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quant-ph2026
A Complete Equational Theory for Real-Clifford+CH Quantum Circuits
Alexandre Clément
We introduce a complete equational theory for the fragment of quantum circuits generated by the real Clifford gates plus the two-qubit controlled-Hadamard gate. That is, we give a…
quant-ph2023
Minimal Equational Theories for Quantum Circuits
Alexandre Clément, Noé Delorme, Simon Perdrix
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…
quant-ph2020
PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations
Alexandre Clément, Simon Perdrix
We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causa…