Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.10112 · Physical Review A

Simulability of partially distinguishable superposition and Gaussian boson sampling

Jelmer J. Renema

Published Jun 29, 2020• 32 citations
arXivHTMLPDF

Abstract

We study the hardness of classically simulating boson sampling with superposition and Gaussian input states at nonzero photon indistinguishability. We find that, similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in both these boson sampling variants. For superposition sampling, we find that it is not simulable with out method at zero indistinguishability, which is evidence for the computational hardness of this problem, and we find that it is simulable at any level of particle distinguishability, similar to regular boson sampling. If an efficient classical algorithm to approximate a given sum over permanents is found, this approach also leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability.

DOI
10.1103/physreva.101.063840

Related papers

Efficient Classical Algorithm for Boson Sampling with Partially Distinguishable Photons

Jelmer J. Renema, Adrian J. Menssen, William R. Clements +3 more

We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.

arXiv:1707.02793•Physical Review Letters•May 30, 2018•111 citations

Gaussian boson sampling with partial distinguishability

Junheng Shi, Tim Byrnes

Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient auxiliary classical simulation algorithm which can be used to calculate the probabilities. Our model and the auxiliary algorithm provide foundations for an approximation method for the probability calculation and simulation algorithms not only compatible with existing state-of-the-art simulation algorithms for ideal GBS but also reduce their complexities exponentially depending on the indistinguishability. Using the approximation method and the simulation algorithms we show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.

arXiv:2105.09583•May 20, 2021•3 citations

Effect of partial distinguishability on quantum supremacy in Gaussian Boson sampling

Junheng Shi, Tim Byrnes

Abstract Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient classical simulation algorithm which can be used to calculate the probabilities. Our model and algorithm provide foundations for an approximate method for calculating probabilities. It also allows for a way to design sampling algorithms that are not only compatible with existing algorithms for ideal GBS, but can also reduce their complexity exponentially, depending on the indistinguishability efficiency. Using this we show how the boundary of quantum supremacy in GBS can be affected by partial distinguishability.

npj Quantum Information•May 11, 2022•23 citations

Classically simulating near-term partially-distinguishable and lossy boson sampling

Alexandra E. Moylett, Raúl García−Patrón, Jelmer J Renema +1 more

Abstract Boson sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of ‘quantum computational supremacy’, this motivates optimising classical simulation schemes for a realistic model of the problem, in this case boson sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised boson sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.

arXiv:1907.00022•Quantum Science and Technology•Nov 7, 2019•32 citations

Efficient classical algorithm for simulating boson sampling with heterogeneous partial distinguishability

S. N. van den Hoven, E. Kanis, Jelmer J. Renema

Boson sampling is one of the leading protocols for demonstrating a quantum advantage, but the theory of how this protocol responds to noise is still incomplete. We extend the theory of classical simulation of boson sampling with partial distinguishability to the case where the degree of indistinguishability between photon pairs is different between different pairs.

Physical Review A•May 28, 2025•4 citations

Efficient classical algorithm for simulating boson sampling with heterogeneous partial distinguishability

S. N. van den Hoven, Kanis, E., Jelmer J. Renema

Boson sampling is one of the leading protocols for demonstrating a quantum advantage, but the theory of how this protocol responds to noise is still incomplete. We extend the theory of classical simulation of boson sampling with partial distinguishability to the case where the degree of indistinguishability between photon pairs is different between different pairs.

arXiv:2406.17682•Jun 25, 2024•1 citation
We study the hardness of classically simulating boson sampling with superposition and Gaussian input states at nonzero photon indistinguishability. We find that, similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference terms in both these boson sampling variants. For superposition sampling, we find that it is not simulable with out method at zero indistinguishability, which is evidence for the computational hardness of this problem, and we find that it is simulable at any level of particle distinguishability, similar to regular boson sampling. If an efficient classical algorithm to approximate a given sum over permanents is found, this approach also leads to an efficient classical algorithm to simulate Gaussian boson sampling in the presence of distinguishability.
We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.
Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient auxiliary classical simulation algorithm which can be used to calculate the probabilities. Our model and the auxiliary algorithm provide foundations for an approximation method for the probability calculation and simulation algorithms not only compatible with existing state-of-the-art simulation algorithms for ideal GBS but also reduce their complexities exponentially depending on the indistinguishability. Using the approximation method and the simulation algorithms we show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.
Abstract Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient classical simulation algorithm which can be used to calculate the probabilities. Our model and algorithm provide foundations for an approximate method for calculating probabilities. It also allows for a way to design sampling algorithms that are not only compatible with existing algorithms for ideal GBS, but can also reduce their complexity exponentially, depending on the indistinguishability efficiency. Using this we show how the boundary of quantum supremacy in GBS can be affected by partial distinguishability.
Abstract Boson sampling is the problem of sampling from the same distribution as indistinguishable single photons at the output of a linear optical interferometer. It is an example of a non-universal quantum computation which is believed to be feasible in the near term and cannot be simulated on a classical machine. Like all purported demonstrations of ‘quantum computational supremacy’, this motivates optimising classical simulation schemes for a realistic model of the problem, in this case boson sampling when the implementations experience lost or distinguishable photons. Although current simulation schemes for sufficiently imperfect boson sampling are classically efficient, in principle the polynomial runtime can be infeasibly large. In this work, we develop a scheme for classical simulation of boson sampling under uniform distinguishability and loss, based on the idea of sampling from distributions where at most k photons are indistinguishable. We show that asymptotically this scheme can provide a polynomial improvement in the runtime compared to classically simulating idealised boson sampling. More significantly, we show that in the regime considered experimentally relevant, our approach gives an substantial improvement in runtime over other classical simulation approaches.