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...
Saved in:
| Main Authors: | , , , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850064644851367936 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-20f0156f26b3498598eed2dfd0d1cd38 |
| 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 |
| work_keys_str_mv | AT michaelschilling exponentiationofparametrichamiltoniansviaunitaryinterpolation AT francescopreti exponentiationofparametrichamiltoniansviaunitaryinterpolation AT matthiasmmuller exponentiationofparametrichamiltoniansviaunitaryinterpolation AT tommasocalarco exponentiationofparametrichamiltoniansviaunitaryinterpolation AT felixmotzoi exponentiationofparametrichamiltoniansviaunitaryinterpolation |