Low-depth quantum state preparation

Zhang, Xiao-Ming1,2; Yung, Man-Hong3,4,5; Yuan, Xiao1

2021-12-21

10.1103/PhysRevResearch.3.043200

PHYSICAL REVIEW RESEARCH   影响因子和分区

2643-1564

A crucial subroutine in quantum computing is to load the classical data of N complex numbers into the amplitude of a superposed n = [log(2) N]-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least O(N) constant weight operations. However, the proof assumes that only n qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with O(n(2)) circuit depth to encode any N complex numbers using only single-and two-qubit gates, and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with O(N-2) ancillary qubits, O(n(2)) circuit depth, and O(n(2)) average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits, and at most O(n) qubits are entangled. We also prove a fundamental lower bound Omega(n) for the minimum circuit depth and runtime with an arbitrary number of ancillary qubits, aligning with our scheme with O(n(2)). The algorithms are expected to have wide applications in both near-term and universal quantum computing.

ESCI ; EI

英语

通讯

Open Project of Shenzhen Institute of Quantum Science and Engineering[SIQSE202008] ; Natural Science Foundation of Guangdong Province[2017B030308003] ; Key R&D Program of Guangdong province[2018B030326001] ; Science,Technology and Innovation Commission of Shenzhen Municipality["JCYJ20170412152620376","JCYJ20170817105046702","KYTDPT20181011104202253"] ; National Natural Science Foundation of China[11875160,"U1801661"] ; Economy, Trade and Information Commission of Shenzhen Municipality[201901161512] ; Guangdong Provincial Key Laboratory[2019B121203002]

Physics

Physics, Multidisciplinary

WOS:000734834100008

AMER PHYSICAL SOC

20220211453055

Quantum entanglement ; Quantum optics

Light, Optics and Optical Devices:741 ; Light/Optics:741.1 ; Nanotechnology:761 ; Quantum Theory; Quantum Mechanics:931.4

Web of Science

1.Peking Univ, Ctr Frontiers Comp Studies, Dept Comp Sci, Beijing 100871, Peoples R China
2.City Univ Hong Kong, Dept Phys, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China
3.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
4.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
5.Southern Univ Sci & Technol, Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China

Zhang, Xiao-Ming,Yung, Man-Hong,Yuan, Xiao. Low-depth quantum state preparation[J]. PHYSICAL REVIEW RESEARCH,2021,3(4).

Zhang, Xiao-Ming,Yung, Man-Hong,&Yuan, Xiao.(2021).Low-depth quantum state preparation.PHYSICAL REVIEW RESEARCH,3(4).

Zhang, Xiao-Ming,et al."Low-depth quantum state preparation".PHYSICAL REVIEW RESEARCH 3.4(2021).