A non-Hermitian Ground State Searching Algorithm Enhanced by Variational Toolbox

TL;DR

This paper introduces a novel non-Hermitian quantum algorithm enhanced with variational techniques to efficiently find ground states, outperforming traditional methods like QAOA in convergence speed and resource usage.

Contribution

It presents a new non-Hermitian ground state search algorithm combined with variational gadgets, improving efficiency and resource management in quantum simulations.

Findings

Outperforms QAOA in convergence speed.

Reduces circuit depth and resource requirements.

Demonstrates effectiveness through numerical simulations.

Abstract

Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the system qubits. To make the method more resource friendly in the noisy intermediate-scale quantum (NISQ) and early fault-tolerant era, we combine the non-Hermitian projection algorithm with multiple variational gadgets, including variational module enhancement and variational state recording, to reduce the required circuit depth and avoid the exponentially vanishing success probability for post-selections. We compare our method, the non-Hermitian-variational algorithm, with a pure variational method -- QAOA for solving the 3-SAT problem and preparing the ground state for the transverse-field Ising model. As demonstrated by numerical evidence, the non-Hermitian-variational algorithm outperforms QAOA in convergence speed with improved quantum resource efficiency.