VQE for Ising Model \& A Comparative Analysis of Classical and Quantum Optimization Methods

• URL: http://arxiv.org/abs/2412.19176v1
• Date: Thu, 26 Dec 2024 11:25:30 GMT
• Title: VQE for Ising Model \& A Comparative Analysis of Classical and Quantum Optimization Methods
• Authors: Duc-Truyen Le, Vu-Linh Nguyen, Triet Minh Ha, Cong-Ha Nguyen, Quoc-Hung Nguyen, Van-Duy Nguyen,
• Abstract summary: We propose a new quantum optimization scheme, QN-SPSA+PSR. It integrates the QN-SPSA computational efficiency with the precise gradient of the PSR, improving both stability and convergence speed. We also conduct a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ.
• Score: 1.03905835096574
• License:
• Abstract: In this study, we delved into several optimization methods, both classical and quantum, and analyzed the quantum advantage that each of these methods offered, and then we proposed a new combinatorial optimization scheme, deemed as QN-SPSA+PSR which combines calculating approximately Fubini-study metric (QN-SPSA) and the exact evaluation of gradient by Parameter-Shift Rule (PSR). The QN-SPSA+PSR method integrates the QN-SPSA computational efficiency with the precise gradient computation of the PSR, improving both stability and convergence speed while maintaining low computational consumption. Our results provide a new potential quantum supremacy in the VQE's optimization subroutine and enhance viable paths toward efficient quantum simulations on Noisy Intermediate-Scale Quantum Computing (NISQ) devices. Additionally, we also conducted a detailed study of quantum circuit ansatz structures in order to find the one that would work best with the Ising model and NISQ, in which we utilized the symmetry of the investigated model.

Related papers

• Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications [0.6361348748202732]
  We report the implementation and performance of ADAPT-VQE with our sparse wavefunction circuit solver (SWCS) The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations. By pre-optimizing a quantum simulation with a parameterized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing.
  arXiv  Detail & Related papers  (2024-11-12T16:52:31Z)
• 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)
• A joint optimization approach of parameterized quantum circuits with a tensor network [0.0]
  Current intermediate-scale quantum (NISQ) devices remain limited in their capabilities. We propose the use of parameterized Networks (TNs) to attempt an improved performance of the Variational Quantum Eigensolver (VQE) algorithm.
  arXiv  Detail & Related papers  (2024-02-19T12:53:52Z)
• Pointer Networks with Q-Learning for Combinatorial Optimization [55.2480439325792]
  We introduce the Pointer Q-Network (PQN), a hybrid neural architecture that integrates model-free Q-value policy approximation with Pointer Networks (Ptr-Nets) Our empirical results demonstrate the efficacy of this approach, also testing the model in unstable environments.
  arXiv  Detail & Related papers  (2023-11-05T12:03:58Z)
• Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems [0.7550566004119158]
  We introduce the Variational Quantum Approximate Spectral Clustering (VQASC) algorithm. VQASC requires optimization of fewer parameters than the system size, N, traditionally required in classical problems. We present numerical results from both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-09-08T17:54:42Z)
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive [52.77024349608834]
  We present a self consistent field approach (SCF) within the Adaptive Derivative-Assembled Problem-Assembled Ansatz Variational Eigensolver (ADAPTVQE) This framework is used for efficient quantum simulations of chemical systems on nearterm quantum computers.
  arXiv  Detail & Related papers  (2022-12-21T23:15:17Z)
• 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)
• Quantum Approximate Optimization Algorithm applied to the binary perceptron [0.46664938579243564]
  We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks. We provide evidence for the existence of optimal smooth solutions for the QAOA parameters, which are transferable among typical instances of the same problem. We prove numerically an enhanced performance of QAOA over traditional QA.
  arXiv  Detail & Related papers  (2021-12-19T18:33:22Z)
• 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)
• Benchmarking adaptive variational quantum eigensolvers [63.277656713454284]
  We benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves. We find both methods provide good estimates of the energy and ground state. gradient-based optimization is more economical and delivers superior performance than analogous simulations carried out with gradient-frees.
  arXiv  Detail & Related papers  (2020-11-02T19:52:04Z)
• Momentum Q-learning with Finite-Sample Convergence Guarantee [49.38471009162477]
  This paper analyzes a class of momentum-based Q-learning algorithms with finite-sample guarantee. We establish the convergence guarantee for MomentumQ with linear function approximations and Markovian sampling. We demonstrate through various experiments that the proposed MomentumQ outperforms other momentum-based Q-learning algorithms.
  arXiv  Detail & Related papers  (2020-07-30T12:27:03Z)

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.