Composite nonadiabatic holonomic quantum computation

Abstract

Nonadiabatic holonomic quantum computation has robust feature in suppressing control errors because of its holonomic feature. However, this kind of robust feature is challenged since the usual way of realizing nonadiabatic holonomic gates introduces errors due to systematic errors in the control parameters. To resolve this problem, we here propose a composite scheme to realize nonadiabatic holonomic gates. Our scheme can suppress systematic errors while preserving holonomic robustness. It is particularly useful when the evolution period is shorter than the coherence time. We further show that our composite scheme can be protected by decoherence-free subspaces. In this case, the strengthened robust feature of our composite gates and the coherence stabilization virtue of decoherence-free subspaces are combined.

Realization of Deutsch–Jozsa Algorithm in Rydberg Atoms by Composite Nonadiabatic Holonomic Quantum Computation with Strong Robustness Against Systematic Errors

“…The fundamental theory of the scheme of composite NHQC to realize the target gate in Equation (4) is that decomposes the target gate into N identical sub‐gate in the form of . [ 42,51,93 ] Compared with the single‐loop NHQC, as shown in Figure 1b, the specific operations of composite NHQC in each sub‐gate divide the whole path of sub‐gate into two parts where the phase of first part is ϕ 1 and the second part is which result in a sub‐gate . Then, repeating these two operations N times, one can realize the total unitary operation .…”

“…The early proposals of GQC, based on adiabatic Abelian [33] or adiabatic non-Abelian geometric phases, [34][35][36][37] always suffer from the detrimental influence of decoherence due to slow operations. [38,39] To deal with this problem, nonadiabatic geometric quantum computation (NGQC) [40][41][42] and nonadiabatic holonomic quantum computation (NHQC), [43][44][45][46][47] based on nonadiabatic Abelian geometric phases [48][49][50] and nonadiabatic non-Abelian geometric phases, [21,35,44,51] respectively, have been proposed. However, in most cases, fast operations generalized by the general NGQC and NHQC cannot work better than the usual dynamic gates in resisting systematic errors.…”

Nonadiabatic holonomic quantum computation with atom-cavity system

“…[12,13] 以来, 非绝 热和乐量子计算在理论和实验两方面都有了很大的进 展. 基于各类不同的量子系统, 人们提出了非绝热和乐 [21,23] 、单路径多脉冲方案 [27] 和复合门方案 [28] , 并把 无退相干子空间的非绝热和乐量子计算推广到了无噪 声子体系 [17] . 特别是, 一步实现方案简化了单比特门的 操作, 使得原方案中需要通过结合两个不对易的π旋转 门而实现任意单比特门的操作简化为通过一步操作即 可实现.…”

One‐Step Implementation of N‐Qubit Nonadiabatic Holonomic Quantum Gates with Superconducting Qubits via Inverse Hamiltonian Engineering

“…In recent researches, it is indicated that, quantum holonomy can also arise in nonadiabatic unitary evolution with certain conditions. By designing nonadiabatic unitary evolution, a lot of protocols have been proposed for realizing the nonadiabatic holonomic quantum computation, which have shown good robustness against decoherence. Moreover, many novel methods and techniques for precisely designing and controlling the dynamics of system, such as shortcuts to adiabaticity, optimal control theory, inverse Hamiltonian engineering, and their combinations, have been exploited in obtaining holonomy, which make the performance of the quantum gates further improved.…”