Exponentiation of parametric Hamiltonians via unitary interpolation

The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte Carlo sampling. We introduce two ideas for the t...

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Main Authors: Michael Schilling, Francesco Preti, Matthias M. Müller, Tommaso Calarco, Felix Motzoi
Format: Article
Language:English
Published: American Physical Society 2024-12-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.6.043278
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author Michael Schilling
Francesco Preti
Matthias M. Müller
Tommaso Calarco
Felix Motzoi
author_facet Michael Schilling
Francesco Preti
Matthias M. Müller
Tommaso Calarco
Felix Motzoi
author_sort Michael Schilling
collection DOAJ
description The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multiparametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation scheme to improve both accuracy and walltime. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. Furthermore, we define the interpolation on a grid of system parameters, and show that the interpolation infidelity converges with fourth-order accuracy in the number of interpolation bins.
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institution DOAJ
issn 2643-1564
language English
publishDate 2024-12-01
publisher American Physical Society
record_format Article
series Physical Review Research
spelling doaj-art-20f0156f26b3498598eed2dfd0d1cd382025-08-20T02:49:15ZengAmerican Physical SocietyPhysical Review Research2643-15642024-12-016404327810.1103/PhysRevResearch.6.043278Exponentiation of parametric Hamiltonians via unitary interpolationMichael SchillingFrancesco PretiMatthias M. MüllerTommaso CalarcoFelix MotzoiThe effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte Carlo sampling. We introduce two ideas for the time-efficient approximation of matrix exponentials of linear multiparametric Hamiltonians. We modify the Suzuki-Trotter product formula from an approximation to an interpolation scheme to improve both accuracy and walltime. This allows us to achieve high fidelities within a single interpolation step, which can be computed directly from cached matrices. Furthermore, we define the interpolation on a grid of system parameters, and show that the interpolation infidelity converges with fourth-order accuracy in the number of interpolation bins.http://doi.org/10.1103/PhysRevResearch.6.043278
spellingShingle Michael Schilling
Francesco Preti
Matthias M. Müller
Tommaso Calarco
Felix Motzoi
Exponentiation of parametric Hamiltonians via unitary interpolation
Physical Review Research
title Exponentiation of parametric Hamiltonians via unitary interpolation
title_full Exponentiation of parametric Hamiltonians via unitary interpolation
title_fullStr Exponentiation of parametric Hamiltonians via unitary interpolation
title_full_unstemmed Exponentiation of parametric Hamiltonians via unitary interpolation
title_short Exponentiation of parametric Hamiltonians via unitary interpolation
title_sort exponentiation of parametric hamiltonians via unitary interpolation
url http://doi.org/10.1103/PhysRevResearch.6.043278
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AT matthiasmmuller exponentiationofparametrichamiltoniansviaunitaryinterpolation
AT tommasocalarco exponentiationofparametrichamiltoniansviaunitaryinterpolation
AT felixmotzoi exponentiationofparametrichamiltoniansviaunitaryinterpolation