Improving application performance with biased distributions of quantum states
We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration para...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-11-01
|
| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.043145 |
| _version_ | 1797210884749131776 |
|---|---|
| author | Sanjaya Lohani Joseph M. Lukens Daniel E. Jones Thomas A. Searles Ryan T. Glasser Brian T. Kirby |
| author_facet | Sanjaya Lohani Joseph M. Lukens Daniel E. Jones Thomas A. Searles Ryan T. Glasser Brian T. Kirby |
| author_sort | Sanjaya Lohani |
| collection | DOAJ |
| description | We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert–Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert–Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert–Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert–Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert–Schmidt distributed states for various experimental conditions. |
| first_indexed | 2024-04-24T10:17:41Z |
| format | Article |
| id | doaj.art-c52c0e2018a146f9bfd2910a25fe36f8 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:17:41Z |
| publishDate | 2021-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-c52c0e2018a146f9bfd2910a25fe36f82024-04-12T17:15:55ZengAmerican Physical SocietyPhysical Review Research2643-15642021-11-013404314510.1103/PhysRevResearch.3.043145Improving application performance with biased distributions of quantum statesSanjaya LohaniJoseph M. LukensDaniel E. JonesThomas A. SearlesRyan T. GlasserBrian T. KirbyWe consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert–Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert–Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert–Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert–Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert–Schmidt distributed states for various experimental conditions.http://doi.org/10.1103/PhysRevResearch.3.043145 |
| spellingShingle | Sanjaya Lohani Joseph M. Lukens Daniel E. Jones Thomas A. Searles Ryan T. Glasser Brian T. Kirby Improving application performance with biased distributions of quantum states Physical Review Research |
| title | Improving application performance with biased distributions of quantum states |
| title_full | Improving application performance with biased distributions of quantum states |
| title_fullStr | Improving application performance with biased distributions of quantum states |
| title_full_unstemmed | Improving application performance with biased distributions of quantum states |
| title_short | Improving application performance with biased distributions of quantum states |
| title_sort | improving application performance with biased distributions of quantum states |
| url | http://doi.org/10.1103/PhysRevResearch.3.043145 |
| work_keys_str_mv | AT sanjayalohani improvingapplicationperformancewithbiaseddistributionsofquantumstates AT josephmlukens improvingapplicationperformancewithbiaseddistributionsofquantumstates AT danielejones improvingapplicationperformancewithbiaseddistributionsofquantumstates AT thomasasearles improvingapplicationperformancewithbiaseddistributionsofquantumstates AT ryantglasser improvingapplicationperformancewithbiaseddistributionsofquantumstates AT briantkirby improvingapplicationperformancewithbiaseddistributionsofquantumstates |