Quantum computation by cooling

Abstract

Adiabatic quantum computation is a paradigmatic model aiming to solve a computational problem by finding the many-body ground state encapsulating the solution. However, its use of an adiabatic evolution depending on the spectral gap of an intricate many-body Hamiltonian makes its analysis daunting. While it is plausible to directly cool the final gapped system of the adiabatic evolution instead, the analysis of such a scheme on a general ground is missing. Here, we propose a specific Hamiltonian model for this purpose. The scheme is inspired by cavity cooling, involving the emulation of a zero-temperature reservoir. Repeated discarding of ancilla reservoir qubits extracts the entropy of the system, driving the system toward its ground state. At the same time, the measurement of the discarded qubits hints at the energy-level structure of the system as a return. We show that quantum computation based on this cooling procedure is equivalent in its computational power to the one based on quantum circuits. We then exemplify the scheme with a few illustrative use cases for combinatorial optimization problems. To circumvent the issue of local energy minima, we implant a mechanism in the Hamiltonian that allows the population trapped in the local minima to tunnel out via high-order transitions, and support the idea with numerical simulations. We also discuss its application to preparing quantum many-body ground states, arguing that the spectral gap is a crucial factor in determining the time scale of the cooling.