Strong Simulation of Linear Optical Processes

• URL: http://arxiv.org/abs/2206.10549v2
• Date: Thu, 3 Aug 2023 09:55:19 GMT
• Title: Strong Simulation of Linear Optical Processes
• Authors: Nicolas Heurtel, Shane Mansfield, Jean Senellart, Beno\^it Valiron
• Abstract summary: Given $n$ photons at the input of an $m$-mode interferometer, our algorithm computes the probabilities of all possible output states. It outperforms the permanent-based method by an exponential factor.
• Score: 2.3131309703965135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we provide an algorithm and general framework for the simulation of photons passing through linear optical interferometers. Given $n$ photons at the input of an $m$-mode interferometer, our algorithm computes the probabilities of all possible output states with time complexity $O\left({n\binom{n+m-1}{m-1}}\right)$, linear in the number of output states $\binom{n+m-1}{m-1}$. It outperforms the permanent-based method by an exponential factor, and for the restricted problem of computing the probability for one given output it improves the time complexity over the state-of-the-art for the permanent of matrices with multiple rows or columns, with a tradeoff in the memory usage. Our algorithm also has additional versatility by virtue of its use of memorisation -- the storing of intermediate results -- which is advantageous in situations where several input states may be of interest. Additionally it allows for hybrid simulations, in which outputs are sampled from output states whose probability exceeds a given threshold, or from a restricted set of states. We consider a concrete, optimised implementation, and we benchmark the efficiency of our approach compared to existing tools.

Related papers

• A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrieval [56.67706781191521]
  In this work, we present a robust phase retrieval problem where the task is to recover an unknown signal. Our proposed oracle avoids the need for computationally spectral descent, using a simple gradient step and outliers.
  arXiv  Detail & Related papers  (2024-09-07T06:37:23Z)
• Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems [9.30306458153248]
  We consider the spectral tail condition number, $kappa_ell$, defined as the ratio between the $ell$th largest and the smallest singular value of the matrix representing the system. Some of the implications of our result, and of the use of $kappa_ell$, include direct improvement over a fine-grained analysis of the Conjugate method.
  arXiv  Detail & Related papers  (2024-05-09T14:56:49Z)
• Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging [8.990961435218544]
  We propose a first-order algorithm named $B$-sample dual averaging with the logarithmic barrier. For the Poisson inverse problem, our algorithm attains an $varepsilon$ solution in $smashtildeO(d3/varepsilon2)$ time. When computing the maximum-likelihood estimate for quantum state tomography, our algorithm yields an $varepsilon$-optimal solution in $smashtildeO(d3/varepsilon2)$ time.
  arXiv  Detail & Related papers  (2023-11-05T03:33:44Z)
• Sublinear scaling in non-Markovian open quantum systems simulations [0.0]
  We introduce a numerically exact algorithm to calculate process tensors. Our approach requires only $mathcalO(nlog n)$ singular value decompositions for environments with infinite memory.
  arXiv  Detail & Related papers  (2023-04-11T15:40:33Z)
• A Quadratic Speedup in the Optimization of Noisy Quantum Optical Circuits [5.074606924176912]
  Linear optical quantum circuits with photon number resolving (PNR) detectors are used for both Gaussian Boson Sampling (GBS) and for the preparation of non-Gaussian states such as Gottesman-Kitaev-Preskill (GKP) We introduce a family of algorithms that calculate detection probabilities, conditional states and their gradients with respect to circuit parametrizations. These algorithms are implemented and ready to use in the open-source photonic optimization library MrMustard.
  arXiv  Detail & Related papers  (2023-03-15T18:51:36Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Sublinear Time Approximation of Text Similarity Matrices [50.73398637380375]
  We introduce a generalization of the popular Nystr"om method to the indefinite setting. Our algorithm can be applied to any similarity matrix and runs in sublinear time in the size of the matrix. We show that our method, along with a simple variant of CUR decomposition, performs very well in approximating a variety of similarity matrices.
  arXiv  Detail & Related papers  (2021-12-17T17:04:34Z)
• Classical simulation of boson sampling based on graph structure [2.5496329090462626]
  We present classical sampling algorithms for single-photon and Gaussian input states that take advantage of a graph structure of a linear-optical circuit. We show that when the circuit depth is less than the quadratic in the lattice spacing, the efficient simulation is possible with an exponentially small error. We implement a likelihood test with a recent numerically Gaussian boson sampling experiment and show that the treewidth-based algorithm with a limited treewidth renders a larger likelihood than the experimental data.
  arXiv  Detail & Related papers  (2021-10-04T17:02:35Z)
• Photonic co-processors in HPC: using LightOn OPUs for Randomized Numerical Linear Algebra [53.13961454500934]
  We show that the randomization step for dimensionality reduction may itself become the computational bottleneck on traditional hardware. We show that randomization can be significantly accelerated, at negligible precision loss, in a wide range of important RandNLA algorithms.
  arXiv  Detail & Related papers  (2021-04-29T15:48:52Z)
• Accelerating Feedforward Computation via Parallel Nonlinear Equation Solving [106.63673243937492]
  Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. We frame the task of feedforward computation as solving a system of nonlinear equations. We then propose to find the solution using a Jacobi or Gauss-Seidel fixed-point method, as well as hybrid methods of both. Our method is guaranteed to give exactly the same values as the original feedforward computation with a reduced (or equal) number of parallelizable iterations, and hence reduced time given sufficient parallel computing power.
  arXiv  Detail & Related papers  (2020-02-10T10:11:31Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.