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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
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 |
| Summary: | 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. |
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