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arXiv:2202.00634 · PRX Quantum

Experimental Demonstration of Gaussian Boson Sampling with Displacement

Guillaume Thekkadath, S. Sempere-Llagostera, Bryn A. Bell, Raj B. Patel, M.S. Kim, Ian A. Walmsley

Published May 17, 2022• 18 citations

Abstract

Gaussian boson sampling (GBS) is a quantum sampling task in which one has to draw samples from the photon-number distribution of a large-dimensional nonclassical squeezed state of light.In an effort to make this task intractable for a classical computer, experiments building GBS machines have mainly focused on increasing the dimensionality and squeezing strength of the nonclassical light.However, no experiment has yet demonstrated the ability to displace the squeezed state in phase space, which is generally required for practical applications of GBS.In this work, we build a GBS machine that achieves the displacement by injecting a laser beam alongside a two-mode squeezed vacuum state into a 15-mode interferometer.We focus on two new capabilities.Firstly, we use the displacement to reconstruct the multimode Gaussian state at the output of the interferometer.Our reconstruction technique is in situ and requires only three measurement settings regardless of the state dimension.Secondly, we study how the addition of classical laser light in our GBS machine affects the complexity of sampling its output photon statistics.We introduce and validate approximate semiclassical models that reduce the computational cost when a significant fraction of the detected light is classical.

DOI: 10.1103/prxquantum.3.020336

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We report phase-programmable Gaussian boson sampling (GBS) which produces up to 113 photon detection events out of a 144-mode photonic circuit. A new high-brightness and scalable quantum light source is developed, exploring the idea of stimulated emission of squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. The obtained samples are efficiently validated by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our GBS experiment passes a nonclassicality test based on inequality constraints, and we reveal nontrivial genuine high-order correlations in the GBS samples, which are evidence of robustness against possible classical simulation schemes. This photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to ∼10^{43}, and a sampling rate ∼10^{24} faster than using brute-force simulation on classical supercomputers.

Gaussian boson sampling (GBS) seeks quantum advantage by sampling photon-number patterns generated with squeezed inputs and passive linear optics. Many proposed GBS applications instead target function computation by applying functions to mode-resolved photon-number outcomes---a natural form of experimental postprocessing that produces classical outputs. Sampling hardness alone, however, does not determine the complexity of these tasks. By analyzing the irreducible decomposition of fixed-photon-number operator spaces, we prove that the expectation value of every such function in the average case over passive linear-optical networks can be classically evaluated for inputs with finite squeezing strength. We also provide a classical algorithm that estimates this value to inverse-polynomial additive error. The result provides new theoretical tools for analyzing linear-optical quantum systems, helps clarify the origin of current GBS hardness evidence, and inspires new applications of GBS with genuine quantum advantages.

Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We show how to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our scheme encompasses other validation methods based on marginal distributions and correlation functions. Additionally, it can accommodate various sources of noise, such as losses and partial distinguishability, a feature that have received limited attention within the GBS framework so far. We also illustrate how binned-detector probability distributions behave when Haar-averaged over all possible interferometric networks, extending known results for Fock boson sampling.