Two-local qubit Hamiltonians: when are they stoquastic?
We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquastic...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2019-05-06-139/pdf/ |
| _version_ | 1818269569286930432 |
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| author | Joel Klassen Barbara M. Terhal |
| author_facet | Joel Klassen Barbara M. Terhal |
| author_sort | Joel Klassen |
| collection | DOAJ |
| description | We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for $n$-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary $n$-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes. |
| first_indexed | 2024-12-12T20:56:28Z |
| format | Article |
| id | doaj.art-59424eb3078a495e89837522cfaca283 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-12T20:56:28Z |
| publishDate | 2019-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-59424eb3078a495e89837522cfaca2832022-12-22T00:12:17ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-05-01313910.22331/q-2019-05-06-13910.22331/q-2019-05-06-139Two-local qubit Hamiltonians: when are they stoquastic?Joel KlassenBarbara M. TerhalWe examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for $n$-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary $n$-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.https://quantum-journal.org/papers/q-2019-05-06-139/pdf/ |
| spellingShingle | Joel Klassen Barbara M. Terhal Two-local qubit Hamiltonians: when are they stoquastic? Quantum |
| title | Two-local qubit Hamiltonians: when are they stoquastic? |
| title_full | Two-local qubit Hamiltonians: when are they stoquastic? |
| title_fullStr | Two-local qubit Hamiltonians: when are they stoquastic? |
| title_full_unstemmed | Two-local qubit Hamiltonians: when are they stoquastic? |
| title_short | Two-local qubit Hamiltonians: when are they stoquastic? |
| title_sort | two local qubit hamiltonians when are they stoquastic |
| url | https://quantum-journal.org/papers/q-2019-05-06-139/pdf/ |
| work_keys_str_mv | AT joelklassen twolocalqubithamiltonianswhenaretheystoquastic AT barbaramterhal twolocalqubithamiltonianswhenaretheystoquastic |