Disentangling magic states with classically simulable quantum circuits
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914238340005888 |
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| author | Fux, Gerald E. Béri, Benjamin Fazio, Rosario Tirrito, Emanuele |
| author_facet | Fux, Gerald E. Béri, Benjamin Fazio, Rosario Tirrito, Emanuele |
| contents | We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or approximately equal to the number of qubits. This implies that Pauli expectation values of such states can be efficiently simulated classically, despite them exhibiting both extensive entanglement and extensive nonstabilizerness. We prove this result analytically using a quantum error correction formulation, demonstrate its applicability numerically, and discuss consequences for the disentanglability of states generated through Hamiltonian dynamics. We show that this result implies a novel representation of approximate state designs that can also facilitate their efficient generation, and we propose a novel quantum circuit compression scheme for Clifford circuits doped with non-Clifford phase gates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disentangling magic states with classically simulable quantum circuits Fux, Gerald E. Béri, Benjamin Fazio, Rosario Tirrito, Emanuele Quantum Physics We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or approximately equal to the number of qubits. This implies that Pauli expectation values of such states can be efficiently simulated classically, despite them exhibiting both extensive entanglement and extensive nonstabilizerness. We prove this result analytically using a quantum error correction formulation, demonstrate its applicability numerically, and discuss consequences for the disentanglability of states generated through Hamiltonian dynamics. We show that this result implies a novel representation of approximate state designs that can also facilitate their efficient generation, and we propose a novel quantum circuit compression scheme for Clifford circuits doped with non-Clifford phase gates. |
| title | Disentangling magic states with classically simulable quantum circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.09001 |