[Paper Review] Classical algorithm for simulating experimental Gaussian boson sampling

Changhun Oh, Minzhao Liu+3 more|arXiv (Cornell University)|Jun 6, 2023

Quantum Computing Algorithms and Architecture62 references11 citations

TL;DR

The paper introduces a tensor-network-based classical algorithm that simulates Gaussian boson sampling by decomposing the output state into a quantum part with reduced squeezing and a dominant classical displacement, enabling efficient simulation in high-loss regimes and challenging claimed quantum advantage.

ABSTRACT

Gaussian boson sampling is a promising candidate for showing experimental quantum advantage. While there is evidence that noiseless Gaussian boson sampling is hard to efficiently simulate using a classical computer, the current Gaussian boson sampling experiments inevitably suffer from loss and other noise models. Despite a high photon loss rate and the presence of noise, they are currently claimed to be hard to classically simulate with the best-known classical algorithm. In this work, we present a classical tensor-network algorithm that simulates Gaussian boson sampling and whose complexity can be significantly reduced when the photon loss rate is high. By generalizing the existing thermal-state approximation algorithm of lossy Gaussian boson sampling, the proposed algorithm allows us to achieve increased accuracy as the running time of the algorithm scales, as opposed to the algorithm that samples from the thermal state, which can give only a fixed accuracy. This generalization enables us to simulate the largest scale Gaussian boson sampling experiment so far using relatively modest computational resources, even though the output state of these experiments is not believed to be close to a thermal state. By demonstrating that our new classical algorithm outperforms the large-scale experiments on the benchmarks used as evidence for quantum advantage, we exhibit evidence that our classical sampler can simulate the ground-truth distribution better than the experiment can, which disputes the experimental quantum advantage claims.

Motivation & Objective

• Understand how noise and loss affect the classical simulability of Gaussian boson sampling.
• Develop a tensor-network method that efficiently simulates the ground-truth distribution under realistic loss.
• Quantify how the quantum resource (V_p) scales with loss and how this impacts simulation complexity.
• Benchmark the algorithm against state-of-the-art Gaussian boson sampling experiments using ground-truth distributions.
• Provide estimates for scalability to larger systems and implications for quantum advantage regimes.

Proposed method

• Decompose the output covariance V into V_p + W, where V_p corresponds to a pure Gaussian resource and W to Gaussian random displacement.
• Generalize thermal-state approximation by enabling V_p to be approximated progressively to control accuracy via bond dimension χ.
• Construct a matrix product state (MPS) representation for the quantum part V_p to efficiently simulate the state before the random displacement.
• Apply local Gaussian random displacement and measurement after obtaining the MPS to sample from the full distribution.
• Transform the sampling problem into sampling conditioned on a random displacement β drawn from p_W(β) and use the chain rule for marginal probabilities.
• Analyze the asymptotic efficiency of the MPS as a function of loss η and system size K, showing improved scaling η = O((log K / K)^{1/2α}) under certain α.

Experimental results

Research questions

• RQ1 Can a classical algorithm efficiently simulate lossy Gaussian boson sampling by exploiting a decomposition into quantum and classical resources?
• RQ2 How does increasing loss (low η) affect the entanglement and the bond dimension required for an efficient MPS representation?
• RQ3 To what extent can a tensor-network-based sampler outperform experimental Gaussian boson sampling on ground-truth distributions?
• RQ4 What are the implications for identifying the Goldilocks regime for quantum advantage in noisy photonic experiments?

Key findings

• A decomposition V = V_p + W isolates quantum resources (V_p) from classical displacement (W).
• The quantum resource V_p can be efficiently represented by an MPS when loss is high, with bond dimension scaling tied to η and network size.
• The algorithm can simulate ground-truth distributions of large Gaussian boson sampling experiments within reasonable time, outperforming some reported experiments on certain benchmarks.
• Increasing the number of squeezed states and improving transmission rate (loss reduction) is more effective for quantum advantage than merely increasing output photon numbers.
• The bond-dimension-based control of approximation error ε provides a polylogarithmic scaling w.r.t. 1/ε for fixed circuits, improving over prior thermal-state approximations.
• Two-point correlations and XEB benchmarks used in experiments align with TVD trends for the proposed simulator across tested sizes.