Diagonal quantum circuits: Their computational power and applications

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 ones 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.