Related papers: A Complete Equational Theory for Quantum Circuits

A Complete Equational Theory for Quantum Circuits

URL: http://arxiv.org/abs/2206.10577v2
Date: Sat, 4 Feb 2023 14:48:11 GMT
Title: A Complete Equational Theory for Quantum Circuits
Authors: Alexandre Cl\'ement, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Beno\^it Valiron
Abstract summary: We introduce the first complete equational theory for quantum circuits. Two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations.
Score: 58.720142291102135
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be transformed one into the other using the equations. The proof is based on the properties of multi-controlled gates -- that are defined using elementary gates -- together with an encoding of quantum circuits into linear optical circuits, which have been proved to have a complete axiomatisation.

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