Identification of topological phases using classically-optimized variational quantum eigensolver

Abstract

Variational quantum eigensolver (VQE) is regarded as a promising candidate of hybrid quantum-classical algorithm for the near-term quantum computers. Meanwhile, VQE is confronted with a challenge that statistical error associated with the measurement as well as systematic error could significantly hamper the optimization. To circumvent this issue, we propose classically-optimized VQE (co-VQE), where the whole process of the optimization is efficiently conducted on a classical computer. The efficacy of the method is guaranteed by the observation that quantum circuits with a constant (or logarithmic) depth are classically tractable via simulations of local subsystems. In co-VQE, we only use quantum computers to measure nonlocal quantities after the parameters are optimized. As proof-of-concepts, we present numerical experiments on quantum spin models with topological phases. After the optimization, we identify the topological phases by nonlocal order parameters as well as unsupervised machine learning on inner products between quantum states. The proposed method maximizes the advantage of using quantum computers while avoiding strenuous optimization on noisy quantum devices. Furthermore, in terms of quantum machine learning, our study shows an intriguing approach that employs quantum computers to generate data of quantum systems while using classical computers for the learning process.

8 pages, 6 figures

References in corpus (19)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• The Variational Quantum Eigensolver: a review of methods and best practices
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Hybrid quantum-classical algorithms and quantum error mitigation
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Measurements as a roadblock to near-term practical quantum advantage in chemistry: resource analysis
• Evaluating the noise resilience of variational quantum algorithms
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation
• Quantum Phase Recognition via Quantum Kernel Methods
• Verifying Random Quantum Circuits with Arbitrary Geometry Using Tensor Network States Algorithm
• Quantum kernels to learn the phases of quantum matter
• The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry
• Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing

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• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Detecting quasi-degenerate ground states in topological models via variational quantum eigensolver
• A quantum computing approach to fixed-node Monte Carlo using classical shadows
• Learning Variational Quantum Circuit Parameters with Classical Artificial Intelligence for Quantum Phase Transition Detection