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arXiv:2012.03967

Quantum Advantage with Timestamp Membosonsampling

Jun Gao, Xiaowei Wang, Wenhao Zhou, Zhi‐Qiang Jiao, Ruo-Jing Ren, Yu-Xuan Fu, Lu‐Feng Qiao, Xiao-Yun Xu, Chao-Ni Zhang, Xiao-Ling Pang, Hang Li, Yao Wang, Xian‐Min Jin

Published Dec 7, 2020• 5 citations
arXivHTMLPDF

Abstract

Quantum computer, harnessing quantum superposition to boost a parallel computational power, promises to outperform its classical counterparts and offer an exponentially increased scaling. The term "quantum advantage" was proposed to mark the key point when people can solve a classically intractable problem by artificially controlling a quantum system in an unprecedented scale, even without error correction or known practical applications. Boson sampling, a problem about quantum evolutions of multi-photons on multimode photonic networks, as well as its variants, has been considered as a promising candidate to reach this milestone. However, the current photonic platforms suffer from the scaling problems, both in photon numbers and circuit modes. Here, we propose a new variant of the problem, timestamp membosonsampling, exploiting the timestamp information of single photons as free resources, and the scaling of the problem can be in principle extended to infinitely large. We experimentally verify the scheme on a self-looped photonic chip inspired by memristor, and obtain multi-photon registrations up to 56-fold in 750,000 modes with a Hilbert space up to $10^{254}$. Our work exhibits an integrated and cost-efficient shortcut stepping into the "quantum advantage" regime in a photonic system far beyond previous scenarios, and provide a scalable and controllable platform for quantum information processing.

DOI
10.48550/arxiv.2012.03967

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Quantum computer, harnessing quantum superposition to boost a parallel computational power, promises to outperform its classical counterparts and offer an exponentially increased scaling. The term "quantum advantage" was proposed to mark the key point when people can solve a classically intractable problem by artificially controlling a quantum system in an unprecedented scale, even without error correction or known practical applications. Boson sampling, a problem about quantum evolutions of multi-photons on multimode photonic networks, as well as its variants, has been considered as a promising candidate to reach this milestone. However, the current photonic platforms suffer from the scaling problems, both in photon numbers and circuit modes. Here, we propose a new variant of the problem, timestamp membosonsampling, exploiting the timestamp information of single photons as free resources, and the scaling of the problem can be in principle extended to infinitely large. We experimentally verify the scheme on a self-looped photonic chip inspired by memristor, and obtain multi-photon registrations up to 56-fold in 750,000 modes with a Hilbert space up to 1025410^{254}10254. Our work exhibits an integrated and cost-efficient shortcut stepping into the "quantum advantage" regime in a photonic system far beyond previous scenarios, and provide a scalable and controllable platform for quantum information processing.
Quantum computer, harnessing quantum superposition to boost a parallel computational power, promises to outperform its classical counterparts and offer an exponentially increased scaling. The term “quantum advantage” was proposed to mark the key point when people can solve a classically intractable problem by artificially controlling a quantum system in an unprecedented scale, even without error correction or known practical applications. Boson sampling, a problem about quantum evolutions of multi-photons on multimode photonic networks, as well as its variants, has been considered as a promising candidate to reach this milestone. However, the current photonic platforms suffer from the scaling problems, both in photon numbers and circuit modes. Here, we propose a new variant of the problem, membosonsampling, exploiting the scaling of the problem can be in principle extended to a large scale. We experimentally verify the scheme on a self-looped photonic chip inspired by memristor, and obtain multi-photon registrations up to 56-fold in 750,000 modes with a Hilbert space up to 10254. The results exhibit an integrated and cost-efficient shortcut stepping into the “quantum advantage” regime in a photonic system far beyond previous scenarios, and provide a scalable and controllable platform for quantum information processing.
Quantum advantage, benchmarking the computational power of quantum machines outperforming all classical computers in a specific task, represents a crucial milestone in developing quantum computers and has been driving different physical implementations since the concept was proposed. A boson sampling machine, an analog quantum computer that only requires multiphoton interference and single-photon detection, is considered to be a promising candidate to reach this goal. However, the probabilistic nature of photon sources and the inevitable loss in evolution network make the execution time exponentially increasing with the problem size. Here, we propose and experimentally demonstrate a timestamp boson sampling scheme that can effectively reduce the execution time for any problem size. By developing a time-of-flight storage technique with a precision up to picosecond level, we are able to detect and record the complete time information of 30 individual modes out of a large-scale 3D photonic chip. We perform the three-photon injection and one external trigger experiment to demonstrate that the timestamp protocol works properly and effectively reduce the execution time. We further verify that timestamp boson sampler is distinguished from other samplers in the case of limited datasets through the three heralded single photons injection experiment. The timestamp protocol can speed up the sampling process, which can be widely applied in multiphoton experiments at low-sampling rate. The approach associated with newly exploited resource from time information can boost all the count-rate-limited experiments, suggesting an emerging field of timestamp quantum optics.
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors, and how do they affect the complexity of the problem solved? Large-scale Gaussian boson sampling (GBS) experiments give an example in which random numbers are generated. Despite classical hardness, these have computable benchmarks for checking data validity. While there are other quantum computing architectures, Gaussian boson sampling is uniquely testable at all scales. Several large, pioneering quantum computing (QC) experiments have been carried out to investigate quantum advantage. Here, we introduce a highly scalable but classical algorithm that can solve GBS approximately. Our numerical simulation of the output count data is closer to the exact solution than current experiments up to 1152 modes. This algorithm outperforms all previous classical, approximate algorithms and scales efficiently to larger experiments. Our results show that effects beyond losses can cause the errors that allow classical simulability. This work will lead to more precise algorithms and is a step towards understanding how QC quantum advantage is affected by the underlying physics.
Understanding the energetic efficiency of quantum computers is essential for assessing their scalability and for determining whether quantum technologies can outperform classical computation beyond runtime alone. In this work, we analyze the energy required to solve the Boson Sampling problem, a paradigmatic task for quantum advantage, using a realistic photonic quantum computing architecture. Using the Metric-Noise-Resource methodology, we establish a quantitative connection between experimental control parameters, dominant noise processes, and energetic resources through a performance metric tailored to Boson Sampling. We estimate the energy cost per sample and identify operating regimes that optimize energetic efficiency. By comparing the energy consumption of quantum and state-of-the-art classical implementations, we demonstrate the existence of a quantum energetic advantage -- defined as a lower energy cost per sample compared to the best-known classical implementation -- that emerges before the onset of computational advantage, even in regimes where classical algorithms remain faster. Finally, we propose an experimentally feasible Boson Sampling architecture, including a complete noise and loss budget, that enables a near-term observation of quantum energetic advantage.
The strong efforts towards the realization of scalable quantum computing are motivated by the promise of super-polynomial speed-up in several computational tasks. A first fundamental step in this route is to provide concrete evidence of ‘quantum supremacy'. Such a regime is obtained when a quantum device is capable of solving a specific problem faster than the best classical hardware. A serious attempt to provide a first demonstration of quantum speed-up with affordable resources is represented by boson sampling [1,2], a non-universal quantum-computational protocol exploiting indistinguishable single photons and linear optical devices. In this context, strong theoretical evidence has been reported that the interference pattern generated by a boson sampler is hard to simulate with classical resources, this pattern being related to the calculation of a hard-to-compute quantity known as a matrix permanent. Formal achievement of the regime of quantum supremacy will answer two very relevant questions: Are we able to benefit from the power of quantum mechanics or does there exist a fundamental reason why this achievement is forbidden? Once this regime has been achieved, are we able to certify the correct functioning of the quantum boson samplers or do we face an undecidability problem? Starting from these intriguing and promising theoretical results, an experimental race kicked off with the aim of reaching the quantum supremacy regime with boson sampling by employing a photonic platform [3]. A large amount of effort has been devoted to pushing the limits of current photonic systems [1], in order to significantly increase the size (number of photons and optical modes) that can be handled with a quantum device. In parallel to this quest for improved quantum performance, it is fundamental to benchmark the limits of a classical simulation of boson sampling. More specifically, in the race for quantum supremacy, what is the best possible classical simulation that can be performed? Such an analysis would be necessary to define the computational capacity possessed by such a classical agent to perform the task (see Fig. 1). In the race for quantum supremacy, a user who employs the best classical hardware and software, and a second agent who exploits a quantum device compete to solve the boson sampling task faster. In a recent article, Wu et al. [4] have provided a fundamental step to define and push the limits of a classical simulation of boson sampling. The authors have employed Tianhe-2, one of the world's most powerful super-computers, to perform such a task. More specifically, by using such high-performance computing hardware and by employing the fastest algorithm to date, Wu et al. have shown that calculating the permanent of a |50×5050 \times 5050×50| matrix can be performed in 100 min. Recent results [5] have shown that this computation corresponds to the classical hardness of drawing a 50-photon sample from a boson sampling distribution. The strong computational capacity of Tianhe-2 also allowed us to address the precision that the known fastest classical algorithms can reach in such a large-scale calculation. This latter aspect is indeed of fundamental importance, since any reliable classical computation must be accompanied by an appropriate error analysis. The study reported in Ref. [4] represents by far the largest calculation to date related to the classical simulation of boson sampling, whose relevance can be found in two different but related aspects. First, it raises the bar for any quantum implementation aimed at reaching quantum advantage, and provides a fundamental benchmark to which any photonic hardware must compare. This result suggests that a larger effort must be dedicated to pushing quantum technologies in this direction. Second, improved classical simulation also has important consequences in the context of boson sampling certification, i.e. the verification that a quantum device is correctly performing the required task. Indeed, first validation procedures in the quantum advantage regime must be assisted by powerful classical computational resources that, while requiring longer processing time than quantum hardware, will necessarily have to perform complex calculations.
This dissertation explores the use of single photons in integrated photonic circuits as a platform for quantum computation and quantum simulation. In the noisy intermediate-scale quantum (NISQ) era, photonic implementations of boson sampling provide one of the most promising routes to demonstrating quantum advantage, while also enabling insight-driven experiments that probe many-body interference and computational complexity. The first part of the thesis is devoted to the hardware development and characterization of programmable silicon nitride photonic processors. We demonstrate large-scale multi-photon interference in a 20-mode universal processor, establishing the potential of integrated photonics for scaling up boson sampling experiments. In parallel, we introduce a validation protocol based on detector binning, implemented on a 12-mode predecessor of the device. Together, these studies advance the photonic platform itself, focusing on scalability, versatility, and benchmarking, rather than direct applications. The second part turns to quantum simulation. We first present a photonic simulation of a spin-foam amplitude from loop quantum gravity, illustrating how multi-photon interference can provide a testbed for problems in fundamental physics. We then implement a particle-number-difference Maxwell demon using conditional operations on photon subsets in a multi-mode interferometer. This experiment probes the link between thermodynamics and information theory, showing how a photonic platform with single-photon resolution and quantum interference can be used to explore information-driven control of physical systems. The final part addresses quantum computation, where we demonstrate a boson-sampling-accelerated Monte Carlo integrator. This hybrid quantum–classical algorithm represents one of the few proposals to extend boson sampling toward practical applications while plausibly retaining its computational hardness. We validate the method in a proof-of-principle experiment reproducing perturbative corrections in a model inspired by Efimov physics. Altogether, the results presented in this thesis position integrated photonics as both a scalable hardware platform for multi-photon experiments and a versatile tool for advancing quantum simulation and computation.