Symmetry-restricted quantum circuits are still well-behaved

Maximilian Balthasar Mansky; Santiago Londoño Castillo; Miguel Armayor-Martínez; Alejandro Bravo de la Serna; Gautham Sathish; Zhihao Wang; Sebastian Wölckerlt; Claudia Linnhoff-Popien

arXiv · 2402.16329

Symmetry-restricted quantum circuits are still well-behaved

Maximilian Balthasar Mansky·Santiago Londoño Castillo·Miguel Armayor-Martínez·Alejandro Bravo de la Serna·Gautham Sathish·Zhihao Wang·Sebastian Wölckerlt·Claudia Linnhoff-Popien

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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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Maximilian Balthasar Mansky, Santiago Londoño Castillo, Miguel Armayor-Martínez, Alejandro Bravo de la Serna, Gautham Sathish, Zhihao Wang, Sebastian Wölckerlt, Claudia Linnhoff-Popien. 2024-02-26. Symmetry-restricted quantum circuits are still well-behaved. https://arxiv.org/abs/2402.16329

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