Quantum Computation by Cooling

Jaeyoon Cho

Published 2024-03-04, updated 2024-03-08Version 2

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, an analysis of such a scheme is surprisingly 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. In the first example, the cooling is free from any local energy minima, reducing the scheme to Grover's search algorithm with a few improvements. In the second example, the cooling suffers from abundant local energy minima. To circumvent this, we implant a mechanism in the Hamiltonian so that the population trapped in the local minima can tunnel out by high-order transitions. We support this idea with a numerical simulation for a particular combinatorial optimization problem. 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.