Relating Measurement Patterns to Circuits via Pauli Flow
Abstract
The oneway model of MeasurementBased Quantum Computing and the gatebased circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gatebased quantum circuit into a oneway computation, whereas the reverse is only efficient given some constraints on the structure of the measurement pattern. Causal flow and generalised flow have already been shown as sufficient, with efficient algorithms for identifying these properties and performing the circuit extraction. Pauli flow is a weaker set of conditions that extends generalised flow to use the knowledge that some vertices are measured in a Pauli basis. In this paper, we show that Pauli flow can similarly be identified efficiently and that any measurement pattern whose underlying graph admits a Pauli flow can be efficiently transformed into a gatebased circuit without using ancilla qubits. We then use this relationship to derive simulation results for the effects of graphtheoretic rewrites in the ZXcalculus using a more circuitlike data structure we call the Pauli Dependency DAG.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.05654
 Bibcode:
 2021arXiv210905654S
 Keywords:

 Quantum Physics;
 Computer Science  Logic in Computer Science;
 F.1.1
 EPrint:
 In Proceedings QPL 2021, arXiv:2109.04886