Non-Abelian holonomic transformation in the presence of classical noise

Abstract

It is proposed that high-speed universal quantum gates can be realized by using non-Abelian holonomic transformation. A cyclic evolution path which brings the system periodically back to a degenerate qubit subspace is crucial to holonomic quantum computing. The cyclic nature and the resulting gate operations are fully dependent on the precise control of driving parameters, such as the modulated envelop function of Rabi frequency and the control phases. We investigate the effects of fluctuations in these driving parameters on the transformation fidelity of a universal set of single-qubit quantum gates. We compare the damage effects from different noise sources and determine the "sweet spots" in the driving parameter space. The nonadiabatic non-Abelian quantum gate is found to be more susceptible to classical noises on the envelop function than that on the control phases. We also extend our study to a two-qubit quantum gate.

7 pages, 3 figures

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Cited by in corpus (21)

• Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces
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• Super-robust nonadiabatic geometric quantum control
• Dynamically Corrected Nonadiabatic Holonomic Quantum Gates
• Superrobust Geometric Control of a Superconducting Circuit
• Nonadiabatic geometric quantum computation with optimal control on superconducting circuits
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion
• Rabi-error and Blockade-error-resilient All-Geometric Rydberg Quantum Gates
• Universal perspective on nonadiabatic quantum control
• Geometric quantum gates via dark paths in Rydberg atoms
• Shortcut Scheme for One-Step Implementation of a Three-Qubit Nonadiabatic Holonomic Gate
• Leakage Suppression for Holonomic Quantum Gates
• Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity
• Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations
• Universal quantum control with dynamical correction
• Error-Resilient Floquet Geometric Quantum Computation
• Floquet geometric entangling gates in ground-state manifolds of Rydberg atoms
• Universal quantum control over Majorana zero modes
• Suppressing classical noise in the accelerated geometric phase gate by optimized dynamical decoupling
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations