Quasiprobabilistic imaginary-time evolution on quantum computers

TL;DR

This paper introduces a novel quantum algorithm for imaginary-time evolution that leverages probabilistic error cancellation, enabling efficient and noise-resilient estimation of thermal properties on current quantum hardware.

Contribution

The proposed algorithm decomposes imaginary-time evolution into a probabilistic linear combination of operations, requiring no ancillary qubits and being inherently noise-resilient, advancing quantum simulation capabilities.

Findings

Numerical simulation of 8-qubit Heisenberg Hamiltonian shows promising accuracy.

Experimental estimation of 2-qubit Hamiltonian energy on IBM quantum computer.

Algorithm effectively estimates thermal expectation values with potential for near-term quantum devices.

Abstract

Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for imaginary-time evolution have resource requirements that are prohibitive for current quantum devices and face performance issues due to noise. Here, we propose a new algorithm for computing imaginary-time evolved expectation values on quantum computers, inspired by probabilistic error cancellation, an error-mitigation technique. Our algorithm works by decomposing a Trotterization of imaginary-time evolution into a probabilistic linear combination of operations, each of which is then implemented on a quantum computer. The measurement data is then classically post-processed to obtain the expectation value of the imaginary-time evolved state. Our algorithm requires no ancillary qubits and can be made noise-resilient without additional error mitigation. It is well-suited for estimating thermal expectation values by making use of the notion of a thermal pure quantum state. We demonstrate our algorithm by performing numerical simulations of thermal pure quantum state preparation for the 1D Heisenberg Hamiltonian on 8 qubits, and by using an IBM quantum computer to estimate the energy of the same Hamiltonian on 2 qubits. We observe promising results compared to the exact values, illustrating the potential of our algorithm for probing the physics of quantum many-body systems on current hardware.