Optimal arbitrarily accurate composite pulse sequences
Implementing a single-qubit unitary is often hampered by imperfect control. Systematic amplitude errors ε, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88731 https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6211-982X https://orcid.org/0000-0001-9614-2836 |
| _version_ | 1826200447130533888 |
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| author | Low, Guang Hao Yoder, Theodore James Chuang, Isaac L. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Low, Guang Hao Yoder, Theodore James Chuang, Isaac L. |
| author_sort | Low, Guang Hao |
| collection | MIT |
| description | Implementing a single-qubit unitary is often hampered by imperfect control. Systematic amplitude errors ε, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of L primitive π or 2π rotations that suppress such errors to arbitrary order O(ε[superscript n]) on arbitrary initial states. Optimality is demonstrated by proving an L = O(n) lower bound and saturating it with L = 2n solutions. Closed-form solutions for arbitrary rotation angles are given for n = 1,2,3,4. Perturbative solutions for any n are proven for small angles, while arbitrary angle solutions are obtained by analytic continuation up to n = 12. The derivation proceeds by a novel algebraic and nonrecursive approach, in which finding amplitude error correcting sequences can be reduced to solving polynomial equations. |
| first_indexed | 2024-09-23T11:36:36Z |
| format | Article |
| id | mit-1721.1/88731 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:36:36Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/887312022-10-01T04:45:15Z Optimal arbitrarily accurate composite pulse sequences Low, Guang Hao Yoder, Theodore James Chuang, Isaac L. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Physics Low, Guang Hao Yoder, Theodore James Chuang, Isaac L. Implementing a single-qubit unitary is often hampered by imperfect control. Systematic amplitude errors ε, caused by incorrect duration or strength of a pulse, are an especially common problem. But a sequence of imperfect pulses can provide a better implementation of a desired operation, as compared to a single primitive pulse. We find optimal pulse sequences consisting of L primitive π or 2π rotations that suppress such errors to arbitrary order O(ε[superscript n]) on arbitrary initial states. Optimality is demonstrated by proving an L = O(n) lower bound and saturating it with L = 2n solutions. Closed-form solutions for arbitrary rotation angles are given for n = 1,2,3,4. Perturbative solutions for any n are proven for small angles, while arbitrary angle solutions are obtained by analytic continuation up to n = 12. The derivation proceeds by a novel algebraic and nonrecursive approach, in which finding amplitude error correcting sequences can be reduced to solving polynomial equations. National Science Foundation (U.S.). Center for Ultracold Atoms (1125846) National Science Foundation (U.S.) (RQCC 1111337) National Science Foundation (U.S.) (iQuISE IGERT) United States. Intelligence Advanced Research Projects Activity (QCS ORAQL project) 2014-08-15T17:44:39Z 2014-08-15T17:44:39Z 2014-02 2014-01 Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/88731 Low, Guang Hao, Theodore J. Yoder, and Isaac L. Chuang. “Optimal Arbitrarily Accurate Composite Pulse Sequences.” Phys. Rev. A 89, no. 2 (February 2014). © 2014 American Physical Society https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6211-982X https://orcid.org/0000-0001-9614-2836 en_US http://dx.doi.org/10.1103/PhysRevA.89.022341 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. application/pdf American Physical Society American Physical Society |
| spellingShingle | Low, Guang Hao Yoder, Theodore James Chuang, Isaac L. Optimal arbitrarily accurate composite pulse sequences |
| title | Optimal arbitrarily accurate composite pulse sequences |
| title_full | Optimal arbitrarily accurate composite pulse sequences |
| title_fullStr | Optimal arbitrarily accurate composite pulse sequences |
| title_full_unstemmed | Optimal arbitrarily accurate composite pulse sequences |
| title_short | Optimal arbitrarily accurate composite pulse sequences |
| title_sort | optimal arbitrarily accurate composite pulse sequences |
| url | http://hdl.handle.net/1721.1/88731 https://orcid.org/0000-0001-7296-523X https://orcid.org/0000-0002-6211-982X https://orcid.org/0000-0001-9614-2836 |
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