Automatic translation of quantum circuits to optimized one-way quantum computation patterns

Abstract

One-way quantum computation (1WQC) is a model of universal quantum computations in which a specific highly entangled state called a cluster state (or graph state) allows for quantum computation by only single-qubit measurements. The needed computations in this model are organized as measurement patterns. Previously, an automatic approach to extract a 1WQC pattern from a quantum circuit has been proposed. It takes a quantum circuit consisting of CZ and $J(\alpha )$ gates and translates it into an optimized 1WQC pattern. However, the quantum synthesis algorithms usually decompose circuits using a library containing CNOT and any single-qubit gates. In this paper, we show how this approach can be modified in a way that it can take a circuit consisting of CNOT and any single-qubit gates to produce an optimized 1WQC pattern. The single-qubit gates are first automatically $J$-decomposed and then added to the measurement patterns. Moreover, a new optimization technique is proposed by presenting some algorithms to add Pauli gates to the measurement patterns directly, i.e., without their $J$-decomposition which leads to more compact patterns for these gates. Using these algorithms, an improved approach for adding single-qubit gates to measurement patterns is proposed. The optimized pattern of CNOT gates is directly added to the measurement patterns. Experimental results show that the proposed approach can efficiently produce optimized patterns for quantum circuits and that adding CNOT gates directly to the measurement patterns decreases the translation runtime.