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A Complete Equational Theory for Quantum Circuits


In this note, 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 quantum evolution 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.

Dates and versions

hal-03926757 , version 1 (06-01-2023)



Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Benoît Valiron. A Complete Equational Theory for Quantum Circuits. 2023. ⟨hal-03926757⟩
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