## Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation

We study two-qubit circuits over the Clifford+CS gate set which consists of Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes with magic state distillation. However, since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is desirable to construct circuits that use few CS gates. In the present paper, we introduce an algorithm to construct optimal circuits for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and efficiently produces a Clifford+CS circuit for U using the least possible number of CS gates. Because our algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for the operator. We give a formal description of these normal forms as walks over certain graphs and use this description to derive an asymptotic lower bound of 5log(1/epsilon)+O(1) on the number CS gates required to epsilon-approximate any 4x4 unitary matrix.

Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation (PlanQC2020.pptx) | 2.84MiB |

#### Sun 19 Jan

15:35 - 15:55Talk | Andrew N. GlaudellUniversity of Maryland, Neil Julien RossDalhousie University, Jacob M. TaylorUniversity of Maryland Pre-print Media Attached File Attached | |||||||||||||||||||||||||||||||||||||||||

15:55 - 16:15Talk | Yu ZhangUniversity of Science and Technology of China, Haowei DengUniversity of Science and Technology of China, Quanxi LiUniversity of Science and Technology of China Pre-print Media Attached | |||||||||||||||||||||||||||||||||||||||||

16:15 - 16:35Talk | Xiang FuInstitute for Quantum Information & State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Jintao YuState Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, China, Xing SuCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha, China, Hanru JiangCenter for Quantum Computing, Peng Cheng Laboratory, Shenzhen, China, Hua WuShanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China, Dong ChenDepartment of Computing Science, College of Computer, National University of Defense Technology, Changsha, China, Fucheng ChengCenter for Quantum Computing, Peng Cheng Laboratory, Shenzhen, China, Xi DengCenter for Quantum Computing, Peng Cheng Laboratory, Shenzhen, China, Jinrong ZhangCenter for Quantum Computing, Peng Cheng Laboratory, Shenzhen, China, Lei JinSchool of Information Engineering, Zhengzhou University, Zhengzhou, China, Yihang YangSchool of Information Engineering, Zhengzhou University, Zhengzhou, China, Le XuSchool of Information Engineering, Zhengzhou University, Zhengzhou, China, Chunchao HuSchool of Information Engineering, Zhengzhou University, Zhengzhou, China, Anqi HuangInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Guangyao HuangInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Xiaogang QiangInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Mingtang DengInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Ping XuInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Wanwei LiuNational University of Defense Technology, Yuxin DengEast China Normal University, Junjie WuInstitute for Quantum Information & State Key Laboratory of High-Performance Computing, College of Computer, National University of Defense Technology, Changsha, China, Yuan FengCentre for Quantum Software and Information, University of Technology Sydney, Australia File Attached |