Classical simulation of photonic linear optics with lost particles

Abstract

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an $n$-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the $m$ output modes. We examine two models of losses. In the first model a fixed number of particles is lost. We prove that in this scenario the output statistics can be well approximated by an efficient classical simulation, provided that the number of photons that is left grows slower than $\sqrt{n}$. In the second loss model, every time a photon passes through a beamsplitter in the network, it has some probability of being lost. For this model the relevant parameter is $s$, the smallest number of beamsplitters that any photon traverses as it propagates through the network. We prove that it is possible to approximately simulate the output statistics already if $s$ grows logarithmically with $m$, regardless of the geometry of the network. The latter result is obtained by proving that it is always possible to commute $s$ layers of uniform losses to the input of the network regardless of its geometry, which could be a result of independent interest. We believe that our findings put strong limitations on future experimental realizations of quantum computational supremacy proposals based on boson sampling.

26 pages, 14 figures, comments and suggestions are welcome

References in corpus (17)

• Quantum metrology from a quantum information science perspective
• Quantum Computational Supremacy
• Matter-wave interferometry in a double well on an atom chip
• Photonic Boson Sampling in a Tunable Circuit
• Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
• Experimental Scattershot Boson Sampling
• One-and-a-half quantum de Finetti theorems
• Preparing and probing atomic number states with an atom interferometer
• The geometric measure of entanglement for symmetric states
• Toward Scalable Boson Sampling with Photon Loss
• Linking a distance measure of entanglement to its convex roof
• Separability of diagonal symmetric states: a quadratic conic optimization problem
• Tight bound on trace distance between a realistic device with partially indistinguishable bosons and the ideal Boson Sampling
• Quantum state discrimination bounds for finite sample size
• The complexity of simulating constant-depth BosonSampling
• Quantum simulation of partially distinguishable boson sampling
• A double-well atom trap for fluorescence detection at the Heisenberg limit

Cited by in corpus (60)

• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• Scalable integrated single-photon source
• Efficient classical simulation of random shallow 2D quantum circuits
• Computational advantage of quantum random sampling
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling
• Simulating boson sampling in lossy architectures
• Regimes of classical simulability for noisy Gaussian boson sampling
• Classical algorithm for simulating experimental Gaussian boson sampling
• Classical simulation of lossy boson sampling using matrix product operators
• From estimation of quantum probabilities to simulation of quantum circuits
• Sample complexity of device-independently certified "quantum supremacy"
• Classical simulation of boson sampling based on graph structure
• Classical simulation of linear optics subject to nonuniform losses
• An atomic boson sampler
• Quantifying n-photon indistinguishability with a cyclic integrated interferometer
• Quantum machine learning with Adaptive Boson Sampling via post-selection
• Classically simulating near-term partially-distinguishable and lossy boson sampling
• Noise in BosonSampling and the threshold of efficient classical simulatability
• Spoofing cross entropy measure in boson sampling
• Simulating lossy Gaussian boson sampling with matrix product operators
• Non-linear Boson Sampling
• Distinguishing noisy boson sampling from classical simulations
• Characterization of multi-mode linear optical networks
• Simulating the Dynamics of Single Photons in BosonSampling Devices with Matrix Product States
• Optimizing spontaneous parametric down-conversion sources for boson sampling
• Cut-resistant links and multipartite entanglement resistant to particle loss
• Certification of Gaussian Boson Sampling via graph theory
• Noise thresholds for classical simulability of non-linear Boson sampling
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Semi-device independent characterization of multiphoton indistinguishability
• Analysis of optical loss thresholds in the fusion-based quantum computing architecture
• Simulating photonic devices with noisy optical elements
• Exploring Shallow-Depth Boson Sampling: Towards Scalable Quantum Supremacy
• Efficient validation of Boson Sampling from binned photon-number distributions
• Classical simulation of boson sampling with sparse output
• Piquasso: A Photonic Quantum Computer Simulation Software Platform
• Quantum error cancellation in photonic systems -- undoing photon losses
• Distinguishability theory for time-resolved photodetection and boson sampling
• General protocols for the efficient distillation of indistinguishable photons
• Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
• Classical simulability of constant-depth linear-optical circuits with noise
• BosonSampling.jl: A Julia package for quantum multi-photon interferometry
• Distinguishability Transitions in Non-Unitary Boson Sampling Dynamics
• Comparison of Controlled-Z operation and beam-splitter transformation for generation of squeezed Fock states by measurement
• Validation of a noisy Gaussian boson sampler via graph theory
• Entanglement, loss, and quantumness: When balanced beam splitters are best
• Advancing Quantum Networking: Some Tools and Protocols for Ideal and Noisy Photonic Systems
• Mitigating photon loss in linear optical quantum circuits
• A dataflow programming framework for linear optical distributed quantum computing
• Robustness of optimized numerical estimation schemes for noisy variational quantum algorithms
• On computational complexity and average-case hardness of shallow-depth boson sampling
• Quantum computational advantage of noisy boson sampling with partially distinguishable photons
• Boosting Gaussian Boson Sampling using Optical Parametric Amplification Networks
• Building a fusion-based quantum computer using teleported gates
• Realistic photon-number resolution in Gaussian boson sampling
• Classical algorithms for measurement-adaptive Gaussian circuits
• Mitigating quantum operation infidelity through engineering the distribution of photon losses
• Optical Quantum Computing
• Characterizing Gaussian quantum processes with Gaussian resources