Marginal probabilities in boson samplers with arbitrary input states

Abstract

With the recent claim of a quantum advantage demonstration in photonics by Zhong et al, the question of the computation of lower-order approximations of boson sampling with arbitrary quantum states at arbitrary distinguishability has come to the fore. In this work, we present results in this direction, building on the results of Clifford and Clifford. In particular, we show:1) How to compute marginal detection probabilities (i.e. probabilities of the detection of some but not all photons) for arbitrary quantum states.2) Using the first result, how to generalize the sampling algorithm of Clifford and Clifford to arbitrary photon distinguishabilities and arbitrary input quantum states.3) How to incorporate truncations of the quantum interference into a sampling algorithm.4) A remark considering maximum likelihood verification of the recent photonic quantum advantage experiment.

Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling

“…More generally, we consider three regimes of interest, and provide evidence for Conjecture 6 in Appendix A. First, the highly sparse regime in which the total number of modes scales as M = ω(K 5 ) and the number of photons is equal to the number of squeezers, N = K, features provable hiding results due to Ref. [15].…”

“…The experiment can be benchmarked either against simulations that try to match a reasonable model of the experiment (constrained adversary) or against simulations that merely try to spoof a given test (unconstrained adversary). The latter approach would be more rigorous as it requires making fewer assumptions; but coming up with good spoofing methods is a problem beyond the scope of this work and should be seen as an ongoing community effort [5,6]. Similar to the approach of the Google and USTC supremacy experiments [49,50], we focus on the former approach-with a classical adversary producing samples according to a noisy model distributionbecause these samples are likely to perform at least as well as the actual device in suitable verification tests [51].…”

“…Notwithstanding, multiple potential loopholes have been pointed out [3][4][5][6][7]. Indeed, QCS will not be marked by a single isolated experiment but rather will be established by gradually improving and scaling up "high complexity" experiments run over the course of many years, which improving classical algorithms will try to simulate.…”

“…On the experimental side, current implementations of GBS either lack programmability [2] or have high loss rates, which could render the system classically simulable [22,23]. Also, from a theoretical standpoint, there is a comparative lack of complexitytheoretic evidence for the hardness of GBS [5][6][7].…”

Many-body coherence and entanglement from randomized correlation measurements

“…Since MBI arises from the inability to assign individual labels to the particles, any distinguishing information carried by unobserved degrees of freedom (dof) of the particles results in a suppression of MBI [14][15][16][17][18][19] and in a reduction of the complexity of associated measurement records. Mapping out the corresponding quantum-toclassical transition is crucial to understand the dynamics and decoherence of many-body quantum systems and, a fortiori, to conceive and assess quantum protocols for communication, metrology or computation with identical particles, such as the boson sampler, which heavily rely on MBI [7,[20][21][22][23][24][25][26][27][28].…”