Quantum search using non-Hermitian adiabatic evolution

We propose a non-Hermitian quantum annealing algorithm which can be useful for solving complex optimization problems. We demonstrate our approach on Grover’s problem of finding a marked item inside of unsorted database. We show that the energy gap between the ground and excited states depends on the relaxation parameters, and is not exponentially small. This allows a significant reduction of the searching time. We discuss the relations between the probabilities of finding the ground state and the survival of a quantum computer in a dissipative environment.

💡 Research Summary

The paper introduces a novel quantum annealing (QA) scheme that deliberately incorporates non‑Hermitian (NH) dynamics in order to overcome the exponential slowdown that plagues conventional adiabatic quantum algorithms. The authors focus on Grover’s unstructured search as a benchmark problem, because the standard Hermitian QA suffers from an energy gap that shrinks as O(1/√N) with the database size N, leading to a total runtime that scales unfavorably compared with the optimal O(√N) quantum speed‑up.

In the proposed NH‑QA the time‑dependent Hamiltonian is written as
(H(t)=\bigl