Fast differentiable evolution of quantum states under Gaussian transformations

• URL: http://arxiv.org/abs/2102.05742v1
• Date: Wed, 10 Feb 2021 21:22:19 GMT
• Title: Fast differentiable evolution of quantum states under Gaussian transformations
• Authors: Yuan Yao, Filippo M. Miatto
• Abstract summary: We present a faster algorithm that computes the final state without having to generate the full transformation matrix first. We benchmark our algorithm by optimizing circuits to produce single photons, Gottesman-Kitaev-Preskill states and NOON states.
• Score: 6.737752058029072
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and subsequently computing the matrix-vector product. Here we present a faster algorithm that computes the final state without having to generate the full transformation matrix first. With this algorithm we bring the time complexity of computing the Gaussian evolution of an $N$-dimensional $M$-mode state from $O(MN^{2M})$ to $O(M(N^2/2)^M)$, which is an exponential improvement in the number of modes. In the special case of high squeezing, the evolved state can be approximated with complexity $O(MN^{M})$. Our new algorithm is differentiable, which means we can use it in conjunction with gradient-based optimizers for circuit optimization tasks. We benchmark our algorithm by optimizing circuits to produce single photons, Gottesman-Kitaev-Preskill states and NOON states, showing that it is up to one order of magnitude faster than the state of the art.

Related papers

• A Quantum Speed-Up for Approximating the Top Eigenvectors of a Matrix [2.7050250604223693]
  Finding a good approximation of the top eigenvector of a given $dtimes d$ matrix $A$ is a basic and important computational problem. We give two different quantum algorithms that output a classical description of a good approximation of the top eigenvector.
  arXiv  Detail & Related papers  (2024-05-23T16:33:13Z)
• Tensor networks based quantum optimization algorithm [0.0]
  In optimization, one of the well-known classical algorithms is power iterations. We propose a quantum realiziation to circumvent this pitfall. Our methodology becomes instance agnostic and thus allows one to address black-box optimization within the framework of quantum computing.
  arXiv  Detail & Related papers  (2024-04-23T13:49:11Z)
• A square-root speedup for finding the smallest eigenvalue [0.6597195879147555]
  We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines Quantum Phase Estimation and Quantum Amplitude Estimation to achieve a quadratic speedup. We also provide a similar algorithm with the same runtime that allows us to prepare a quantum state lying mostly in the matrix's low-energy subspace.
  arXiv  Detail & Related papers  (2023-11-07T22:52:56Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Improved Rate of First Order Algorithms for Entropic Optimal Transport [2.1485350418225244]
  This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. We propose an accelerated primal-dual mirror descent algorithm with variance reduction. Our algorithm may inspire more research to develop accelerated primal-dual algorithms that have rate $widetildeO(n2/epsilon)$ for solving OT.
  arXiv  Detail & Related papers  (2023-01-23T19:13:25Z)
• A Fully Single Loop Algorithm for Bilevel Optimization without Hessian Inverse [121.54116938140754]
  We propose a new Hessian inverse free Fully Single Loop Algorithm for bilevel optimization problems. We show that our algorithm converges with the rate of $O(epsilon-2)$.
  arXiv  Detail & Related papers  (2021-12-09T02:27:52Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Higher-order Derivatives of Weighted Finite-state Machines [68.43084108204741]
  This work examines the computation of higher-order derivatives with respect to the normalization constant for weighted finite-state machines. We provide a general algorithm for evaluating derivatives of all orders, which has not been previously described in the literature. Our algorithm is significantly faster than prior algorithms.
  arXiv  Detail & Related papers  (2021-06-01T19:51:55Z)
• Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles [12.005731086591139]
  Householder Dice (HD) is an algorithm for simulating dynamics on dense random matrix ensembles with translation-invariant properties. The memory and costs of the HD algorithm are $mathcalO(nT)$ and $mathcalO(nT2)$, respectively. Numerical results demonstrate the promise of the HD algorithm as a new computational tool in the study of high-dimensional random systems.
  arXiv  Detail & Related papers  (2021-01-19T04:50:53Z)
• Quantum algorithms for spectral sums [50.045011844765185]
  We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. We show how the algorithms and techniques used in this work can be applied to three problems in spectral graph theory.
  arXiv  Detail & Related papers  (2020-11-12T16:29:45Z)
• Optimal Iterative Sketching with the Subsampled Randomized Hadamard Transform [64.90148466525754]
  We study the performance of iterative sketching for least-squares problems. We show that the convergence rate for Haar and randomized Hadamard matrices are identical, andally improve upon random projections. These techniques may be applied to other algorithms that employ randomized dimension reduction.
  arXiv  Detail & Related papers  (2020-02-03T16:17:50Z)

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.