A variational quantum algorithm for Hamiltonian diagonalization

Abstract

Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational algorithm for Hamiltonians diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.

9 pages, 4 figures

References in corpus (6)

• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Subspace-search variational quantum eigensolver for excited states
• Variational Quantum State Diagonalization
• Variational Thermal Quantum Simulation via Thermofield Double States
• Quantum Singular Value Decomposer

Cited by in corpus (8)

• Quantum Approximate Optimization Algorithm with Adaptive Bias Fields
• Quantum imaginary time evolution steered by reinforcement learning
• Mitigating algorithmic errors in quantum optimization through energy extrapolation
• Double-bracket quantum algorithms for diagonalization
• Enhancing variational quantum state diagonalization using reinforcement learning techniques
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Simulating thermodynamic properties of dinuclear metal complexes using Variational Quantum Algorithms
• Unraveling Rodeo Algorithm Through the Zeeman Model