Minimal nonorthogonal gate decomposition for qubits with limited control

Zhang, Xiao-Ming1,2,3,4; Li, Jianan1,2; Wang, Xin3,4; Yung, Man-Hong1,2,5,6

2019-05-24

10.1103/PhysRevA.99.052339

PHYSICAL REVIEW A   影响因子和分区

2469-9926

2469-9934

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.

SCI ; EI

英语

第一

Science, Technology and Innovation Commission of Shenzhen Municipality[JCYJ20170412152620376] ; Science, Technology and Innovation Commission of Shenzhen Municipality[JCYJ20170817105046702] ; Science, Technology and Innovation Commission of Shenzhen Municipality[ZDSYS201703031659262]

Optics ; Physics

Optics ; Physics, Atomic, Molecular & Chemical

WOS:000469017100003

AMER PHYSICAL SOC

20192407029727

Control theory ; Quantum optics ; Semiconductor quantum dots

Semiconductor Devices and Integrated Circuits:714.2 ; Control Systems:731.1 ; Light/Optics:741.1

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
3.City Univ Hong Kong, Dept Phys, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
4.City Univ Hong Kong, Shenzhen Res Inst, Shenzhen 518057, Guangdong, Peoples R China
5.Southern Univ Sci & Technol, Shenzhen Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
6.Cent Res Inst, Huawei Technol, Shenzhen 518129, Peoples R China

Zhang, Xiao-Ming,Li, Jianan,Wang, Xin,et al. Minimal nonorthogonal gate decomposition for qubits with limited control[J]. PHYSICAL REVIEW A,2019,99(5).

Zhang, Xiao-Ming,Li, Jianan,Wang, Xin,&Yung, Man-Hong.(2019).Minimal nonorthogonal gate decomposition for qubits with limited control.PHYSICAL REVIEW A,99(5).

Zhang, Xiao-Ming,et al."Minimal nonorthogonal gate decomposition for qubits with limited control".PHYSICAL REVIEW A 99.5(2019).