Scaling of symmetry-restricted quantum circuits
| Autor: | Mansky, Maximilian Balthasar, Martinez, Miguel Armayor, de la Serna, Alejandro Bravo, Castillo, Santiago Londoño, Nikoladou, Dimitra, Sathish, Gautham, Wang, Zhihao, Wölckert, Sebastian, Linnhoff-Popien, Claudia |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 27 pages, 6 figures, 1 table |
| Databáze: | arXiv |
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