Quantum simulation of partially distinguishable boson sampling

Abstract

Boson Sampling is the problem of sampling from the same output probability distribution as a collection of indistinguishable single photons input into a linear interferometer. It has been shown that, subject to certain computational complexity conjectures, in general the problem is difficult to solve classically, motivating optical experiments aimed at demonstrating quantum computational "supremacy". There are a number of challenges faced by such experiments, including the generation of indistinguishable single photons. We provide a quantum circuit that simulates bosonic sampling with arbitrarily distinguishable particles. This makes clear how distinguishabililty leads to decoherence in the standard quantum circuit model, allowing insight to be gained. At the heart of the circuit is the quantum Schur transform, which follows from a representation theoretic approach to the physics of distinguishable particles in first quantisation. The techniques are quite general and have application beyond boson sampling.

25 pages, 4 figures, 2 algorithms, comments welcome

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• Classically simulating near-term partially-distinguishable and lossy boson sampling
• Quantum machine learning with adaptive linear optics
• Discriminating distinguishability
• Signatures of Many-Particle Interference
• Proof-of-work consensus by quantum sampling
• Many-body interference in bosonic dynamics
• Distinguishability in quantum interference with the squeezed states
• A Classical Algorithm for Quantum $\text{SU}(2)$ Schur Sampling
• Quantum advantage from energy measurements of many-body quantum systems
• Realistic photon-number resolution in generalized Hong-Ou-Mandel experiment
• Distinguishability theory for time-resolved photodetection and boson sampling