Journal ref: Quantum 4, 303 (2020)

Regularity of SLE in $(t,κ)$ and refined GRR estimates

Authors: Peter K. Friz, Huy Tran, Yizheng Yuan

Abstract: …), a.k.a. SLE trace, has been considered by many authors, starting with Rohde-Schramm (2005). Subsequently, Johansson Viklund, Rohde, and Wong (2014) showed a.s. Hölder continuity of this random field for $κ< 8(2-\sqrt{3})$. In this paper, we improve their result to joint Hölder continuity up to $κ< 8/3$. Moreove… ▽ More Schramm-Loewner evolution (SLE$_κ$) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by $\sqrtκ$ times Brownian motion. This yields a (half-plane) valued random field $γ= γ(t, κ; ω)$. (Hölder) regularity of in $γ(\cdot,κ;ω$), a.k.a. SLE trace, has been considered by many authors, starting with Rohde-Schramm (2005). Subsequently, Johansson Viklund, Rohde, and Wong (2014) showed a.s. Hölder continuity of this random field for $κ< 8(2-\sqrt{3})$. In this paper, we improve their result to joint Hölder continuity up to $κ< 8/3$. Moreover, we show that the SLE$_κ$ trace $γ(\cdot,κ)$ (as a continuous path) is stochastically continuous in $κ$ at all $κ\neq 8$. Our proofs rely on a novel variation of the Garsia-Rodemich-Rumsey (GRR) inequality, which is of independent interest. △ Less

Submitted 17 April, 2021; v1 submitted 27 June, 2019; originally announced June 2019.

MSC Class: 30C20; 60G17; 60G60; 60J67; 60K35

Journal ref: Probab. Theory Relat. Fields (2021)

Photonic quantum data locking

Authors: Zixin Huang, Peter P. Rohde, Dominic W. Berry, Pieter Kok, Jonathan P. Dowling, Cosmo Lupo

Abstract: Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-p… ▽ More Quantum data locking is a quantum phenomenon that allows us to encrypt a long message with a small secret key with information-theoretic security. This is in sharp contrast with classical information theory where, according to Shannon, the secret key needs to be at least as long as the message. Here we explore photonic architectures for quantum data locking, where information is encoded in multi-photon states and processed using multi-mode linear optics and photo-detection, with the goal of extending an initial secret key into a longer one. % The secret key consumption depends on the number of modes and photons employed. In the no-collision limit, where the likelihood of photon bunching is suppressed, the key consumption is shown to be logarithmic in the dimensions of the system. Our protocol can be viewed as an application of the physics of Boson Sampling to quantum cryptography. Experimental realisations are challenging but feasible with state-of-the-art technology, as techniques recently used to demonstrate Boson Sampling can be adapted to our scheme (e.g., Phys. Rev. Lett. 123, 250503, 2019). △ Less

Submitted 24 April, 2021; v1 submitted 8 May, 2019; originally announced May 2019.

Journal ref: Quantum 5, 447 (2021)

Homomorphic encryption of linear optics quantum computation on almost arbitrary states of light with asymptotically perfect security

Authors: Yingkai Ouyang, Si-Hui Tan, Joseph Fitzsimons, Peter P. Rohde

Abstract: Future quantum computers are likely to be expensive and affordable outright by few, motivating client/server models for outsourced computation. However, the applications for quantum computing will often involve sensitive data, and the client would like to keep her data secret, both from eavesdroppers and the server itself. Homomorphic encryption is an approach for encrypted, outsourced quantum com… ▽ More Future quantum computers are likely to be expensive and affordable outright by few, motivating client/server models for outsourced computation. However, the applications for quantum computing will often involve sensitive data, and the client would like to keep her data secret, both from eavesdroppers and the server itself. Homomorphic encryption is an approach for encrypted, outsourced quantum computation, where the client's data remains secret, even during execution of the computation. We present a scheme for the homomorphic encryption of arbitrary quantum states of light with no more than a fixed number of photons, under the evolution of both passive and adaptive linear optics, the latter of which is universal for quantum computation. The scheme uses random coherent displacements in phase-space to obfuscate client data. In the limit of large coherent displacements, the protocol exhibits asymptotically perfect information-theoretic secrecy. The experimental requirements are modest, and easily implementable using present-day technology. △ Less

Submitted 19 March, 2020; v1 submitted 28 February, 2019; originally announced February 2019.

Comments: 14 pages, 3 figures

Journal ref: Phys. Rev. Research 2, 013332 (2020)

Relativity of quantum states in entanglement swapping: Violation of Bell's inequality with no entanglement

Authors: Chris Nagele, Ebubechukwu O. Ilo-Okeke, Peter P. Rohde, Jonathan P. Dowling, Tim Byrnes

Abstract: The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though… ▽ More The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell violation measurement is performed. From an observer in the laboratory frame, a Bell violation is observed due to entanglement swapping taking place, but in a moving frame the order of the measurements is reversed, and a Bell violation is observed even though no entanglement is present. Although the measurement results are identical, the wavefunctions for the two frames are different--- one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that a maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both the non-local and non-simultaneous feature of entanglement. △ Less

Submitted 16 February, 2020; v1 submitted 6 June, 2018; originally announced June 2018.

Journal ref: Physics Letters A, Volume 384, Issue 15, 29 May 2020

The resurgence of the linear optics quantum interferometer --- recent advances & applications

Authors: Si-Hui Tan, Peter P. Rohde

Abstract: Linear optics has seen a resurgence for applications in quantum information processing owing to its miniaturisation on-chip, and increase in production efficiency and quality of single photons. Time-bin encodings have also become feasible owing to architectural breakthroughs, and new processing capabilities. Theoretical efforts have found new ways to implement universal quantum computations with l… ▽ More Linear optics has seen a resurgence for applications in quantum information processing owing to its miniaturisation on-chip, and increase in production efficiency and quality of single photons. Time-bin encodings have also become feasible owing to architectural breakthroughs, and new processing capabilities. Theoretical efforts have found new ways to implement universal quantum computations with linear optics requiring less resources, and to demonstrate the capabilities of linear optics without requiring a universal optical quantum computer. △ Less

Submitted 30 May, 2018; originally announced May 2018.

Demonstration of Topological Data Analysis on a Quantum Processor

Authors: He-Liang Huang, Xi-Lin Wang, Peter P. Rohde, Yi-Han Luo, You-Wei Zhao, Chang Liu, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan

Abstract: Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat. Commun. 7, 10138 (2016)] for calculating Betti numbers of data points -- topological features that count the number of topological holes of various dimensions in a sc… ▽ More Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Lloyd, Garnerone, Zanardi, Nat. Commun. 7, 10138 (2016)] for calculating Betti numbers of data points -- topological features that count the number of topological holes of various dimensions in a scatterplot. Here, we implement a proof-of-principle demonstration of this quantum algorithm by employing a six-photon quantum processor to successfully analyze the topological features of Betti numbers of a network including three data points, providing new insights into data analysis in the era of quantum computing. △ Less

Submitted 17 December, 2019; v1 submitted 19 January, 2018; originally announced January 2018.

Comments: Typos and minor corrections. For the first time, we have experimentally demonstrated that quantum computing can analyze big data using techniques from topology. Any comments are welcome

Journal ref: Optica 5(2),193(2018)

Practical quantum somewhat-homomorphic encryption with coherent states

Authors: Si-Hui Tan, Yingkai Ouyang, Peter P. Rohde

Abstract: We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme… ▽ More We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted codewords. Whilst we focus on coherent state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation. △ Less

Submitted 11 October, 2017; originally announced October 2017.

Journal ref: Phys. Rev. A 97, 042308 (2018)

Passive quantum error correction of linear optics networks through error averaging

Authors: Ryan J. Marshman, Austin P. Lund, Peter P. Rohde, Timothy C. Ralph

Abstract: We propose and investigate a method of error detection and noise correction for bosonic linear networks using a method of unitary averaging. The proposed error averaging does not rely on ancillary photons or control and feed-forward correction circuits, remaining entirely passive in its operation. We construct a general mathematical framework for this technique then give a series of proof of princ… ▽ More We propose and investigate a method of error detection and noise correction for bosonic linear networks using a method of unitary averaging. The proposed error averaging does not rely on ancillary photons or control and feed-forward correction circuits, remaining entirely passive in its operation. We construct a general mathematical framework for this technique then give a series of proof of principle examples including numerical analysis. Two methods for the construction of averaging are then compared to determine the most effective manner of implementation and probe the related error thresholds. Finally we discuss some of the potential uses of this scheme. △ Less

Submitted 7 September, 2017; originally announced September 2017.

Comments: 18 pages, 13 figures and 6 tables

Journal ref: Phys. Rev. A 97, 022324 (2018)

Multiphoton interference in quantum Fourier transform circuits and applications to quantum metrology

Authors: Zu-En Su, Yuan Li, Peter P. Rohde, He-Liang Huang, Xi-Lin Wang, Li Li, Nai-Le Liu, Jonathan P. Dowling, Chao-Yang Lu, Jian-Wei Pan

Abstract: Quantum Fourier transforms (QFT) have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology. Here we present and demonstrate a general technique that simplifies the construction of QFT interferometers using both path and polarization modes. On that basis, we first observed the generalized Hong-Ou-Mandel effect with up to four photons. Furthermore, we dire… ▽ More Quantum Fourier transforms (QFT) have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology. Here we present and demonstrate a general technique that simplifies the construction of QFT interferometers using both path and polarization modes. On that basis, we first observed the generalized Hong-Ou-Mandel effect with up to four photons. Furthermore, we directly exploited number-path entanglement generated in these QFT interferometers and demonstrated optical phase supersensitivities deterministically. △ Less

Submitted 1 August, 2017; originally announced August 2017.

Comments: 8 pages, 10 figures. To appear in Physical Review Letters

Linear optical quantum metrology with single photons --- Experimental errors, resource counting, and quantum Cramér-Rao bounds

Authors: Jonathan P. Olson, Keith R. Motes, Patrick M. Birchall, Nick M. Studer, Margarite LaBorde, Todd Moulder, Peter P. Rohde, Jonathan P. Dowling

Abstract: Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward,… ▽ More Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward, which are difficult to implement. Recently in [Phys. Rev. Lett. 114, 170802 (2015)] we showed that number-path entanglement from a BosonSampling inspired interferometer can be used to beat the shot-noise limit. In this manuscript we compare and contrast different interferometric schemes, discuss resource counting, calculate exact quantum Cramér-Rao bounds, and study details of experimental errors. △ Less

Submitted 7 March, 2017; v1 submitted 23 October, 2016; originally announced October 2016.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. A 96, 013810 (2017)

A Quantum Optics Argument for the #P-hardness of a Class of Multidimensional Integrals

Authors: Peter P. Rohde, Dominic W. Berry, Keith R. Motes, Jonathan P. Dowling

Abstract: Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large matrices using a simple quantum optics argument. In this way we prove that evaluating integrals in this class is \textbf{\#P}-hard. Our work provides a new approach… ▽ More Matrix permanents arise naturally in the context of linear optical networks fed with nonclassical states of light. In this letter we tie the computational complexity of a class of multi-dimensional integrals to the permanents of large matrices using a simple quantum optics argument. In this way we prove that evaluating integrals in this class is \textbf{\#P}-hard. Our work provides a new approach for using methods from quantum physics to prove statements in computer science. △ Less

Submitted 18 July, 2016; originally announced July 2016.

Comments: 6 pages

Measurement-Based Linear Optics

Authors: Rafael N. Alexander, Natasha C. Gabay, Peter P. Rohde, Nicolas C. Menicucci

Abstract: A major challenge in optical quantum processing is implementing large, stable interferometers. Here we propose a virtual, measurement-based interferometer that is programmed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its perform… ▽ More A major challenge in optical quantum processing is implementing large, stable interferometers. Here we propose a virtual, measurement-based interferometer that is programmed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate post-classical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting. △ Less

Submitted 10 March, 2017; v1 submitted 1 June, 2016; originally announced June 2016.

Comments: (v2) consistent with published version; (v1) 6 pages, 5 figures

Journal ref: Phys. Rev. Lett. 118, 110503 (2017)

Efficient recycling strategies for preparing large Fock states from single-photon sources --- Applications to quantum metrology

Authors: Keith R. Motes, Ryan L. Mann, Jonathan P. Olson, Nicholas M. Studer, E. Annelise Bergeron, Alexei Gilchrist, Jonathan P. Dowling, Dominic W. Berry, Peter P. Rohde

Abstract: Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with large photon number remains challenging. We present and analyze a bootstrapped approach for non-deterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a be… ▽ More Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with large photon number remains challenging. We present and analyze a bootstrapped approach for non-deterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photo-detectors, fast-feedforward, and an optical quantum memory. △ Less

Submitted 13 March, 2018; v1 submitted 1 March, 2016; originally announced March 2016.

Comments: 10 pages, 11 figures

Journal ref: Phys. Rev. A 94, 012344 (2016)

Implementing Scalable Boson Sampling with Time-Bin Encoding: Analysis of Loss, Mode Mismatch, and Time Jitter

Authors: Keith R. Motes, Jonathan P. Dowling, Alexei Gilchrist, Peter P. Rohde

Abstract: It was recently shown by Motes, Gilchrist, Dowling & Rohde [PRL 113, 120501 (2014)] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are p… ▽ More It was recently shown by Motes, Gilchrist, Dowling & Rohde [PRL 113, 120501 (2014)] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are present, which corrupt the output of the transformation. We investigate the dominant sources of error in this architecture --- loss and mode-mismatch --- and consider how it affects the BosonSampling protocol, a key application for passive linear optics. For our loss analysis we consider two major components that contribute to loss --- fiber and switches --- and calculate how this affects the success probability and fidelity of the device. Interestingly, we find that errors due to loss are not uniform (unique to time-bin encoding), which asymmetrically biases the implemented unitary. Thus, loss necessarily limits the class of unitaries that may be implemented, and therefore future implementations must prioritise minimising loss rates if arbitrary unitaries are to be implemented. Our formalism for mode-mismatch is generlized to account for various phenomenon that may cause mode-mismatch, but we focus on two --- errors in fiber-loop lengths, and time-jitter of the photon source. These results provide a guideline for how well future experimental implementations might perform in light of these error mechanisms. △ Less

Submitted 26 July, 2015; originally announced July 2015.

Comments: 11 pages, 13 figures

Journal ref: Phys. Rev. A 92, 052319 (2015)

Quantum leap: how to complete a quantum walk in a single step

Authors: Magdalena Stobińska, Peter P. Rohde, Paweł Kurzyński

Abstract: Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows w… ▽ More Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows with their length or spread $n$. We introduce the concept of a quantum leap, a process which can be achieved with fewer or complementary resources and which in a single step simulates another long process. The process and its leap are described by the same Hamiltonian but, the latter parametrizes the evolution with a tunable parameter of a setup. In the case of walks, a leap immediately gives a probability distribution which results only after many steps. This may be appealing for simulation of processes which are lengthy or require dynamical control. We discuss a leap based on the multi-particle Hong--Ou--Mandel interference, an inherently quantum phenomenon. It reproduces a quantum walk enabling perfect state transfer through spin chains. It requires a beam splitter, two detectors and $n$ particles to mimic a walk on a chain of size $O(n)$, for time fixed by beam-splitter's reflectivity. Our results apply to a broad class of systems where the HOM-like effects can be observed, and may constitute a new approach to simulation of complex Hamiltonians with passive interferometers. △ Less

Submitted 2 November, 2015; v1 submitted 21 April, 2015; originally announced April 2015.

Comments: 10 pages, 9 figures

Multiplexed single-photon state preparation using a fibre-loop architecture

Authors: Peter P. Rohde, L. G. Helt, M. J. Steel, Alexei Gilchrist

Abstract: Heralded spontaneous parametric down-conversion (SPDC) has become the mainstay for single-photon state preparation in present-day photonics experiments. Because they are heralded, in principle one knows when a single photon has been prepared. However, the heralding efficiencies in experimentally realistic SPDC sources are typically very low. To overcome this, multiplexing techniques have been prop… ▽ More Heralded spontaneous parametric down-conversion (SPDC) has become the mainstay for single-photon state preparation in present-day photonics experiments. Because they are heralded, in principle one knows when a single photon has been prepared. However, the heralding efficiencies in experimentally realistic SPDC sources are typically very low. To overcome this, multiplexing techniques have been proposed which employ a bank of SPDC sources in parallel, and route successfully heralded photons to the output, thereby effectively boosting the heralding efficiency. However, running a large bank of independent SPDC sources is costly and requires complex switching. We analyse a multiplexing technique based on time-bin encoding that allows the heralding efficiency of just a single SPDC source to be increased. The scheme is simple and experimentally viable using present-day technology. We analyse the operation of the scheme in terms of experimentally realistic considerations, such as losses, detector inefficiency, and pump-power. △ Less

Submitted 6 April, 2015; v1 submitted 11 March, 2015; originally announced March 2015.

Comments: Major update including several new results. Additional references and figures

Journal ref: Phys. Rev. A 92, 053829 (2015)

Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

Authors: Keith R. Motes, Jonathan P. Olson, Evan J. Rabeaux, Jonathan P. Dowling, S. Jay Olson, Peter P. Rohde

Abstract: Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward,… ▽ More Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multi-photon walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer --- fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection --- is capable of significantly beating the shotnoise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology. △ Less

Submitted 4 May, 2015; v1 submitted 5 January, 2015; originally announced January 2015.

Comments: 10 pages, 8 figures

Report number: LB14398

Journal ref: Phys. Rev. Lett. 114, 170802 (2015)

Multi-scale quantum simulation of quantum field theory using wavelets

Authors: Gavin K. Brennen, Peter Rohde, Barry C. Sanders, Sukhwinder Singh

Abstract: A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis---a multi-scale description of the theory. Since wavelets are compact wavefunctions, this encoding allows for quantum simulatio… ▽ More A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis---a multi-scale description of the theory. Since wavelets are compact wavefunctions, this encoding allows for quantum simulations to create particle excitations with compact support and provides a natural way to associate observables in the theory to finite resolution detectors. We show that the wavelet basis is well suited to compute subsystem entanglement entropy by dividing the field into contributions from short-range wavelet degrees of freedom and long-range scale degrees of freedom, of which the latter act as renormalized modes which capture the essential physics at a renormalization fixed point. △ Less

Submitted 1 December, 2014; originally announced December 2014.

Comments: 11 pages, 5 figures

Journal ref: Phys. Rev. A 92, 032315 (2015)

Boson-sampling with photons of arbitrary spectral structure

Authors: Peter P. Rohde

Abstract: Boson-sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson-sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson-sampling with photon… ▽ More Boson-sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson-sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson-sampling with photons of arbitrary spectral structure and relate the sampling statistics of the device to matrix permanents. This sheds light on the computational complexity of different regimes of the photons' spectral characteristics, and provides very general results for the operation of linear optics interferometers in the presence of partially distinguishable photons. Our results apply to both the cases of spectrally resolving and non-spectrally resolving detectors. △ Less

Submitted 15 October, 2014; originally announced October 2014.

Journal ref: Phys. Rev. A 91, 012307 (2015)

A simple scheme for universal linear optics quantum computing with constant experimental complexity using fiber-loops

Authors: Peter P. Rohde

Abstract: Recently, Motes, Gilchrist, Dowling & Rohde [Phys. Rev. Lett. 113, 120501 (2014)] presented a scheme for photonic boson-sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear optics quantum computing, in various incarnations. The scheme employs two embedded fiber-loops, a sing… ▽ More Recently, Motes, Gilchrist, Dowling & Rohde [Phys. Rev. Lett. 113, 120501 (2014)] presented a scheme for photonic boson-sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear optics quantum computing, in various incarnations. The scheme employs two embedded fiber-loops, a single push-button photon source, three dynamically controlled beamsplitters, and a single time-resolved photo-detector. The architecture has only a single point of interference, and thus may be significantly easier to align than other schemes. The experimental complexity of the scheme is constant, irrespective of the size of the computation, limited only by fiber lengths and their respective loss rates. △ Less

Submitted 1 October, 2014; originally announced October 2014.

Journal ref: Phys. Rev. A 91, 012306 (2015)

Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling

Authors: Jonathan P. Olson, Kaushik P. Seshadreesan, Keith R. Motes, Peter P. Rohde, Jonathan P. Dowling

Abstract: Boson sampling is a simple model for non-universal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single photon states is fed through a Haar-random linear optics network and sampled at the output using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an ana… ▽ More Boson sampling is a simple model for non-universal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single photon states is fed through a Haar-random linear optics network and sampled at the output using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of new quantum states of light in the same complexity class as boson sampling. △ Less

Submitted 22 February, 2015; v1 submitted 30 June, 2014; originally announced June 2014.

Comments: 5 pages, 2 figures

Journal ref: Phys. Rev. A 91, 022317 (2015)

An introduction to boson-sampling

Authors: Bryan T. Gard, Keith R. Motes, Jonathan P. Olson, Peter P. Rohde, Jonathan P. Dowling

Abstract: Boson-sampling is a simplified model for quantum computing that may hold the key to implementing the first ever post-classical quantum computer. Boson-sampling is a non-universal quantum computer that is significantly more straightforward to build than any universal quantum computer proposed so far. We begin this chapter by motivating boson-sampling and discussing the history of linear optics quan… ▽ More Boson-sampling is a simplified model for quantum computing that may hold the key to implementing the first ever post-classical quantum computer. Boson-sampling is a non-universal quantum computer that is significantly more straightforward to build than any universal quantum computer proposed so far. We begin this chapter by motivating boson-sampling and discussing the history of linear optics quantum computing. We then summarize the boson-sampling formalism, discuss what a sampling problem is, explain why boson-sampling is easier than linear optics quantum computing, and discuss the Extended Church-Turing thesis. Next, sampling with other classes of quantum optical states is analyzed. Finally, we discuss the feasibility of building a boson-sampling device using existing technology. △ Less

Submitted 26 June, 2014; originally announced June 2014.

Comments: 13 pages, 8 figures

Journal ref: Chapter 8, contained in Book: From Atomic to Mesoscale: The Role of Quantum Coherence in Systems of Various Complexities , Publisher: World Scientific Publishing Co (August 25, 2015), ISBN-10: 9814678694

Scalable boson-sampling with time-bin encoding using a loop-based architecture

Authors: Keith R. Motes, Alexei Gilchrist, Jonathan P. Dowling, Peter P. Rohde

Abstract: We present an architecture for arbitrarily scalable boson-sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically contro… ▽ More We present an architecture for arbitrarily scalable boson-sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson-sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies. △ Less

Submitted 17 March, 2014; originally announced March 2014.

Comments: 7 pages, 7 figures

Journal ref: Phys. Rev. Lett. 113, 120501 (2014)

Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states---The quantum-classical divide and computational-complexity transitions in linear optics

Authors: Kaushik P. Seshadreesan, Jonathan P. Olson, Keith R. Motes, Peter P. Rohde, Jonathan P. Dowling

Abstract: Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed with single-photon Fock state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other t… ▽ More Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon number distribution of a linear optical interferometric network, which is fed with single-photon Fock state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon number detection scheme demonstrates a computational complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small, to a classically simulatable problem in the limit of large coherent amplitudes. △ Less

Submitted 27 February, 2015; v1 submitted 3 February, 2014; originally announced February 2014.

Comments: 7 pages, 3 figures; published version

Journal ref: Phys. Rev. A 91, 022334 (2015)

Will boson-sampling ever disprove the Extended Church-Turing thesis?

Authors: Peter P. Rohde, Keith R. Motes, Paul A. Knott, William J. Munro

Abstract: Boson-sampling is a highly simplified, but non-universal, approach to implementing optical quantum computation. It was shown by Aaronson and Arkhipov that this protocol cannot be efficiently classically simulated unless the polynomial hierarchy collapses, which would be a shocking result in computational complexity theory. Based on this, numerous authors have made the claim that experimental boson… ▽ More Boson-sampling is a highly simplified, but non-universal, approach to implementing optical quantum computation. It was shown by Aaronson and Arkhipov that this protocol cannot be efficiently classically simulated unless the polynomial hierarchy collapses, which would be a shocking result in computational complexity theory. Based on this, numerous authors have made the claim that experimental boson-sampling would provide evidence against, or disprove, the Extended Church-Turing thesis -- that any physically realisable system can be efficiently simulated on a Turing machine. We argue against this claim on the basis that, under a general, physically realistic independent error model, boson-sampling does not implement a provably hard computational problem in the asymptotic limit of large systems. △ Less

Submitted 25 May, 2014; v1 submitted 9 January, 2014; originally announced January 2014.

Comments: 3 pages, 0 figures; added references and separated a some references into separate categories

Self-avoiding quantum walks

Authors: Elizabeth Camilleri, Peter P. Rohde, Jason Twamley

Abstract: Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random walks have found numerous applications, most notably in the modeling of protein folding. We consider the analogous problem in the quantum setting. We complement… ▽ More Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random walks have found numerous applications, most notably in the modeling of protein folding. We consider the analogous problem in the quantum setting. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker's motion, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk. △ Less

Submitted 8 January, 2014; originally announced January 2014.

Journal ref: Sci. Rep. 4, 4791 (2014)

Quantum random walks on congested lattices

Authors: Keith R. Motes, Alexei Gilchrist, Peter P. Rohde

Abstract: We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walker's direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walkers as well as study the effect of dephasing on the quantum walk. O… ▽ More We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walker's direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walkers as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. Also, we observe that a quantum walker is extremely sensitive to our model of dephasing. △ Less

Submitted 30 October, 2013; originally announced October 2013.

Comments: 8 pages, 8 figures

Journal ref: Scientific Reports 6, 19864 (2016)

Sampling generalized cat states with linear optics is probably hard

Authors: Peter P. Rohde, Keith R. Motes, Paul Knott, Joseph Fitzsimons, William Munro, Jonathan P. Dowling

Abstract: Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been shown that this sampling problem likely cannot be efficiently classically simulated. This raises the question as to whether there are other quantum states of ligh… ▽ More Boson-sampling has been presented as a simplified model for linear optical quantum computing. In the boson-sampling model, Fock states are passed through a linear optics network and sampled via number-resolved photodetection. It has been shown that this sampling problem likely cannot be efficiently classically simulated. This raises the question as to whether there are other quantum states of light for which the equivalent sampling problem is also computationally hard. We present evidence, without using a full complexity proof, that a very broad class of quantum states of light --- arbitrary superpositions of two or more coherent states --- when evolved via passive linear optics and sampled with number-resolved photodetection, likely implements a classically hard sampling problem. △ Less

Submitted 20 December, 2014; v1 submitted 1 October, 2013; originally announced October 2013.

Comments: 8 pages, 2 figures

Report number: LK13673A

Journal ref: Phys. Rev. A 91, 012342 (2015)

Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson-sampling

Authors: Keith R. Motes, Jonathan P. Dowling, Peter P. Rohde

Abstract: Boson-sampling has emerged as a promising avenue towards post-classical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to-date. Here we present a simple architectur… ▽ More Boson-sampling has emerged as a promising avenue towards post-classical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to-date. Here we present a simple architecture for boson-sampling based on multiplexed SPDC sources and demonstrate that the architecture is limited only by the post-selection detection efficiency assuming that other errors, such as spectral impurity, dark counts, and interferometric instability are negligible. For any given number of input photons, there exists a minimum detector efficiency that allows post selection. If this efficiency is achieved, photon-number errors in the SPDC sources are sufficiently low as to guarantee correct boson-sampling most of the time. In this scheme the required detector efficiency must increase exponentially in the photon number. Thus, we show that idealised SPDC sources will not present a bottleneck for future boson-sampling implementations. Rather, photodetection efficiency is the limiting factor and thus future implementations may continue to employ SPDC sources. △ Less

Submitted 14 April, 2014; v1 submitted 31 July, 2013; originally announced July 2013.

Comments: 6 pages, 5 figures; added reference to Meany et al

Journal ref: Phys. Rev. A 88, 063822 (2013)

Quantum walks with memory - goldfish, elephants and wise old men

Authors: Peter P. Rohde, Gavin K. Brennen, Alexei Gilchrist

Abstract: Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observ… ▽ More Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic speed up over classical walks just as found in previous studies of multi-coined walks with trivial memory function. However, measurement of the multi-coin state can dramatically shift the mean of the spatial distribution. Second, we consider spatial entanglement in a two-dimensional quantum walk with memory and find that memory destroys entanglement between the spatial dimensions, even when entangling coins are employed. Finally, we explore behaviour in the presence of spatial randomness and find that in contrast to single coined walks, multi-coined walks do not localise and in fact a memory function can speed up the walk relative to a fully decohered multi-coin walker with trivial memory. We explicitly show how to construct linear optics circuits implementing the walks, and discuss prospects for classical simulation. △ Less

Submitted 18 December, 2012; originally announced December 2012.

Journal ref: Phys. Rev. A, 87, 052302 (2013)

The information capacity of a single photon

Authors: Peter P. Rohde, Joseph F. Fitzsimons, Alexei Gilchrist

Abstract: Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarisation states of single photons has been widely used as these states form an natural closed two state qubit. However, photons are able to encode much more -- in principle infinite -- information via the continuous spatio-temporal degrees of freedom. Here we consider th… ▽ More Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarisation states of single photons has been widely used as these states form an natural closed two state qubit. However, photons are able to encode much more -- in principle infinite -- information via the continuous spatio-temporal degrees of freedom. Here we consider the information capacity of an optical quantum channel, such as an optical fibre, where a spectrally encoded single photon is the means of communication. We use the Holevo bound to calculate an upper bound on the channel capacity, and relate this to the spectral encoding basis and the spectral properties of the channel. Further, we derive analytic bounds on the capacity of such channels, and in the case of a symmetric two-state encoding calculate the exact capacity of the corresponding channel. △ Less

Submitted 6 November, 2012; originally announced November 2012.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. A 88, 022310 (2013)

Optical quantum computing with photons of arbitrarily low fidelity and purity

Authors: Peter P. Rohde

Abstract: Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatio-temporal structure of photons -- they must be completely indistinguishabl… ▽ More Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatio-temporal structure of photons -- they must be completely indistinguishable and of very high purity. We show that in the Boson-sampling model for LOQC these conditions may be significantly relaxed. We present evidence that by increasing the size of the system we can implement a computationally hard algorithm even if our photons have arbitrarily low fidelity and purity. These relaxed conditions make Boson-sampling LOQC within reach of present-day technology. △ Less

Submitted 23 September, 2012; v1 submitted 12 August, 2012; originally announced August 2012.

Comments: Version submitted to Phys. Rev. A

Journal ref: Phys. Rev. A 86, 052321 (2012)

Increasing the dimensionality of quantum walks using multiple walkers

Authors: Peter P. Rohde, Andreas Schreiber, Martin Stefanak, Igor Jex, Alexei Gilchrist, Christine Silberhorn

Abstract: We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures… ▽ More We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures and how they relate to linear optics quantum computing. In particular we show that multi-walker quantum walks are equivalent to the BosonSampling model for linear optics quantum computation proposed by Aaronson & Arkhipov. With the addition of control over phase-defects in the lattice, which can be simulated with entangling gates, asymmetric lattice structures can be constructed which are universal for quantum computation. △ Less

Submitted 8 May, 2012; originally announced May 2012.

Comments: 9 pages

Journal ref: Journal of Computational and Theoretical Nanoscience, 10, 1644 (2013)

A 2D Quantum Walk Simulation of Two-Particle Dynamics

Authors: Andreas Schreiber, Aurel Gabris, Peter P. Rohde, Kaisa Laiho, Martin Stefanak, Vaclav Potocek, Craig Hamilton, Igor Jex, Christine Silberhorn

Abstract: Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a lattice, demonstrating a scalable quantum walk on a non-trivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions using an o… ▽ More Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a lattice, demonstrating a scalable quantum walk on a non-trivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions using an optical fiber network. With our broad spectrum of quantum coins we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong non-linearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems. △ Less

Submitted 16 April, 2012; originally announced April 2012.

Journal ref: Science 336 55-58 (2012)