Avoiding local minima in Variational Quantum Algorithms with Neural Networks

• URL: http://arxiv.org/abs/2104.02955v2
• Date: Mon, 18 Oct 2021 09:41:09 GMT
• Title: Avoiding local minima in Variational Quantum Algorithms with Neural Networks
• Authors: Javier Rivera-Dean, Patrick Huembeli, Antonio Ac\'in and Joseph Bowles
• Abstract summary: Variational Quantum Algorithms have emerged as a leading paradigm for near-term computation. In this paper we present two algorithms within benchmark them on instances of the gradient landscape problem. We suggest that our approach suggests that the cost landscape is a fruitful path to improving near-term quantum computing algorithms.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a problem-dependent cost function. Although such algorithms are powerful in principle, the non-convexity of the associated cost landscapes and the prevalence of local minima means that local optimization methods such as gradient descent typically fail to reach good solutions. In this work we suggest a method to improve gradient-based approaches to variational quantum circuit optimization, which involves coupling the output of the quantum circuit to a classical neural network. The effect of this neural network is to peturb the cost landscape as a function of its parameters, so that local minima can be escaped or avoided via a modification to the cost landscape itself. We present two algorithms within this framework and numerically benchmark them on small instances of the Max-Cut optimization problem. We show that the method is able to reach deeper minima and lower cost values than standard gradient descent based approaches. Moreover, our algorithms require essentially the same number of quantum circuit evaluations per optimization step as the standard approach since, unlike the gradient with respect to the circuit, the neural network updates can be estimated in parallel via the backpropagation method. More generally, our approach suggests that relaxing the cost landscape is a fruitful path to improving near-term quantum computing algorithms.

Related papers

• Scalable circuit depth reduction in feedback-based quantum optimization with a quadratic approximation [0.6834295298053009]
  We propose a new feedback law for parameter determination by introducing the second-order approximation with respect to time interval. We demonstrate that our proposal significantly reduces circuit depth, with its linear scaling with the problem size smaller by more than an order of magnitude.
  arXiv  Detail & Related papers  (2024-07-25T06:44:41Z)
• Qudit inspired optimization for graph coloring [0.0]
  We introduce a quantum-inspired algorithm for Graph Coloring Problems (GCPs) We use qudits in a product state, with each qudit representing a node in the graph and parameterized by d-dimensional spherical coordinates. We benchmark two optimization strategies: qudit gradient descent (QdGD), initiating qudits in random states and employing gradient descent to minimize a cost function.
  arXiv  Detail & Related papers  (2024-06-02T16:19:55Z)
• Variational quantum algorithm for enhanced continuous variable optical phase sensing [0.0]
  Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy quantum devices. We implement a variational algorithm designed for optimized parameter estimation on a continuous variable platform based on squeezed light.
  arXiv  Detail & Related papers  (2023-12-21T14:11:05Z)
• 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)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes [0.0]
  Variational quantum algorithms (VQAs) represent a promising approach to utilizing current quantum computing infrastructures. We propose the quantum Broyden adaptive natural gradient (qBang) approach, a novel that aims to distill the best aspects of existing approaches.
  arXiv  Detail & Related papers  (2023-04-27T00:06:48Z)
• Quadratic Unconstrained Binary Optimisation via Quantum-Inspired Annealing [58.720142291102135]
  We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. We benchmark our approach for large scale problem instances with tuneable hardness and planted solutions.
  arXiv  Detail & Related papers  (2021-08-18T09:26:17Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Cross Entropy Hyperparameter Optimization for Constrained Problem Hamiltonians Applied to QAOA [68.11912614360878]
  Hybrid quantum-classical algorithms such as Quantum Approximate Optimization Algorithm (QAOA) are considered as one of the most encouraging approaches for taking advantage of near-term quantum computers in practical applications. Such algorithms are usually implemented in a variational form, combining a classical optimization method with a quantum machine to find good solutions to an optimization problem. In this study we apply a Cross-Entropy method to shape this landscape, which allows the classical parameter to find better parameters more easily and hence results in an improved performance.
  arXiv  Detail & Related papers  (2020-03-11T13:52:41Z)

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.