Catastrophic failure of quantum annealing owing to non-stoquastic Hamiltonian and its avoidance by decoherence

TL;DR

This paper demonstrates that non-stoquastic Hamiltonians can cause catastrophic failure in quantum annealing, but introducing decoherence can prevent this failure by breaking symmetries and enabling ground state preparation.

Contribution

It reveals that non-stoquastic terms can lead to QA failure and shows how decoherence can be used to avoid such failures, providing new insights into QA mechanisms.

Findings

Non-stoquastic Hamiltonians can cause QA failure due to symmetry-induced crossings.

Decoherence can break symmetries and enable successful ground state preparation.

Counterintuitive role of decoherence in improving QA outcomes.

Abstract

Quantum annealing (QA) is a promising method for solving combinatorial optimization problems whose solutions are embedded into a ground state of the Ising Hamiltonian. This method employs two types of Hamiltonians: a driver Hamiltonian and a problem Hamiltonian. After a sufficiently slow change from the driver Hamiltonian to the problem Hamiltonian, we can obtain the target ground state that corresponds to the solution. The inclusion of non-stoquastic terms in the driver Hamiltonian is believed to enhance the efficiency of the QA. Meanwhile, decoherence is regarded as of the main obstacles for QA. Here, we present examples showing that non-stoaquastic Hamiltonians can lead to catastrophic failure of QA, whereas a certain decoherence process can be used to avoid such failure. More specifically, when we include anti-ferromagnetic interactions (i.e., typical non-stoquastic terms) in the Hamiltonian, we are unable to prepare the target ground state even with an infinitely long annealing time for some specific cases. In our example, owing to a symmetry, the Hamiltonian is block-diagonalized, and a crossing occurs during the QA, which leads to a complete failure of the ground-state search. Moreover, we show that, when we add a certain type of decoherence, we can obtain the ground state after QA for these cases. This is because, even when symmetry exists in isolated quantum systems, the environment breaks the symmetry. Our counter intuitive results provide a deep insight into the fundamental mechanism of QA.