Efficient Quantum Algorithm for Filtering Product States

Irmejs, Reinis; Bañuls, Mari Carmen; Cirac, J. Ignacio

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Efficient Quantum Algorithm for Filtering Product States

Irmejs, R., Bañuls, M. C., & Cirac, J. I. (submitted). Efficient Quantum Algorithm for Filtering Product States.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000E-49AA-1 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-49AD-E

Genre: Preprint

Alternative Title : Preprint arXiv: 2312.13892 Submitted on 21 Dec 2023

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Creators:
Irmejs, Reinis^{1, 2}, Author
Bañuls, Mari Carmen^{1, 2}, Author
Cirac, J. Ignacio^{1, 2}, Author

Affiliations:
1Theory, Max Planck Institute of Quantum Optics, Max Planck Society, ou_1445571
2MCQST - Munich Center for Quantum Science and Technology, External Organizations, ou_3330166

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Free keywords: Quantum Physics, quant-ph

Abstract: We introduce a quantum algorithm to efficiently prepare states with an
arbitrarily small energy variance at the target energy. We achieve it by
filtering a product state at the given energy with a Lorentzian filter of width
$\delta$. Given a local Hamiltonian on $N$ qubits, we construct a parent
Hamiltonian whose ground state corresponds to the filtered product state with
variable energy variance proportional to $\delta\sqrt{N}$. We prove that the
parent Hamiltonian is gapped and its ground state can be efficiently
implemented in $\mathrm{poly}(N,1/\delta)$ time via adiabatic evolution. We
numerically benchmark the algorithm for a particular non-integrable model and
find that the adiabatic evolution time to prepare the filtered state with a
width $\delta$ is independent of the system size $N$. Furthermore, the
adiabatic evolution can be implemented with circuit depth
$\mathcal{O}(N^2\delta^{-4})$. Our algorithm provides a way to study the finite
energy regime of many body systems in quantum simulators by directly preparing
a finite energy state, providing access to an approximation of the
microcanonical properties at an arbitrary energy.

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Language(s): eng - English

Dates: Submitted: 2023-12-21

Publication Status: Submitted

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Identifiers: arXiv: 2312.13892v1

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Project name : FermiQP, EQUAHUMO

Grant ID : 13N15890, 13N16066

Funding program : Quantum technologies—from basic research to market

Funding organization : German Federal Ministry of Education and Research (BMBF), Munich Quantum Valley (MQV),Bavarian state government with funds from the Hightech Agenda Bayern Plus

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Funding program : Germany’s Excellence Strategy – EXC- 2111 – 39081486

Funding organization : Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)

Project name : EU-QUANTERA project TNiSQ (BA 6059/1-1)

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Funding program : -

Funding organization : European Commission (EC)

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