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Gaussian Boson Sampling Compilation

Sonia López Alarcón, Federico Rueda

Published Jul 11, 2022• 0 citations
Publisher

Abstract

Abstract Gaussian Boson Sampling is gaining relevance among the multiple technologies currently implementing quantum computing. The problem of sampling out of a boson distribution across multiple modes has a strong mathematical connection with combinatorics problems, with multiple practical applications that would classically be unfeasible to solve within reasonable time. The software stack that accompanies this GBS approach, and that takes the application from its high level description to the hardware implementation, is the main focus of this paper. The general compilation process of Gaussian Boson Samplers is described in detail. The specifics of the Strawberry Fields (Xanadu) compilation and simulation framework are discussed, along with its time profiling, and time implications on computationally significant problem sizes. Last, a compilation step to reduce the hardware description complexity is presented, demonstrating a linear reduction on the overall number of operators when the number of Gaussian operators increases.

DOI
10.21203/rs.3.rs-1813584/v1

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Abstract Gaussian Boson Sampling is gaining relevance among the multiple technologies currently implementing quantum computing. The problem of sampling out of a boson distribution across multiple modes has a strong mathematical connection with combinatorics problems, with multiple practical applications that would classically be unfeasible to solve within reasonable time. The software stack that accompanies this GBS approach, and that takes the application from its high level description to the hardware implementation, is the main focus of this paper. The general compilation process of Gaussian Boson Samplers is described in detail. The specifics of the Strawberry Fields (Xanadu) compilation and simulation framework are discussed, along with its time profiling, and time implications on computationally significant problem sizes. Last, a compilation step to reduce the hardware description complexity is presented, demonstrating a linear reduction on the overall number of operators when the number of Gaussian operators increases.
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Abstract Gaussian boson sampling (GBS) is a near-term platform for photonic quantum computing. Recent efforts have led to the discovery of GBS algorithms with applications to graph-based problems, point processes, and molecular vibronic spectra in chemistry. The development of dedicated quantum software is a key enabler in permitting users to program devices and implement algorithms. In this work, we introduce a new applications layer for the Strawberry Fields photonic quantum computing library. The applications layer provides users with the necessary tools to design and implement algorithms using GBS with only a few lines of code. This paper serves a dual role as an introduction to the software, supported with example code, and also a review of the current state of the art in GBS algorithms.
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.
Gaussian Boson Sampling (GBS) have shown advantages over classical methods for performing some specific sampling tasks. To fully harness the computational power of GBS, there has been great interest in identifying their practical applications. In this study, we explore the use of GBS samples for computing a numerical approximation to the Gaussian expectation problem, that is to integrate a multivariate function against a Gaussian distribution. We propose two estimators using GBS samples, and show that they both can bring an exponential speedup over the plain Monte Carlo (MC) estimator. Precisely speaking, the exponential speedup is defined in terms of the guaranteed sample size for these estimators to reach the same level of accuracy εεε and the same success probability δδδ in the (ε,δ)(ε, δ)(ε,δ) multiplicative error approximation scheme. We prove that there is an open and nonempty subset of the Gaussian expectation problem space for such computational advantage.
Abstract Gaussian Boson Sampling (GBS) is a non-universal model for quantum computing inspired by the original formulation of the Boson Sampling (BS) problem. Nowadays, it represents a paradigmatic quantum platform to reach the quantum advantage regime in a specific computational model. Indeed, thanks to the implementation in photonics-based processors, the latest GBS experiments have reached a level of complexity where the quantum apparatus has solved the task faster than currently up-to-date classical strategies. In addition, recent studies have identified possible applications beyond the inherent sampling task. In particular, a direct connection between photon counting of a genuine GBS device and the number of perfect matchings in a graph has been established. In this work, we propose to exploit such a connection to benchmark GBS experiments. We interpret the properties of the feature vectors of the graph encoded in the device as a signature of correct sampling from the true input state. Within this framework, two approaches are presented. The first method exploits the distributions of graph feature vectors and classification via neural networks. The second approach investigates the distributions of graph kernels. Our results provide a novel approach to the actual need for tailored algorithms to benchmark large-scale Gaussian Boson Samplers.
Boson-sampling problems are specific cases of multi-photon quantum interference in which the complexity of sampling from the output distribution of multiple photons on multiple modes arises from its relation to certain matrix functions that cannot be efficiently computed in polynomial time using the best-known classical algorithms. Specifically, gaussian boson sampling (GBS) is a protocol that employs Gaussian states as inputs to a linear interferometer, and whose output samples can be used to accelerate graph search and optimization problems [1]. To date, GBS experiments have been reported by using path or time-bin encoding of the optical modes.