Dissipative ground state preparation and the Dissipative Quantum Eigensolver

TL;DR

This paper introduces a dissipative quantum eigensolver that iteratively applies local measurements to reliably converge to the ground state of a local Hamiltonian, offering advantages like simplicity, noise resilience, and hardware compatibility.

Contribution

The paper presents a novel dissipative quantum eigensolver that converges to the ground state without variational optimization, with robustness to errors and simple implementation on certain quantum hardware.

Findings

Monotonically increasing overlap with ground state over time

Converges unconditionally without prior Hamiltonian knowledge

Inherently error- and noise-resilient

Abstract

For any local Hamiltonian H, I construct a local CPT map and stopping condition which converges to the ground state subspace of H. Like any ground state preparation algorithm, this algorithm necessarily has exponential run-time in general (otherwise BQP=QMA), even for gapped, frustration-free Hamiltonians (otherwise BQP is in NP). However, this dissipative quantum eigensolver has a number of interesting characteristics, which give advantages over previous ground state preparation algorithms. - The entire algorithm consists simply of iterating the same set of local measurements repeatedly. - The expected overlap with the ground state subspace increases monotonically with the length of time this process is allowed to run. - It converges to the ground state subspace unconditionally, without any assumptions on or prior information about the Hamiltonian. - The algorithm does not require any variational optimisation over parameters. - It is often able to find the ground state in low circuit depth in practice. - It has a simple implementation on certain types of quantum hardware, in particular photonic quantum computers. - The process is immune to errors in the initial state. - It is inherently error- and noise-resilient, i.e. to errors during execution of the algorithm and also to faulty implementation of the algorithm itself, without incurring any computational overhead: the overlap of the output with the ground state subspace degrades smoothly with the error rate, independent of the algorithm's run-time. I give rigorous proofs of the above claims, and benchmark the algorithm on some concrete examples numerically.