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arXiv:2403.03184 · Physical Review A

Realistic photon-number resolution in Gaussian boson sampling

I. S. Yeremenko, M. A. Dmytruk, А. А. Семенов

Published Oct 18, 2024• 0 citations
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Abstract

Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024

DOI
10.1103/physreva.110.043715

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Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024
Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however, these are not widely available. Nevertheless, inexpensive threshold detectors can be combined into a single click-counting detector to achieve approximate photon-number resolution. We investigate the problem of sampling from a general multimode Gaussian state using click-counting detectors and show that the probability of obtaining a given outcome is related to a matrix function which is dubbed as the Kensingtonian. We show how the Kensingtonian relates to the Torontonian and the Hafnian, thus bridging the gap between known Gaussian boson sampling variants. We then prove that, under standard complexity-theoretical conjectures, the model cannot be simulated efficiently. Published by the American Physical Society 2024
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 develop the theoretical framework 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 theoretical framework encompasses other validation methods based onmarginal distributions and correlation functions. Additionally, it can analytically accommodate various sources of noise, such as losses and partial distinguishability, a feature that has received limited attention within the GBS framework so far. We also derive how binned-detector probability distributions behave when Haar averaged over all possible interferometric networks, extending known results for Fock boson sampling.
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.
Abstract An important challenge with the current generation of noisy, large-scale quantum computers is the question of validation. Does the hardware generate correct answers? If not, what are the errors? This issue is often combined with questions of computational advantage, but it is a fundamentally distinct issue. In current experiments, complete validation of the output statistics is generally not possible because it is exponentially hard to do so. Here, we apply phase-space simulation methods to partially verify recent experiments on Gaussian boson sampling (GBS) implementing photon-number resolving detectors. The positive-P phase-space distribution is employed, as it uses probabilistic sampling to reduce complexity. It is ∼ 10 18 times faster than direct classical simulation for experiments on 288 modes where quantum computational advantage is claimed. When combined with binning and marginalization to improve statistics, multiple validation tests are efficiently computable, of which some tests can be carried out on experimental data. We show that the data as a whole has discrepancies with theoretical predictions for perfect squeezing. However, a modification of the GBS parameters greatly improves agreement for some tests. We suggest that such validation tests could form the basis of feedback methods to improve GBS experiments.
Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient auxiliary classical simulation algorithm which can be used to calculate the probabilities. Our model and the auxiliary algorithm provide foundations for an approximation method for the probability calculation and simulation algorithms not only compatible with existing state-of-the-art simulation algorithms for ideal GBS but also reduce their complexities exponentially depending on the indistinguishability. Using the approximation method and the simulation algorithms we show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.
We report new Gaussian boson sampling experiments with pseudo-photon-number-resolving detection, which register up to 255 photon-click events. We consider partial photon distinguishability and develop a more complete model for the characterization of the noisy Gaussian boson sampling. In the quantum computational advantage regime, we use Bayesian tests and correlation function analysis to validate the samples against all current classical spoofing mockups. Estimating with the best classical algorithms to date, generating a single ideal sample from the same distribution on the supercomputer Frontier would take $\ensuremath{\sim}600\text{ }\text{ }\mathrm{yr}$ using exact methods, whereas our quantum computer, Ji\ifmmode \check{u}\else \v{u}\fi{}zh\ifmmode \bar{a}\else \={a}\fi{}ng 3.0, takes only $1.27\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{s}$ to produce a sample. Generating the hardest sample from the experiment using an exact algorithm would take $\mathrm{Frontier}\ensuremath{\sim}3.1\ifmmode\times\else\texttimes\fi{}{10}^{10}\text{ }\text{ }\mathrm{yr}$.