电路量子电动力学中基于超绝热捷径的控制相位门实现

Implementation of controlled phase gate based on superadiabatic shortcut in circuit quantum electrodynamics

针对绝热算法在系统演化过程中需要较长操作时间的问题,本文提出了电路量子电动力学系统中基于超绝热捷径的两量子比特控制相位门的快速制备方案.首先将量子比特的能级进行编码,针对不同初始态分类讨论,获得系统的有效哈密顿量.通过反绝热驱动,推导出系统有效哈密顿量的修正项,以抑制不同本征态之间不必要的跃迁,从而获得了高保真度的基于超绝热捷径控制相位门.数值模拟验证了本方案的有效性,最终保真度为0.991.所提方案可以加速演化,并且比绝热通道更有效.此外,本方案对谐振器的衰减和超导量子比特的退相干具有鲁棒性.通过对谐振腔的泄漏、量子比特的自发辐射和退相位的影响分析,得到的系统最终保真度始终保持在0.984以上.

With high speed and big storage power,quantum computer has received increasing attention.The operation on the quantum computer can be composed of several single-bit and multi-bit quantum logic gates,among which the controlled phase gate is one of the essential two-qubit logic gates.Usually,the quantum gate is realized in a real physical system,and the circuit quantum electrodynamics system(QED) has become a promising candidate due to its long coherent time,easily coupled with other physical system and scaled up to large scale.In this work,we propose a scheme to fast implement a two-qubit controlled phase gate based on the circuit QED by using the superadiabatic-based shortcut,in order to solve the problem that the adiabatic algorithm needs a long time in the process of system evolution.Here,a coding strategy is first designed for the circuit QED system and the two transmon qubits,and the effective Hamiltonian of the system is then presented by dividing different initial states in the rotating-wave approximation.By using the superadiabatic-based shortcut algorithm for two iterations,a correction term in the same form as the system effective Hamiltonian is obtained through anti-diabatic driving,so that the effective Hamiltonian can suppress unwanted transitions between different instantaneous eigenstates.According to the evolution path,the appropriate boundary conditions are also obtained to complete the preparation of the controlled phase gate.The numerical simulation results show the availability of the proposed scheme,that is,the-|11> state can be obtained by system evolution when the initial state is |11>,while the system does not change at all when the other initial states are prepared.Furthermore,the controlled phase gate with high-fidelity can be obtained.It is shown that the fidelity of the controlled phase gate is stable and greater than 0.991 when the evolution time is greater than0.7t/tf.In addition,the proposed scheme can accelerate the evolution and is robust to decoherence.By the resonator decay and the spontaneous emission and dephasing of qubit,the final fidelity of the controlled phase gate is greater than 0.984.Since the controlled phase gate does not need additional parameters,the propsoed scheme is feasible in experiment.