Adiabatic quantum imaginary time evolution

TL;DR

This paper presents an adiabatic quantum imaginary time evolution protocol that avoids quantum state tomography and extends adiabatic state preparation to a broader class of states, demonstrated through classical simulations.

Contribution

It introduces a novel adiabatic approach to quantum imaginary time evolution that does not require the system Hamiltonian as the final Hamiltonian, broadening the scope of adiabatic state preparation.

Findings

The protocol can be implemented on resource-limited quantum architectures.

Classical simulations show effective ground-state preparation in a 1D spin model.

The method expands the set of states accessible via adiabatic techniques.

Abstract

We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime, and unlike standard adiabatic state preparation, the final Hamiltonian is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic Hamiltonian by integrating a classical differential equation that ensures that one follows the imaginary time evolution state trajectory. We introduce some heuristics that allow this protocol to be implemented on quantum architectures with limited resources. We explore the performance of this algorithm via classical simulations in a one-dimensional spin model and highlight essential features that determine its cost, performance, and implementability for longer times, and compare to the original quantum imaginary time evolution for ground-state preparation. More generally, our algorithm expands the range of states accessible to adiabatic state preparation methods beyond those that are expressed as ground-states of simple explicit Hamiltonians.