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Conference Papers Year : 2023

A Complete Equational Theory for Quantum Circuits


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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hal-04318291 , version 1 (01-12-2023)




  • HAL Id : hal-04318291 , version 1


Alexandre Clément, Nicolas Heurtel, Shane Mansfield, Simon Perdrix, Benoît Valiron. A Complete Equational Theory for Quantum Circuits. 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023), Jul 2023, Aveiro, Portugal. ⟨hal-04318291⟩
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