Efficient classical algorithms for simulating symmetric quantum systems
In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specific...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-11-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-11-28-1189/pdf/ |
| _version_ | 1827631438763130880 |
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| author | Eric R. Anschuetz Andreas Bauer Bobak T. Kiani Seth Lloyd |
| author_facet | Eric R. Anschuetz Andreas Bauer Bobak T. Kiani Seth Lloyd |
| author_sort | Eric R. Anschuetz |
| collection | DOAJ |
| description | In light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements. |
| first_indexed | 2024-03-09T14:20:55Z |
| format | Article |
| id | doaj.art-b6d033b0fecc4b15871a187bf5040193 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-09T14:20:55Z |
| publishDate | 2023-11-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-b6d033b0fecc4b15871a187bf50401932023-11-28T11:55:44ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-11-017118910.22331/q-2023-11-28-118910.22331/q-2023-11-28-1189Efficient classical algorithms for simulating symmetric quantum systemsEric R. AnschuetzAndreas BauerBobak T. KianiSeth LloydIn light of recently proposed quantum algorithms that incorporate symmetries in the hope of quantum advantage, we show that with symmetries that are restrictive enough, classical algorithms can efficiently emulate their quantum counterparts given certain classical descriptions of the input. Specifically, we give classical algorithms that calculate ground states and time-evolved expectation values for permutation-invariant Hamiltonians specified in the symmetrized Pauli basis with runtimes polynomial in the system size. We use tensor-network methods to transform symmetry-equivariant operators to the block-diagonal Schur basis that is of polynomial size, and then perform exact matrix multiplication or diagonalization in this basis. These methods are adaptable to a wide range of input and output states including those prescribed in the Schur basis, as matrix product states, or as arbitrary quantum states when given the power to apply low depth circuits and single qubit measurements.https://quantum-journal.org/papers/q-2023-11-28-1189/pdf/ |
| spellingShingle | Eric R. Anschuetz Andreas Bauer Bobak T. Kiani Seth Lloyd Efficient classical algorithms for simulating symmetric quantum systems Quantum |
| title | Efficient classical algorithms for simulating symmetric quantum systems |
| title_full | Efficient classical algorithms for simulating symmetric quantum systems |
| title_fullStr | Efficient classical algorithms for simulating symmetric quantum systems |
| title_full_unstemmed | Efficient classical algorithms for simulating symmetric quantum systems |
| title_short | Efficient classical algorithms for simulating symmetric quantum systems |
| title_sort | efficient classical algorithms for simulating symmetric quantum systems |
| url | https://quantum-journal.org/papers/q-2023-11-28-1189/pdf/ |
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