Scaling of symmetry-restricted quantum circuits
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arXiv
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| Auteurs principaux: | , , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908493675495424 |
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| author | Mansky, Maximilian Balthasar Martinez, Miguel Armayor de la Serna, Alejandro Bravo Castillo, Santiago Londoño Nikolaidou, Dimitra Sathish, Gautham Wang, Zhihao Wölckert, Sebastian Linnhoff-Popien, Claudia |
| author_facet | Mansky, Maximilian Balthasar Martinez, Miguel Armayor de la Serna, Alejandro Bravo Castillo, Santiago Londoño Nikolaidou, Dimitra Sathish, Gautham Wang, Zhihao Wölckert, Sebastian Linnhoff-Popien, Claudia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling of symmetry-restricted quantum circuits Mansky, Maximilian Balthasar Martinez, Miguel Armayor de la Serna, Alejandro Bravo Castillo, Santiago Londoño Nikolaidou, Dimitra Sathish, Gautham Wang, Zhihao Wölckert, Sebastian Linnhoff-Popien, Claudia Quantum Physics 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. |
| title | Scaling of symmetry-restricted quantum circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.09962 |