Behavior of Analog Quantum Algorithms

• URL: http://arxiv.org/abs/2107.01218v1
• Date: Fri, 2 Jul 2021 18:00:07 GMT
• Title: Behavior of Analog Quantum Algorithms
• Authors: Lucas T. Brady, Lucas Kocia, Przemyslaw Bienias, Aniruddha Bapat, Yaroslav Kharkov, Alexey V. Gorshkov
• Abstract summary: We show that different analog quantum algorithms can emulate the optimal protocol under different limits and approximations. We present a new algorithm for better approximating the optimal protocol using the analytic and numeric insights from the rest of the paper.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are promising candidates for near-term quantum applications, but they often require fine tuning via the annealing schedule or variational parameters. In this work, we explore connections between these analog algorithms, as well as limits in which they become approximations of the optimal procedure.Notably, we explore how the optimal procedure approaches a smooth adiabatic procedure but with a superposed oscillatory pattern that can be explained in terms of the interactions between the ground state and first excited state that effect the coherent error cancellation of diabatic transitions. Furthermore, we provide numeric and analytic evidence that QAOA emulates this optimal procedure with the length of each QAOA layer equal to the period of the oscillatory pattern. Additionally, the ratios of the QAOA bangs are determined by the smooth, non-oscillatory part of the optimal procedure. We provide arguments for these phenomena in terms of the product formula expansion of the optimal procedure. With these arguments, we conclude that different analog algorithms can emulate the optimal protocol under different limits and approximations. Finally, we present a new algorithm for better approximating the optimal protocol using the analytic and numeric insights from the rest of the paper. In practice, numerically, we find that this algorithm outperforms standard QAOA and naive quantum annealing procedures.

Related papers

• Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm [47.47843839099175]
  A Quantum Natural Gradient (QNG) algorithm for optimization of variational quantum circuits has been proposed recently. In this study, we employ the Langevin equation with a QNG force to demonstrate that its discrete-time solution gives a generalized form, which we call Momentum-QNG.
  arXiv  Detail & Related papers  (2024-09-03T15:21:16Z)
• 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)
• A Review on Quantum Approximate Optimization Algorithm and its Variants [47.89542334125886]
  The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve intractable optimization problems. This comprehensive review offers an overview of the current state of QAOA, encompassing its performance analysis in diverse scenarios. We conduct a comparative study of selected QAOA extensions and variants, while exploring future prospects and directions for the algorithm.
  arXiv  Detail & Related papers  (2023-06-15T15:28:12Z)
• Iteration Complexity of Variational Quantum Algorithms [5.203200173190989]
  We argue that noise makes evaluations of the objective function via quantum circuits biased. We derive the missing guarantees and find that the rate of convergence is unaffected.
  arXiv  Detail & Related papers  (2022-09-21T19:18:41Z)
• Bayesian Optimization for QAOA [0.0]
  We present a Bayesian optimization procedure to optimise a quantum circuit. We show that our approach allows for a significant reduction in the number of calls to the quantum circuit. Our results suggest that the method proposed here is a promising framework to leverage the hybrid nature of QAOA on the noisy intermediate-scale quantum devices.
  arXiv  Detail & Related papers  (2022-09-08T13:59:47Z)
• An entanglement perspective on the quantum approximate optimization algorithm [0.0]
  We study the entanglement growth and spread resulting from randomized and optimized QAOA circuits. We also investigate the entanglement spectrum in connection with random matrix theory.
  arXiv  Detail & Related papers  (2022-06-14T17:37:44Z)
• 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)
• Analog Quantum Approximate Optimization Algorithm [3.5558885788605332]
  We present an analog version of the quantum approximate optimization algorithm suitable for current quantum annealers. The central idea of this algorithm is to optimize the schedule function, which defines the adiabatic evolution. It is achieved by choosing a suitable parametrization of the schedule function based on methods for a fixed time, with the potential to generate any function.
  arXiv  Detail & Related papers  (2021-12-14T15:16:46Z)
• 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)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• 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.