Symmetry-restricted quantum circuits are still well-behaved

• URL: http://arxiv.org/abs/2402.16329v1
• Date: Mon, 26 Feb 2024 06:23:39 GMT
• Title: Symmetry-restricted quantum circuits are still well-behaved
• Authors: Maximilian Balthasar Mansky, Santiago Londo\~no Castillo, Miguel Armayor-Mart\'inez, Alejandro Bravo de la Serna, Gautham Sathish, Zhihao Wang, Sebastian W\"olckerlt, Claudia Linnhoff-Popien
• Abstract summary: We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
• Score: 45.89137831674385
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2^n)$, in particular composition, algebraic and topological closedness and connectedness. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space. The well-behavedness is independent of the symmetry requirement imposed on the subgroup. We provide an example of a permutation invariance across all qubits.

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