Sample-efficient benchmarking of multiphoton interference on a boson sampler in the sparse regime

Verification of a quantum advantage in the presence of noise is a key open problem in the study of near-term quantum devices. In this work, we show how to assess the quality of photonic interference in a linear optical quantum device (boson sampler) by using a maximum likelihood method to measure the strength at which various noise sources are present in the experiment. This allows us to use a sparse set of samples to test whether a given boson-sampling experiment meets known upper bounds on the level of noise permissible to demonstrate a quantum advantage. Furthermore, this method allows us to monitor the evolution of noise in real time, creating a valuable diagnostic tool. Finally, we observe that sources of noise in the experiment compound, meaning that the observed value of the mutual photon indistinguishability, which is the main imperfection in our study, is an effective value taking into account all sources of error in the experiment.

Figure 1

A sketch of a boson sampler. A series of $n$ modes out of a large linear interferometer are fed with single photons, and samples from the resulting distribution are recorded at the output.

Figure 2

The probability of observing 10 arbitrarily chosen output configurations (i.e., sets of photon detection events) as a function of partial photon indistinguishability $x$. Note the nonmonotonic behavior in some of these curves. Inset: Monte Carlo estimate of the correction factor arising from the restriction of our data set to collisionless samples.

Figure 3

(a) Maximum likelihood estimation of the partial indistinguishability $x=\langle {\psi }_i|{\psi }_j\rangle ,$ from a sparse series of samples. (b) Log-likelihood functions plotted between $0\le x\le 1.$ The colors indicate the number of photons. (c) Numerical simulation of the accuracy of our experiment, normalized to a constant number of samples.

Figure 4

Real-time monitoring of the effective degree of photon indistinguishability in a boson sampler as a function of excitation power. To decrease the effective degree of indistinguishability, the pump power on the quantum dot single photon source was increased to push the excitation away from the ideal $\pi$ pulse (indicated with a dashed line). The black curve shows a rolling average estimate of $x,$ averaging over 10 000 consecutive samples, with the gray band showing the 95% confidence interval.