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Conference Papers Year : 2024

Quantum Circuit Completeness: Extensions and Simplifications


Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits can be derived from the equational theory. We improve this completeness result in two ways: (i) We simplify the equational theory by proving that several rules can be derived from the remaining ones. In particular, two out of the three most intricate rules are removed, the third one being slightly simplified. (ii) The complete equational theory can be extended to quantum circuits with ancillae or qubit discarding, to represent respectively quantum computations using an additional workspace, and hybrid quantum computations. We show that the remaining intricate rule can be greatly simplified in these more expressive settings, leading to equational theories where all equations act on a bounded number of qubits. The development of simple and complete equational theories for expressive quantum circuit models opens new avenues for reasoning about quantum circuits. It provides strong formal foundations for various compiling tasks such as circuit optimisation, hardware constraint satisfaction and verification.
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Dates and versions

hal-04016498 , version 1 (06-03-2023)
hal-04016498 , version 2 (17-08-2023)
hal-04016498 , version 3 (04-12-2023)


  • HAL Id : hal-04016498 , version 2


Alexandre Clément, Noé Delorme, Simon Perdrix, Renaud Vilmart. Quantum Circuit Completeness: Extensions and Simplifications. International Conference on Computer Science Logic CSL 2024, Feb 2024, Naples, Italy. ⟨hal-04016498v2⟩
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