Diagonal quantum circuits: their computational power and applications

TL;DR

Diagonal quantum circuits, composed of commuting diagonal gates, have significant computational power and practical applications, including state generation and thermalization, which are feasible with current technology.

Contribution

This paper reviews the computational capabilities of diagonal quantum circuits, focusing on IQP circuits and their applications in state generation and thermalization.

Findings

Diagonal quantum circuits outperform classical computation in certain tasks.

IQP circuits are a key subclass with notable computational power.

Applications include approximate random state generation and classical Hamiltonian thermalization.

Abstract

Diagonal quantum circuits are quantum circuits comprising only diagonal gates in the computational basis. In spite of a classical feature of diagonal quantum circuits in the sense of commutativity of all gates, their computational power is highly likely to outperform classical one and they are exploited for applications in quantum informational tasks. We review computational power of diagonal quantum circuits and their applications. We focus on the computational power of instantaneous quantum polynomial-time (IQP) circuits, which are a special type of diagonal quantum circuits. We then review an approximate generation of random states as an application of diagonal quantum circuits, where random states are an ensemble of pure states uniformly distributed in a Hilbert space. We also present a thermalizing algorithm of classical Hamiltonians by using diagonal quantum circuits. These applications are feasible to be experimentally implemented by current technology due to a simple and robust structure of diagonal gates.