Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer

Abstract

Ground-state preparation is an important task in quantum computation. The probabilistic imaginary-time evolution (PITE) method is a promising candidate for preparing the ground state of the Hamiltonian, which comprises a single ancilla qubit and forward- and backward-controlled real-time evolution operators. The ground state preparation is a challenging task even in the quantum computation, classified as complexity-class quantum Merlin-Arthur. However, optimal parameters for PITE could potentially enhance the computational efficiency to a certain degree. In this study, we analyze the computational costs of the PITE method for both linear and exponential scheduling of the imaginary-time step size for reducing the computational cost. First, we analytically discuss an error defined as the closeness between the states acted on by exact and approximate imaginary-time evolution operators. The optimal imaginary-time step size and rate of change of imaginary time are also discussed. Subsequently, the analytical discussion is validated using numerical simulations for a one-dimensional Heisenberg chain. From the results, we find that linear scheduling works well in the case of unknown eigenvalues of the Hamiltonian. For a wide range of eigenstates, the linear scheduling returns smaller errors on average. However, the linearity of the scheduling causes problems for some specific energy regions of eigenstates. To avoid these problems, incorporating a certain level of nonlinearity into the scheduling, such as by inclusion of an exponential character, is preferable for reducing the computational costs of the PITE method. The findings of this study can make a significant contribute to the field of ground-state preparation of many-body Hamiltonians on quantum computers.

16 pages, 9 figures

References in corpus (5)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Simulated Quantum Computation of Molecular Energies
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Hybrid quantum-classical algorithms and quantum error mitigation
• Polynomial-time quantum algorithm for the simulation of chemical dynamics

Cited by in corpus (5)

• Noise-Robust Detection of Quantum Phase Transitions
• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
• Probabilistic imaginary-time evolution in state-vector-based and shot-based simulations and on quantum devices
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms