Efficient quantum simulation algorithms in the path integral formulation.
Saved in:
| Title: | Efficient quantum simulation algorithms in the path integral formulation. |
|---|---|
| Authors: | Shum, Serene1 (AUTHOR) serene.shum@mail.utoronto.ca, Wiebe, Nathan2,3 (AUTHOR) |
| Source: | Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 25, p1-52. 52p. |
| Subjects: | Path integrals, Quantum computing, Lagrangian mechanics, Hamiltonian operator, Monte Carlo method, Quantum field theory |
| Abstract: | We provide a new paradigm for quantum simulation based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional Hamiltonian formalism. We provide two novel quantum algorithms based on Hamiltonian versions of the path integral formulation and another for Lagrangians of the form m 2 x ˙ 2 − V (x) , while avoiding the sign problems that preclude efficient Monte-Carlo algorithms for such problems. This Lagrangian path integral algorithm is based on a new rigorous derivation of a discrete version of the Lagrangian path integral. Our first Hamiltonian path integral method breaks up the paths into short timesteps. It is efficient under appropriate sparsity assumptions and requires a number of queries to oracles that give the eigenvalues and overlaps between the eigenvectors of the Hamiltonian terms that scales as t o (1) / ϵ o (1) for simulation time t and error ϵ . The second approach uses long-time path integrals for near-adiabatic systems and has query complexity that scales as O (1 / ϵ) if the energy eigenvalue gaps and simulation time is sufficiently long. Finally, we show that our Lagrangian simulation algorithm requires a number of queries to an oracle that computes the discrete Lagrangian that scales for a system with η particles in D + 1 dimensions as O ~ (η D t 2 / ϵ) if V (x) is bounded and finite and the wavefunction obeys appropriate position and momentum cutoffs. This shows that Lagrangian dynamics can be efficiently simulated on quantum computers and opens up the possibility for quantum field theories for which the Hamiltonian is unknown to be efficiently simulated on quantum computers. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 194757905 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Efficient quantum simulation algorithms in the path integral formulation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shum%2C+Serene%22">Shum, Serene</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> serene.shum@mail.utoronto.ca</i><br /><searchLink fieldCode="AR" term="%22Wiebe%2C+Nathan%22">Wiebe, Nathan</searchLink><relatesTo>2,3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 2026, Vol. 59 Issue 25, p1-52. 52p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Path+integrals%22">Path integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+computing%22">Quantum computing</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrangian+mechanics%22">Lagrangian mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+operator%22">Hamiltonian operator</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+field+theory%22">Quantum field theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We provide a new paradigm for quantum simulation based on path integration that allows quantum speedups to be observed for problems that are more naturally expressed using the path integral formalism rather than the conventional Hamiltonian formalism. We provide two novel quantum algorithms based on Hamiltonian versions of the path integral formulation and another for Lagrangians of the form m 2 x ˙ 2 − V (x) , while avoiding the sign problems that preclude efficient Monte-Carlo algorithms for such problems. This Lagrangian path integral algorithm is based on a new rigorous derivation of a discrete version of the Lagrangian path integral. Our first Hamiltonian path integral method breaks up the paths into short timesteps. It is efficient under appropriate sparsity assumptions and requires a number of queries to oracles that give the eigenvalues and overlaps between the eigenvectors of the Hamiltonian terms that scales as t o (1) / ϵ o (1) for simulation time t and error ϵ . The second approach uses long-time path integrals for near-adiabatic systems and has query complexity that scales as O (1 / ϵ) if the energy eigenvalue gaps and simulation time is sufficiently long. Finally, we show that our Lagrangian simulation algorithm requires a number of queries to an oracle that computes the discrete Lagrangian that scales for a system with η particles in D + 1 dimensions as O ~ (η D t 2 / ϵ) if V (x) is bounded and finite and the wavefunction obeys appropriate position and momentum cutoffs. This shows that Lagrangian dynamics can be efficiently simulated on quantum computers and opens up the possibility for quantum field theories for which the Hamiltonian is unknown to be efficiently simulated on quantum computers. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=194757905 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1751-8121/ae751c Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 52 StartPage: 1 Subjects: – SubjectFull: Path integrals Type: general – SubjectFull: Quantum computing Type: general – SubjectFull: Lagrangian mechanics Type: general – SubjectFull: Hamiltonian operator Type: general – SubjectFull: Monte Carlo method Type: general – SubjectFull: Quantum field theory Type: general Titles: – TitleFull: Efficient quantum simulation algorithms in the path integral formulation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shum, Serene – PersonEntity: Name: NameFull: Wiebe, Nathan IsPartOfRelationships: – BibEntity: Dates: – D: 26 M: 06 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 17518113 Numbering: – Type: volume Value: 59 – Type: issue Value: 25 Titles: – TitleFull: Journal of Physics A: Mathematical & Theoretical Type: main |
| ResultId | 1 |
