State-Based Quantum Simulation of Imaginary-Time Evolution

TL;DR

This paper introduces a fully quantum method for simulating imaginary-time evolution, enabling ground state computation without classical or state tomography steps, using controlled-SWAP gates and quantum states.

Contribution

It presents a novel quantum approach that simulates nonunitary imaginary-time evolution directly on quantum hardware, bypassing classical computation and state tomography.

Findings

Successfully simulates imaginary-time evolution using controlled-SWAP gates.

Eliminates need for intermediate classical computation or state tomography.

Demonstrates the method with a specific example.

Abstract

Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum computers is challenging due to its nonunitary nature. Here, we propose a fully quantum approach for simulation of imaginary time evolutions which eliminates the need for intermediate classical computation or state tomography. Our method leverages the recently introduced state-based quantum simulation technique, in which using quantum states besides quantum gates allows to simulate a broader class of evolutions beyond the natural quantum dynamics. Specifically, we demonstrate how by using a set of quantum states and by applying only controlled-SWAP gates and measurements, one can simulate the nonunitary imaginary time evolution. We illustrate our results in an example.