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Europhysics Letters (EPL)

Experimental simulation of solution to boson sampling based on classical electronic circuits with exponential frequency bandwidth

Zhenwei Yang, Jiacheng Bao, H. J. Sun, X. D. Zhang

Published Oct 2, 2018• 2 citations
Publisher

Abstract

A Boson sampling device is believed to be a specific quantum computer which is more efficient than its classical counterpart. Recently, a number of experimental realizations have been reported, all were based on multi-photon interference in multimode interferometers. Because of the probabilistic nature of single photons, the technique of coincidence counting has to be used in these schemes, it remains a great challenge to scale up the number of photons. Here, we present a novel way to simulate the solution of the boson sampling problem based on classical electronic circuits. Although an exponential frequency bandwidth is used, thus limiting the scalability of the scheme, the running time of our scheme is equivalent to those based on quantum optics. It is also notable that our method has good stability of classical circuits. In addition, some other related problems, which are computationally hard for classical computers, can also be simulated using our scheme. Thus, our findings are advantageous for information processing in the era of big data.

DOI
10.1209/0295-5075/123/50003

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A Boson sampling device is believed to be a specific quantum computer which is more efficient than its classical counterpart. Recently, a number of experimental realizations have been reported, all were based on multi-photon interference in multimode interferometers. Because of the probabilistic nature of single photons, the technique of coincidence counting has to be used in these schemes, it remains a great challenge to scale up the number of photons. Here, we present a novel way to simulate the solution of the boson sampling problem based on classical electronic circuits. Although an exponential frequency bandwidth is used, thus limiting the scalability of the scheme, the running time of our scheme is equivalent to those based on quantum optics. It is also notable that our method has good stability of classical circuits. In addition, some other related problems, which are computationally hard for classical computers, can also be simulated using our scheme. Thus, our findings are advantageous for information processing in the era of big data.
Boson sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialized quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, scattershot boson sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric down-conversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. We report the first scattershot boson sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We use recently proposed statistical tools to analyze our experimental data, providing strong evidence that our photonic quantum simulator works as expected. This approach represents an important leap toward a convincing experimental demonstration of the quantum computational supremacy.
Boson Sampling is a computational task strongly believed to be hard for classical computers, but efficiently solvable by orchestrated bosonic interference in a specialised quantum computer. Current experimental schemes, however, are still insufficient for a convincing demonstration of the advantage of quantum over classical computation. A new variation of this task, Scattershot Boson Sampling, leads to an exponential increase in speed of the quantum device, using a larger number of photon sources based on parametric downconversion. This is achieved by having multiple heralded single photons being sent, shot by shot, into different random input ports of the interferometer. Here we report the first Scattershot Boson Sampling experiments, where six different photon-pair sources are coupled to integrated photonic circuits. We employ recently proposed statistical tools to analyse our experimental data, providing strong evidence that our photonic quantum simulator works as expected.This approach represents an important leap towards a convincing experimental demonstration of the quantum computational supremacy.
Multiphoton interference is at the very heart of quantum foundations and applications in quantum sensing and information processing. In particular, boson-sampling experiments have the potential to demonstrate quantum computational supremacy while relying on only multiphoton interference in linear optical interferometers. However, even when photonic losses are negligible, scalable experiments are challenged by the rapid decrease of the probability of the success of current schemes with probabilistic sources for a large number of single photons in each experimental sample. Remarkably, we show a boson sampling scheme in which the probability of success increases instead of decreasing with the number of input photons, eventually approaching a unit value even with nondeterministic sources. It is achieved by sampling measurements not only at the interferometer output but also over all the possible numbers of photons at each input port and, different from scattershot boson sampling, allowing a random number of occupied input ports from one experimental run to another. Therefore, these results provide an exciting route toward future demonstrations of quantum computational supremacy with scalable experimental resources.
The #P problem is believed to be intractable using classical computers due to difficulties presented by exponential time. It is generally assumed that the best way to solve this problem is to use an algorithm based on quantum mechanics. Here, we propose and demonstrate experimentally an alternative way to solve the #P problem by implementing classical electronic circuits. The typical #P problem to calculate the permanent of a matrix and the related boson sampling problem are solved in polynomial time with exponential frequency bandwidth which limits the scalability of the scheme. The running time of our scheme to solve these problems is equivalent to those based on quantum mechanics. It is also important that our method has good stability of classical circuits. Thus, our findings are advantageous for information processing in the era of big data.
Boson sampling is a computational problem that has recently been proposed as a candidate to obtain an unequivocal quantum computational advantage. The problem consists in sampling from the output distribution of indistinguishable bosons in a linear interferometer. There is strong evidence that such an experiment is hard to classically simulate, but it is naturally solved by dedicated photonic quantum hardware, comprising single photons, linear evolution, and photodetection. This prospect has stimulated much effort resulting in the experimental implementation of progressively larger devices. We review recent advances in photonic boson sampling, describing both the technological improvements achieved and the future challenges. We also discuss recent proposals and implementations of variants of the original problem, theoretical issues occurring when imperfections are considered, and advances in the development of suitable techniques for validation of boson sampling experiments. We conclude by discussing the future application of photonic boson sampling devices beyond the original theoretical scope.
The non-classical interference undergone by multiple photons in passive, linear optical networks gives rise to a surprising computational power of such quantum systems. This is prominently highlighted by boson sampling, a scheme for quantum computation which relies solely on such multiphoton interference and omits the usage of more sophisticated techniques such as entangling gates or feed-forward control. Despite these limitations, it still allows to efficiently solve a class of computational problems which is intractable for classical computers. In this thesis, several open challenges on the way to an experimental realization of boson sampling are addressed. To that end, the idealized model for boson sampling is extended to account, for example, for inner degrees of freedom of the single-photon pulses or the probabilistic nature of single-photon sources. It is shown that the difficulties arising from these real-world effects can be overcome by suitably adapting existing boson sampling schemes. Additionally, the extended model for such interference is applied to reveal its intricate dependence on input state, evolution inside the interferometer, and the detection process. Finally, a novel description of SPDC in terms of temporal Bogoliubov transformations is provided, revealing new, intuitive insights into the temporal structure of photon correlations for such sources.