Related papers: Scaling of symmetry-restricted quantum circuits

Scaling of symmetry-restricted quantum circuits

URL: http://arxiv.org/abs/2406.09962v1
Date: Fri, 14 Jun 2024 12:12:15 GMT
Title: Scaling of symmetry-restricted quantum circuits
Authors: Maximilian Balthasar Mansky, Miguel Armayor Martinez, Alejandro Bravo de la Serna, Santiago Londoño Castillo, Dimitra Nikoladou, Gautham Sathish, Zhihao Wang, Sebastian Wölckert, Claudia Linnhoff-Popien,
Abstract summary: In this work, we investigate the properties of $mathcalMSU(2N)$, $mathcalM$-invariant subspaces of the special unitary Lie group $SU(2N)$.
Score: 42.803917477133346
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The intrinsic symmetries of physical systems have been employed to reduce the number of degrees of freedom of systems, thereby simplifying computations. In this work, we investigate the properties of $\mathcal{M}SU(2^N)$, $\mathcal{M}$-invariant subspaces of the special unitary Lie group $SU(2^N)$ acting on $N$ qubits, for some $\mathcal{M}\subseteq M_{2^N}(\mathbb{C})$. We demonstrate that for certain choices of $\mathcal{M}$, the subset $\mathcal{M}SU(2^N)$ inherits many topological and group properties from $SU(2^N)$. We then present a combinatorial method for computing the dimension of such subspaces when $\mathcal{M}$ is a representation of a permutation group acting on qubits $(GSU(2^N))$, or a Hamiltonian $(H^{(N)}SU(2^N))$. The Kronecker product of $\mathfrak{su}(2)$ matrices is employed to construct the Lie algebras associated with different permutation-invariant groups $GSU(2^N)$. Numerical results on the number of dimensions support the the developed theory.

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