arXiv subjects

Alexander S. Dellios

Publications and source records attributed to Alexander S. Dellios.

6 recordsLinked to original sources

arXiv2026

Matrix phase-space representations for quantum symmetries

We introduce a general phase-space representation that includes global quantum symmetries in the basis expansion. This method, called matrix phase-space, projects the basis onto a reduced Hilbert space, which can greatly reduce sampling errors of many-body quantum simulations and unifies several previous phase-space methods. The purpose of this paper is to provide detailed proofs of basic theorems and operator identities. We also treat several different types of symmetries. To illustrate the benefits of matrix phase-space methods, we give a detailed derivation of a recent application to the topical problem of verifying the outputs of Gaussian boson sampling (GBS) quantum computers with photon number resolving detectors. This has exponential complexity, and using parity symmetry reduces sampling errors by very large factors relative to earlier methods.

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arXiv2026

Matrix phase-space representations for gaussian boson sampling

We introduce coherent matrix phase-space distributions. These use conservation laws and symmetries to improve the accuracy and speed of quantum phase-space representations. As an example, this is applied to validation of low-loss Gaussian boson sampling (GBS) quantum computational advantage experiments, where classical generation of the random photon-number counts is exponentially hard. Large improvements in sampling errors are demonstrated compared to previous methods. Matrix phase-space representations also provide a large numerical speed-up, due to their (at worst) quadratic scaling, compared to other methods for validating total count probabilities of large-scale, low-loss GBS networks.

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arXiv2026

Gaussian boson sampling: Benchmarking quantum advantage

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.

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arXiv2025

Validation tests of Gaussian boson samplers with photon-number resolving detectors

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 (PNR) detectors. The positive-P phase-space distribution is employed, as it uses probabilistic sampling to reduce complexity. It is \sim10^{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 shows discrepancies with theoretical predictions for perfect squeezing. However, a small 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.

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arXiv2023

Simulating Gaussian boson sampling quantum computers

A growing cohort of experimental linear photonic networks implementing Gaussian boson sampling (GBS) have now claimed quantum advantage. However, many open questions remain on how to effectively verify these experimental results, as scalable methods are needed that fully capture the rich array of quantum correlations generated by these photonic quantum computers. In this paper, we briefly review recent theoretical methods to simulate experimental GBS networks. We focus mostly on methods that use phase-space representations of quantum mechanics, as these methods are highly scalable and can be used to validate experimental outputs and claims of quantum advantage for a variety of input states, ranging from the ideal pure squeezed vacuum state to more realistic thermalized squeezed states. A brief overview of the theory of GBS, recent experiments and other types of methods are also presented. Although this is not an exhaustive review, we aim to provide a brief introduction to phase-space methods applied to linear photonic networks to encourage further theoretical investigations.

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arXiv2023

Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target

Computational validation is vital for all large-scale quantum computers. One needs computers that are both fast and accurate. Here we apply precise, scalable, high order statistical tests to data from large Gaussian boson sampling (GBS) quantum computers that claim quantum computational advantage. These tests can be used to validate the output results for such technologies. Our method allows investigation of accuracy as well as quantum advantage. Such issues have not been investigated in detail before. Our highly scalable technique is also applicable to other applications of linear bosonic networks. We utilize positive-P phase-space simulations of grouped count probabilities (GCP) as a fingerprint for verifying multi-mode data. This is exponentially more efficient than other phase-space methods, due to much lower sampling errors. We randomly generate tests from exponentially many high-order, grouped count tests. Each of these can be efficiently measured and simulated, providing a quantum verification method that is hard to replicate classically. We give a detailed comparison of theory with a 144-channel GBS experiment, including grouped correlations up to the largest order measured. We show how one can disprove faked data, and apply this to a classical count algorithm. There are multiple distance measures for evaluating the fidelity and computational complexity of a distribution. We compute these and explain them. The best fit to the data is a partly thermalized Gaussian model, which is neither the ideal case, nor the model that gives classically computable counts. Even with this model, discrepancies of $Z>100$ were observed from some $χ^2$ tests, indicating likely parameter estimation errors. Total count distributions were much closer to a thermalized quantum model than the classical model, giving evidence consistent with quantum computational advantage for a modified target problem.

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