Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit

Chao Song,Keqiang Huang,Xiaobo Zhu,Da Xu,Kai Xu,Libo Zhang,Wuxin Liu,Pengfei Zhang,Shi-Biao Zheng,H Wang,Dongning Zheng,Qiujiang Guo,Hui Deng

doi:10.1038/s41467-017-01156-5

Abstract

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a paradigm, where quantum logic operations are realized through geometric phase manipulation that has some intrinsic noise-resilient advantages and may enable simplified implementation of multi-qubit gates compared to the dynamical approach. Here we report observation of a continuous-variable geometric phase and demonstrate a quantum gate protocol based on this phase in a superconducting circuit, where five qubits are controllably coupled to a resonator. Our geometric approach allows for one-step implementation of n-qubit controlled-phase gates, which represents a remarkable advantage compared to gate decomposition methods, where the number of required steps dramatically increases with n. Following this approach, we realize these gates with n up to 4, verifying the high efficiency of this geometric manipulation for quantum computation.

Highlights

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect
A quantum system, when undergoing a cyclic evolution in the quantum state space, will acquire a geometric phase that is determined by the path traversed by the system[1, 2]
In a recent experiment[20], the adiabatic geometric phase of the quantized electromagnetic field stored in a resonator was measured in a circuit quantum electrodynamics (QED) device, where the resonator was dispersively coupled to a qubit and driven by a microwave pulse whose amplitude and phase were slowly and cyclically changed

Summary

Introduction

Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. The state of the resonator is nonadiabatically displaced with a constant-amplitude microwave drive along a circuit in phase space conditional on the state of the qubit coupled to the resonator, and the geometric phase associated with this cyclic evolution is measured by the qubit’s Ramsey interference experiment. Using this phase, we realize the two-qubit controlledphase (CZ) gate, the three-qubit controlled–controlled-phase (CCZ) gate—the equivalent of the Toffoli gate under a change of a

Methods

Results

Conclusion