Error suppression in Hamiltonian-based quantum computation using energy penalties
We consider the use of quantum error-detecting codes, together with energy penalties against leaving the code space, as a method for suppressing environmentally induced errors in Hamiltonian-based quantum computation. This method was introduced in Jordan et al. [Phys. Rev. A 74, 052322 (2006)]PLRAAN...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/98076 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0001-9475-2091 https://orcid.org/0000-0001-7598-8621 |
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| author | Bookatz, Adam D. Farhi, Edward Zhou, Leo |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Bookatz, Adam D. Farhi, Edward Zhou, Leo |
| author_sort | Bookatz, Adam D. |
| collection | MIT |
| description | We consider the use of quantum error-detecting codes, together with energy penalties against leaving the code space, as a method for suppressing environmentally induced errors in Hamiltonian-based quantum computation. This method was introduced in Jordan et al. [Phys. Rev. A 74, 052322 (2006)]PLRAAN1050-294710.1103/PhysRevA.74.052322 in the context of quantum adiabatic computation, but we consider it more generally. Specifically, we consider a computational Hamiltonian, which has been encoded using the logical qubits of a single-qubit error-detecting code, coupled to an environment of qubits by interaction terms that act one-locally on the system. Additional energy penalty terms penalize states outside of the code space. We prove that in the limit of infinitely large penalties, one-local errors are completely suppressed, and we derive some bounds for the finite penalty case. Our proof technique involves exact integration of the Schrodinger equation, making no use of master equations or their assumptions. We perform long time numerical simulations on a small (one logical qubit) computational system coupled to an environment and the results suggest that the energy penalty method achieves even greater protection than our bounds indicate. |
| first_indexed | 2024-09-23T12:10:02Z |
| format | Article |
| id | mit-1721.1/98076 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:10:02Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/980762022-10-01T08:35:45Z Error suppression in Hamiltonian-based quantum computation using energy penalties Bookatz, Adam D. Farhi, Edward Zhou, Leo Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Bookatz, Adam D. Farhi, Edward Zhou, Leo We consider the use of quantum error-detecting codes, together with energy penalties against leaving the code space, as a method for suppressing environmentally induced errors in Hamiltonian-based quantum computation. This method was introduced in Jordan et al. [Phys. Rev. A 74, 052322 (2006)]PLRAAN1050-294710.1103/PhysRevA.74.052322 in the context of quantum adiabatic computation, but we consider it more generally. Specifically, we consider a computational Hamiltonian, which has been encoded using the logical qubits of a single-qubit error-detecting code, coupled to an environment of qubits by interaction terms that act one-locally on the system. Additional energy penalty terms penalize states outside of the code space. We prove that in the limit of infinitely large penalties, one-local errors are completely suppressed, and we derive some bounds for the finite penalty case. Our proof technique involves exact integration of the Schrodinger equation, making no use of master equations or their assumptions. We perform long time numerical simulations on a small (one logical qubit) computational system coupled to an environment and the results suggest that the energy penalty method achieves even greater protection than our bounds indicate. United States. Dept. of Energy (Cooperative Research Agreement Contract DE-FG02-05ER41360) United States. Army Research Office (Grant W911NF-12-1-0486) National Science Foundation (U.S.) (Award CCF-121-8176) Massachusetts Institute of Technology. Undergraduate Research Opportunities Program 2015-08-11T16:51:55Z 2015-08-11T16:51:55Z 2015-08 2015-02 2015-08-10T22:00:10Z Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/98076 Bookatz, Adam D., Edward Farhi, and Leo Zhou. "Error suppression in Hamiltonian-based quantum computation using energy penalties." Phys. Rev. A 92, 022317 (August 2015). © 2015 American Physical Society https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0001-9475-2091 https://orcid.org/0000-0001-7598-8621 en http://dx.doi.org/10.1103/PhysRevA.92.022317 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Bookatz, Adam D. Farhi, Edward Zhou, Leo Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title | Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title_full | Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title_fullStr | Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title_full_unstemmed | Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title_short | Error suppression in Hamiltonian-based quantum computation using energy penalties |
| title_sort | error suppression in hamiltonian based quantum computation using energy penalties |
| url | http://hdl.handle.net/1721.1/98076 https://orcid.org/0000-0002-7309-8489 https://orcid.org/0000-0001-9475-2091 https://orcid.org/0000-0001-7598-8621 |
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