Quantum search using non-Hermitian adiabatic evolution

Abstract

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.

5 pages, 3 figures

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Cited by in corpus (7)

• Adiabaticity condition for non-Hermitian Hamiltonians
• Optimization by a quantum reinforcement algorithm
• Non-Hermitian Quantum Annealing in the Ferromagnetic Ising Model
• Non-Hermitian Quantum Annealing in the Antiferromagnetic Ising Chain
• Time reversal of a discrete system coupled to a continuum based on non-Hermitian flip
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement