Experimental demonstration of boson sampling as a hardware accelerator for monte carlo integration

TL;DR

This work demonstrates a hybrid quantum–classical approach that uses boson sampling to accelerate Monte Carlo integration via importance sampling. By factorizing the target integrand as $f(\mathbf{X}) = g(\mathbf{X}) h(\mathbf{X})$, where $g$ is samplable on a photonic boson sampler and $h$ is computed classically, the authors validate a practical use case for near-term quantum devices. They implement a proof-of-principle on a 12-mode photonic processor to estimate the first-order energy correction in an Efimov-inspired three-body perturbation, showing quantitative agreement with theory within a detailed error budget dominated by unitary fidelity and discretization effects. The results identify a sweet spot where quantum sampling offers advantages for scientific computing and outline concrete paths to improve hardware and broaden applicability to other many-body problems.

Abstract

We present an experimental demonstration of boson sampling as a hardware accelerator for Monte Carlo integration. Our approach leverages importance sampling to factorize an integrand into a distribution that can be sampled using quantum hardware and a function that can be evaluated classically, enabling hybrid quantum-classical computation. We argue that for certain classes of integrals, this method offers a quantum advantage by efficiently sampling from probability distributions that are hard to simulate classically. We also identify structural criteria that must be satisfied to preserve computational hardness, notably the sensitivity of the classical post-processing function to high-order quantum correlations. To validate our protocol, we implement a proof-of-principle experiment on a programmable photonic platform to compute the first-order energy correction of a three-boson system in a harmonic trap under an Efimov-inspired three-body perturbation. The experimental results are consistent with theoretical predictions and numerical simulations, with deviations explained by photon distinguishability, discretization, and unitary imperfections. Additionally, we provide an error budget quantifying the impact of these same sources of noise. Our work establishes a concrete use case for near-term photonic quantum devices and highlights a viable path toward practical quantum advantage in scientific computing.

Figures (8)

• Figure 1: Illustration of Boson-sampling-assisted Monte Carlo integration over a domain $\mathcal{D}$ based on importance sampling. The target function $f(\mathbf{X})$ is factorized into $g(\mathbf{X})$ and $h(\mathbf{X})$. The function $g(\mathbf{X})$ can be implemented in a Boson Sampler, which allows for sampling with a quantum advantage over classical methods. The generated samples are then evaluated using $h(\mathbf{X})$ and summed to efficiently estimate the integral of $f(\mathbf{X})$.
• Figure 2: A Ti:Sapphire laser pumps two parallel single-photon sources. The beam is focused onto a periodically poled KTP (ppKTP) crystal, generating photon pairs (red wave packets) via type-II spontaneous parametric down-conversion (SPDC), followed by filtering through a high-pass filter (HPF). The generated photons are separated at a polarizing beam splitter (PBS), further filtered with bandpass filters (BPF), and then coupled into optical fibers. Linear stages are used to control the path lengths, adjusting the relative delays to modulate photon distinguishability. Three photons are directed into the photonic chip for the experiment, while the fourth serves as a herald. A 12-mode unitary transformation $U$ is implemented in the chip. The output photons are measured using superconducting nanowire single-photon detectors (SNSPDs)
• Figure 3: Mapping Boson-Sampling-accelerated Monte Carlo integration to first-order perturbation theory in a harmonic potential. The orbitals (eigenfunctions) of the system are encoded as input modes of the photonic processor (a), while space is discretized and mapped onto the output modes. The transformation between input and output is described by the unitary matrix $U$(b), which defines the operation of the photonic chip. The three-particle wavefunction $\Psi$(c) is constructed as a bosonic symmetrized product of the individual eigenfunctions of a harmonic potential $V(x)$(d). The positions of the three bosons are measured, generating samples (e), which are then used in classical post-processing to estimate first-order energy corrections (f).
• Figure 4: The experimental (blue) and noiseless numerical simulation (gold) probability distributions of photon detection events are shown for every detection pattern (bit string indicating occupied output modes). Data correspond to the near-indistinguishable photon configuration. The x-axis represents distinct multi-photon detection events, while the y-axis indicates their respective probabilities. The inset provides a zoomed-in view of the first 100 detection patterns. Error bars represent statistical uncertainties in the experiment.
• Figure A.1: (a) Illustration of boundary ambiguity in deterministic integration. When particle positions are fixed at bin centers, grid alignment effects cause certain points to lie exactly on the boundary of the exclusion zone. Including such points leads to overestimation; excluding them leads to underestimation. (b) To eliminate this bias, we randomly select positions within the mode bins corresponding to the detected click pattern. The hard-shell constraint is evaluated on these randomized coordinates, and the result is averaged over $N$ repetitions. This procedure removes boundary artifacts and yields an unbiased estimate of the integral.