Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators
Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously mad...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-12-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-12-17-1567/pdf/ |
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| _version_ | 1846118573509967872 |
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| author | Pablo Antonio Moreno Casares Modjtaba Shokrian Zini Juan Miguel Arrazola |
| author_facet | Pablo Antonio Moreno Casares Modjtaba Shokrian Zini Juan Miguel Arrazola |
| author_sort | Pablo Antonio Moreno Casares |
| collection | DOAJ |
| description | Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers. |
| format | Article |
| id | doaj-art-8b133c36f7af4b48b5a5020e1565d446 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-8b133c36f7af4b48b5a5020e1565d4462024-12-17T13:40:02ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-12-018156710.22331/q-2024-12-17-156710.22331/q-2024-12-17-1567Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operatorsPablo Antonio Moreno CasaresModjtaba Shokrian ZiniJuan Miguel ArrazolaHamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.https://quantum-journal.org/papers/q-2024-12-17-1567/pdf/ |
| spellingShingle | Pablo Antonio Moreno Casares Modjtaba Shokrian Zini Juan Miguel Arrazola Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators Quantum |
| title | Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators |
| title_full | Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators |
| title_fullStr | Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators |
| title_full_unstemmed | Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators |
| title_short | Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators |
| title_sort | quantum simulation of time dependent hamiltonians via commutator free quasi magnus operators |
| url | https://quantum-journal.org/papers/q-2024-12-17-1567/pdf/ |
| work_keys_str_mv | AT pabloantoniomorenocasares quantumsimulationoftimedependenthamiltoniansviacommutatorfreequasimagnusoperators AT modjtabashokrianzini quantumsimulationoftimedependenthamiltoniansviacommutatorfreequasimagnusoperators AT juanmiguelarrazola quantumsimulationoftimedependenthamiltoniansviacommutatorfreequasimagnusoperators |