Phase estimation of local Hamiltonians on NISQ hardware
In this work we investigate a binned version of quantum phase estimation (QPE) set out by Somma (2019 New J. Phys. 21 123025) and known as the quantum eigenvalue estimation problem ( QEEP ). Specifically, we determine whether the circuit decomposition techniques we set out in previous work, Clinton...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/acc26d |
| _version_ | 1797629329245470720 |
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| author | Laura Clinton Johannes Bausch Joel Klassen Toby Cubitt |
| author_facet | Laura Clinton Johannes Bausch Joel Klassen Toby Cubitt |
| author_sort | Laura Clinton |
| collection | DOAJ |
| description | In this work we investigate a binned version of quantum phase estimation (QPE) set out by Somma (2019 New J. Phys. 21 123025) and known as the quantum eigenvalue estimation problem ( QEEP ). Specifically, we determine whether the circuit decomposition techniques we set out in previous work, Clinton et al (2021 Nat. Commun. 12 1–10), can improve the performance of QEEP in the noisy intermediate scale quantum (NISQ) regime. To this end we adopt a physically motivated abstraction of NISQ device capabilities as in Clinton et al (2021 Nat. Commun. 12 1–10). Within this framework, we find that our techniques reduce the threshold at which it becomes possible to perform the minimum two-bin instance of this algorithm by an order of magnitude. This is for the specific example of a two dimensional spin Fermi-Hubbard model. For example, we estimate that the depolarizing single qubit error rate required to implement a minimum two bin example of QEEP —with a $5\times5$ Fermi-Hubbard model and up to a precision of $10\%$ —can be reduced from 10 ^−7 to 10 ^−5 . We explore possible modifications to this protocol and propose an application, which we dub randomized quantum eigenvalue estimation problem ( rQEEP ). rQEEP outputs estimates on the fraction of eigenvalues which lie within randomly chosen bins and upper bounds the total deviation of these estimates from the true values. One use case we envision for this algorithm is resolving density of states features of local Hamiltonians. |
| first_indexed | 2024-03-11T10:52:55Z |
| format | Article |
| id | doaj.art-30aebbc7b5824022aac1bd8d7c431765 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-11T10:52:55Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-30aebbc7b5824022aac1bd8d7c4317652023-11-13T14:09:47ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125303302710.1088/1367-2630/acc26dPhase estimation of local Hamiltonians on NISQ hardwareLaura Clinton0https://orcid.org/0000-0002-4102-4741Johannes Bausch1Joel Klassen2Toby Cubitt3Phasecraft Ltd , London, United Kingdom; Department of Computer Science, University College London , London, United KingdomPhasecraft Ltd , London, United Kingdom; CQIF, DAMTP, University of Cambridge , Cambridge, United KingdomPhasecraft Ltd , London, United KingdomPhasecraft Ltd , London, United KingdomIn this work we investigate a binned version of quantum phase estimation (QPE) set out by Somma (2019 New J. Phys. 21 123025) and known as the quantum eigenvalue estimation problem ( QEEP ). Specifically, we determine whether the circuit decomposition techniques we set out in previous work, Clinton et al (2021 Nat. Commun. 12 1–10), can improve the performance of QEEP in the noisy intermediate scale quantum (NISQ) regime. To this end we adopt a physically motivated abstraction of NISQ device capabilities as in Clinton et al (2021 Nat. Commun. 12 1–10). Within this framework, we find that our techniques reduce the threshold at which it becomes possible to perform the minimum two-bin instance of this algorithm by an order of magnitude. This is for the specific example of a two dimensional spin Fermi-Hubbard model. For example, we estimate that the depolarizing single qubit error rate required to implement a minimum two bin example of QEEP —with a $5\times5$ Fermi-Hubbard model and up to a precision of $10\%$ —can be reduced from 10 ^−7 to 10 ^−5 . We explore possible modifications to this protocol and propose an application, which we dub randomized quantum eigenvalue estimation problem ( rQEEP ). rQEEP outputs estimates on the fraction of eigenvalues which lie within randomly chosen bins and upper bounds the total deviation of these estimates from the true values. One use case we envision for this algorithm is resolving density of states features of local Hamiltonians.https://doi.org/10.1088/1367-2630/acc26dquantum phase estimationquantum computingHamiltonian simulationpulse efficient compilation |
| spellingShingle | Laura Clinton Johannes Bausch Joel Klassen Toby Cubitt Phase estimation of local Hamiltonians on NISQ hardware New Journal of Physics quantum phase estimation quantum computing Hamiltonian simulation pulse efficient compilation |
| title | Phase estimation of local Hamiltonians on NISQ hardware |
| title_full | Phase estimation of local Hamiltonians on NISQ hardware |
| title_fullStr | Phase estimation of local Hamiltonians on NISQ hardware |
| title_full_unstemmed | Phase estimation of local Hamiltonians on NISQ hardware |
| title_short | Phase estimation of local Hamiltonians on NISQ hardware |
| title_sort | phase estimation of local hamiltonians on nisq hardware |
| topic | quantum phase estimation quantum computing Hamiltonian simulation pulse efficient compilation |
| url | https://doi.org/10.1088/1367-2630/acc26d |
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