Quantum Circuit Synthesis Targeting to Improve One-Way Quantum Computation Pattern Cost Metrics

Abstract

One-way quantum computation (1WQC) is a model of universal quantum computations in which a specific highly entangled state called a cluster state allows for quantum computation by single-qubit measurements. The needed computations in this model are organized as measurement patterns. The traditional approach to obtain a measurement pattern is by translating a quantum circuit that solely consists of CZ and J (α) gates into the corresponding measurement patterns and then performing some optimizations by using techniques proposed for the 1WQC model. However, in these cases, the input of the problem is a quantum circuit, not an arbitrary unitary matrix. Therefore, in this article, we focus on the first phase—that is, decomposing a unitary matrix into CZ and J (α) gates. Two well-known quantum circuit synthesis methods, namely cosine-sine decomposition and quantum Shannon decomposition are considered and then adapted for a library of gates containing CZ and J (α), equipped with optimizations. By exploring the solution space of the combinations of these two methods in a bottom-up approach of dynamic programming, a multiobjective quantum circuit synthesis method is proposed that generates a set of quantum circuits. This approach attempts to simultaneously improve the measurement pattern cost metrics after the translation from this set of quantum circuits.