Implementation of Quantum Weyl Transformations on Cirq

Abstract

Quantum computing is based on the principle of encoding the solution space of quantum algorithms into qubits in the evolutionary process of an unknown quantum state. In order for an initial quantum state to transition to a solution state, a series of basic quantum gates must be applied and are abstracted by mathematical matrices. The matrices of fundamental quantum gates are obtained by Weyl transformations. Although these transformations can be simulated in binary quantum systems, there is no ready-made library or similar coding that can be used for simulators in high-dimensional quantum systems. In this study, the matrices of quantum high-dimensional Weyl transformations were coded and these transformations were coded as gates for the Cirq quantum simulator. Thus, quantum gates running in the Cirq simulator are easily accessible for researchers and field enthusiasts.