4.6 Article

Minimal nonorthogonal gate decomposition for qubits with limited control

期刊

PHYSICAL REVIEW A
卷 99, 期 5, 页码 -

出版社

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.99.052339

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资金

  1. National Natural Science Foundation of China [11875160, 11604277, 11874312]
  2. NSFC Guangdong Joint Fund [U1801661]
  3. Guangdong Innovative and Entrepreneurial Research Team Program [2016ZT06D348]
  4. Key RAMP
  5. D Program of Guangdong province [2018B030326001]
  6. Research Grants Council of the Hong Kong Special Administrative Region, China [CityU 21300116, CityU 11303617, CityU 11304018]
  7. Natural Science Foundation of Guangdong Province [2017B030308003]
  8. Science, Technology and Innovation Commission of Shenzhen Municipality [JCYJ20170412152620376, JCYJ20170817105046702, ZDSYS201703031659262]

向作者/读者索取更多资源

In quantum control theory, a question of fundamental and practical interest is how an arbitrary unitary transformation can be decomposed into a minimum number of elementary rotations for implementation, subject to various physical constraints. Examples include the singlet-triplet (ST) and exchange-only (EO) qubits in quantum-dot systems, and gate construction in the Solovay-Kitaev algorithm. For two important scenarios, we present complete solutions to the problems of optimal decomposition of single-qubit unitary gates with non-orthogonal rotations. For each unitary gate, the criteria for determining the minimal number of pieces is given, the explicit gate construction procedure, as well as a computer code for practical uses. Our results include an analytic explanation to the four-gate decomposition of EO qubits, previously determined numerically by Divincenzo et al. [Nature (London) 408, 339 (2000)]. Furthermore, compared with the approaches of Ramon sequence and its variant [Phys. Rev. Lett. 118, 216802 (2017)], our method can reduce about 50% of gate time for ST qubits. Finally, our approach can be extended to solve the problem of optimal control of topological qubits, where gate construction is achieved through the braiding operations.

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