Geometry-based signal shifting of one-way quantum computation measurement patterns

In one-way quantum computation (1WQC) model, an initial highly entangled state called a graph state is used to perform universal quantum computations by a sequence of adaptive single-qubit measurements and post-measurement Pauli-X and Pauli-Z corrections. The needed computations are organized as measurement patterns or simply patterns in the 1WQC model. The entanglement operations in a pattern can be shown by a graph which together with the set of its input and output qubits is called the geometry of the pattern. Causal flow is a sufficient condition to identify a dependency structure for measurement sequences in order to obtain determinism. Signal shifting is an optimization technique which uses a set of rewrite rules to propagate the Pauli-Z corrections on the measured qubits to the end of patterns. However, automatically applying these rules has difficulties for implementation and is time consuming due to using many ineffective commutation rules. To overcome this problem, in this paper, a new automatic approach is proposed to perform signal shifting on patterns with flows based on their geometries instead of using rewriting rules. It is shown that the time complexity of the proposed approach is improved compared to the previous ones.