Denoising Gradient Descent in Variational Quantum Algorithms

• URL: http://arxiv.org/abs/2403.03826v1
• Date: Wed, 6 Mar 2024 16:15:25 GMT
• Title: Denoising Gradient Descent in Variational Quantum Algorithms
• Authors: Lars Simon, Holger Eble, Hagen-Henrik Kowalski, Manuel Radons
• Abstract summary: We introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. We empirically demonstrate the advantages offered by our algorithm on randomized parametrized quantum circuits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the objective function at every gradient descent step. The computational overhead of our algorithm is entirely classical, i.e., the number of circuit evaluations is exactly the same as when carrying out gradient descent using the parameter-shift rules. We empirically demonstrate the advantages offered by our algorithm on randomized parametrized quantum circuits.

Related papers

• Bregman-divergence-based Arimoto-Blahut algorithm [53.64687146666141]
  We generalize the Arimoto-Blahut algorithm to a general function defined over Bregman-divergence system. We propose a convex-optimization-free algorithm that can be applied to classical and quantum rate-distortion theory.
  arXiv  Detail & Related papers  (2024-08-10T06:16:24Z)
• Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits [4.112419132722306]
  This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting amenable to analysis.
  arXiv  Detail & Related papers  (2023-10-31T18:55:45Z)
• Pure Quantum Gradient Descent Algorithm and Full Quantum Variational Eigensolver [0.7149735232319818]
  gradient-based gradient descent algorithm is a widely adopted optimization method. We propose a novel quantum-based gradient calculation method that requires only a single oracle calculation. We successfully implemented the quantum gradient descent algorithm and applied it to the Variational Quantum Eigensolver (VQE)
  arXiv  Detail & Related papers  (2023-05-07T05:52:41Z)
• Gradient-Free optimization algorithm for single-qubit quantum classifier [0.3314882635954752]
  A gradient-free optimization algorithm is proposed to overcome the effects of barren plateau caused by quantum devices. The proposed algorithm is demonstrated for a classification task and is compared with that using Adam. The proposed gradient-free optimization algorithm can reach a high accuracy faster than that using Adam.
  arXiv  Detail & Related papers  (2022-05-10T08:45:03Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Amortized Implicit Differentiation for Stochastic Bilevel Optimization [53.12363770169761]
  We study a class of algorithms for solving bilevel optimization problems in both deterministic and deterministic settings. We exploit a warm-start strategy to amortize the estimation of the exact gradient. By using this framework, our analysis shows these algorithms to match the computational complexity of methods that have access to an unbiased estimate of the gradient.
  arXiv  Detail & Related papers  (2021-11-29T15:10:09Z)
• Random-reshuffled SARAH does not need a full gradient computations [61.85897464405715]
  The StochAstic Recursive grAdientritHm (SARAH) algorithm is a variance reduced variant of the Gradient Descent (SGD) algorithm. In this paper, we remove the necessity of a full gradient. The aggregated gradients serve as an estimate of a full gradient in the SARAH algorithm.
  arXiv  Detail & Related papers  (2021-11-26T06:00:44Z)
• Using gradient-based algorithms to determine ground state energies on a quantum computer [0.0]
  Variational algorithms are promising candidates to be implemented on near-term quantum computers. We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and noise of the quantum computer.
  arXiv  Detail & Related papers  (2021-09-17T09:12:43Z)
• Single-component gradient rules for variational quantum algorithms [1.3047205680129093]
  A common bottleneck of any such algorithm is constituted by the optimization of the variational parameters. A popular set of optimization methods work on the estimate of the gradient, obtained by means of circuit evaluations. This work provides a comprehensive picture of the family of gradient rules that vary parameters of quantum gates individually.
  arXiv  Detail & Related papers  (2021-06-02T18:00:10Z)
• Accelerated Message Passing for Entropy-Regularized MAP Inference [89.15658822319928]
  Maximum a posteriori (MAP) inference in discrete-valued random fields is a fundamental problem in machine learning. Due to the difficulty of this problem, linear programming (LP) relaxations are commonly used to derive specialized message passing algorithms. We present randomized methods for accelerating these algorithms by leveraging techniques that underlie classical accelerated gradient.
  arXiv  Detail & Related papers  (2020-07-01T18:43:32Z)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)

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.