Relating Measurement Patterns to Circuits via Pauli Flow

09/13/2021
by   Will Simmons, et al.
0

The one-way model of Measurement-Based Quantum Computing and the gate-based circuit model give two different presentations of how quantum computation can be performed. There are known methods for converting any gate-based quantum circuit into a one-way 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 gate-based circuit without using ancilla qubits. We then use this relationship to derive simulation results for the effects of graph-theoretic rewrites in the ZX-calculus using a more circuit-like data structure we call the Pauli Dependency DAG.

READ FULL TEXT

page 1

page 2

page 3

page 4

02/08/2019

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

We present a new circuit-to-circuit optimisation routine based on an equ...
04/19/2022

Quartz: Superoptimization of Quantum Circuits (Extended Version)

Existing quantum compilers optimize quantum circuits by applying circuit...
07/05/2019

Optimization of Quantum Circuit Mapping using Gate Transformation and Commutation

This paper addresses quantum circuit mapping for Noisy Intermediate-Scal...
08/05/2021

Extending the Graph Formalism to Higher-Order Gates

We present an algorithm for efficiently simulating a quantum circuit in ...
12/13/2021

A Case For Noisy Shallow Gate-Based Circuits In Quantum Machine Learning

There is increasing interest in the development of gate-based quantum ci...
11/14/2018

Faster manipulation of large quantum circuits using wire label reference diagrams

Large scale quantum computing is highly anticipated, and quantum circuit...
09/13/2021

Generators and Relations for Real Stabilizer Operators

Real stabilizer operators, which are also known as real Clifford operato...