dc.contributor.author | Low, Guang Hao | |
dc.contributor.author | Chuang, Isaac L. | |
dc.date.accessioned | 2021-02-18T18:26:07Z | |
dc.date.available | 2021-02-18T18:26:07Z | |
dc.date.issued | 2019-07 | |
dc.identifier.issn | 2521-327X | |
dc.identifier.uri | https://hdl.handle.net/1721.1/129822 | |
dc.description.abstract | We present the problem of approximating the time-evolution operator e-iHt to error ϵ, where the Hamiltonian H = ((G|⊗I)U (|Gi⊗I) is the projection of a unitary oracle U onto the state |Gi created by another unitary oracle. Our algorithm solves this with a query complexity O ( t + log(1/ϵ) ) to both oracles that is optimal with respect to all parameters in both the asymptotic and non-asymptotic regime, and also with low overhead, using at most two additional ancilla qubits. This approach to Hamiltonian simulation subsumes important prior art considering Hamiltonians which are d-sparse or a linear combination of unitaries, leading to significant improvements in space and gate complexity, such as a quadratic speed-up for precision simulations. It also motivates useful new instances, such as where H is a density matrix. A key technical result is 'qubitization', which uses the controlled version of these oracles to embed any H in an invariant SU(2) subspace. A large class of operator functions of H can then be computed with optimal query complexity, of which e-iHt is a special case. | en_US |
dc.language.iso | en | |
dc.publisher | Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften | en_US |
dc.relation.isversionof | http://dx.doi.org/10.22331/q-2019-07-12-163 | en_US |
dc.rights | Creative Commons Attribution 4.0 International license | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en_US |
dc.source | Quantum | en_US |
dc.title | Hamiltonian Simulation by Qubitization | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Low, Guang Hao and Isaac L. Chuang. "Hamiltonian Simulation by Qubitization." Quantum 3 (July 2019): 163 © Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Physics | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Research Laboratory of Electronics | en_US |
dc.relation.journal | Quantum | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2020-12-04T19:38:06Z | |
dspace.orderedauthors | Low, GH; Chuang, IL | en_US |
dspace.date.submission | 2020-12-04T19:38:08Z | |
mit.journal.volume | 3 | en_US |
mit.license | PUBLISHER_CC | |
mit.metadata.status | Complete | |