Backens, M;
Miller-Bakewell, H;
De Felice, G;
Lobski, L;
van de Wetering, J;
(2021)
There and back again: A circuit extraction tale.
Quantum
, 5
, Article 421. 10.22331/q-2021-03-25-421.
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Abstract
Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for one-way computations allowing measurements in three different planes of the Bloch sphere, most research so far has focused on computations containing only measurements in the XY-plane. Here, we give the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow. The algorithm is efficient and the resulting circuits do not contain ancillae. One-way computations are represented using the ZX-calculus, hence the algorithm also represents the most general known procedure for extracting circuits from ZX-diagrams. In developing this algorithm, we generalise several concepts and results previously known for computations containing only XY-plane measurements. We bring together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus. These rules are used to simplify measurement patterns by reducing the number of qubits while preserving both the semantics and the existence of gflow. The results can be applied to circuit optimisation by translating circuits to patterns and back again.
| Type: | Article |
|---|---|
| Title: | There and back again: A circuit extraction tale |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.22331/q-2021-03-25-421 |
| Publisher version: | https://doi.org/10.22331/q-2021-03-25-421 |
| Language: | English |
| Additional information: | This is an Open Access article published under a Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10139449 |
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