Connecting geometry and performance of two-qubit parameterized quantum circuits

• URL: http://arxiv.org/abs/2106.02593v2
• Date: Fri, 12 Aug 2022 11:17:37 GMT
• Title: Connecting geometry and performance of two-qubit parameterized quantum circuits
• Authors: Amara Katabarwa, Sukin Sim, Dax Enshan Koh, Pierre-Luc Dallaire-Demers
• Abstract summary: We use principal bundles to geometrically characterize two-qubit quantum circuits (PQCs) By calculating the Ricci scalar during a variational quantum eigensolver (VQE) optimization process, this offers us a new perspective. We argue that the key to the Quantum Natural Gradient's superior performance is its ability to find regions of high negative curvature.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Parameterized quantum circuits (PQCs) are a central component of many variational quantum algorithms, yet there is a lack of understanding of how their parameterization impacts algorithm performance. We initiate this discussion by using principal bundles to geometrically characterize two-qubit PQCs. On the base manifold, we use the Mannoury-Fubini-Study metric to find a simple equation relating the Ricci scalar (geometry) and concurrence (entanglement). By calculating the Ricci scalar during a variational quantum eigensolver (VQE) optimization process, this offers us a new perspective to how and why Quantum Natural Gradient outperforms the standard gradient descent. We argue that the key to the Quantum Natural Gradient's superior performance is its ability to find regions of high negative curvature early in the optimization process. These regions of high negative curvature appear to be important in accelerating the optimization process.

Related papers

• Quantum Boltzmann machine learning of ground-state energies [3.187381965457262]
  Esting the ground-state energy of Hamiltonians is a fundamental task for which quantum computers can be helpful. We analyze the performance of quantum Boltzmann machines for this task. Our algorithm estimates the gradient of the energy function efficiently by means of a novel quantum circuit construction.
  arXiv  Detail & Related papers  (2024-10-16T18:22:03Z)
• Efficient Quantum Gradient and Higher-order Derivative Estimation via Generalized Hadamard Test [2.5545813981422882]
  Gradient-based methods are crucial for understanding the behavior of parameterized quantum circuits (PQCs) Existing gradient estimation methods, such as Finite Difference, Shift Rule, Hadamard Test, and Direct Hadamard Test, often yield suboptimal gradient circuits for certain PQCs. We introduce the Flexible Hadamard Test, which, when applied to first-order gradient estimation methods, can invert the roles of ansatz generators and observables. We also introduce Quantum Automatic Differentiation (QAD), a unified gradient method that adaptively selects the best gradient estimation technique for individual parameters within a PQ
  arXiv  Detail & Related papers  (2024-08-10T02:08:54Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• Gradient-descent quantum process tomography by learning Kraus operators [63.69764116066747]
  We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems. We use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes.
  arXiv  Detail & Related papers  (2022-08-01T12:48:48Z)
• 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)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• Gradient-free quantum optimization on NISQ devices [0.0]
  We consider recent advances in weight-agnostic learning and propose a strategy that addresses the trade-off between finding appropriate circuit architectures and parameter tuning. We investigate the use of NEAT-inspired algorithms which evaluate circuits via genetic competition and thus circumvent issues due to exceeding numbers of parameters.
  arXiv  Detail & Related papers  (2020-12-23T10:24:54Z)
• Natural Evolutionary Strategies for Variational Quantum Computation [0.7874708385247353]
  Natural evolutionary strategies (NES) are a family of gradient-free black-box optimization algorithms. This study illustrates their use for the optimization of randomly-d parametrized quantum circuits (PQCs) in the region of vanishing gradients.
  arXiv  Detail & Related papers  (2020-11-30T21:23:38Z)
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms [105.54048699217668]
  A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. Here, we show that this approach is not always advantageous by introducing ans"atze that incorporate symmetry-breaking unitaries. This work constitutes a first step towards the development of a more general class of symmetry-breaking ans"atze with applications to physics and chemistry problems.
  arXiv  Detail & Related papers  (2020-08-03T18:00:05Z)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

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.