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Preprints, Working Papers, ... Year : 2023

Minimal Equational Theories for Quantum Circuits

Alexandre Clément
Noé Delorme
  • Function : Author
  • PersonId : 1234319
  • IdHAL : noedelorme
Simon Perdrix

Abstract

We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one which states that a multi-control $2\pi$ rotation is nothing but the identity. Our work improves on the recent complete equational theories for quantum circuits, by getting rid of several rules including a fairly unpractical one. One of our main contributions is to prove the minimality of the equational theory, i.e. none of the rules can be derived from the other ones. More generally, we demonstrate that any complete equational theory on quantum circuits (when all gates are unitary) requires rules acting on an unbounded number of qubits. Finally, we also simplify the complete equational theories for quantum circuits with ancillary qubits and/or qubit discarding.

Dates and versions

hal-04399210 , version 1 (17-01-2024)

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Alexandre Clément, Noé Delorme, Simon Perdrix. Minimal Equational Theories for Quantum Circuits. 2024. ⟨hal-04399210⟩
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