Measurement-based deterministic imaginary time evolution

TL;DR

This paper presents a measurement-based method for deterministic imaginary time evolution in quantum systems, combining weak measurements and conditional unitaries to efficiently approximate ground states.

Contribution

It introduces a novel measurement-driven approach to simulate imaginary time evolution with deterministic outcomes, improving control and efficiency.

Findings

The method converges below a certain energy threshold.

The algorithm's complexity is analyzed for specific problems.

Measurements and unitaries are efficiently constructed.

Abstract

We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by a Suzuki-Trotter decomposition, an evolution approximating imaginary time evolution can be realized. The randomness due to measurement is corrected using conditional unitary operations, making the evolution deterministic. Both the measurements required for the algorithm and the conditional unitary operations can be constructed efficiently. We show that the algorithm converges only below a specified energy threshold and the complexity is estimated for some specific problem instances.