Geometric Quantum Gates of Non-closed Paths Under Counterdiabatic Driving

Abstract

Non-adiabatic and non-closed evolutionary paths play a significant role in the fidelity of quantum gates. We propose a high-fidelity quantum control framework based on the quasi-topological number (${\nu }_{\text{qua}}$), which extends the traditional Chern number to characterize geometric responses in non-closed paths. By introducing a counterdiabatic gauge potential (AGP) that dynamically suppresses non-adiabatic transitions and reconstructs path curvature, we demonstrate that ${\nu }_{\text{qua}}$ -a relative homotopy invariant of compact manifolds in parameter space-quantifies the robustness of geometric phases during open-path quantum evolution. This integer invariant ensures gauge-invariant suppression of decoherence errors arising from dynamical phase coupling. By introducing nonlinear parametric ring paths, we address the defects caused by intermediate states in the Rydberg atomic system. Numerical simulations in the Kitaev superconducting chain and 2D transverse-field Ising model confirm that our protocol achieves quantum gate fidelity exceeding $\mathcal{F}>0.9999$. We bridges geometric quantum control with topological protection, offering a universal approach to noise-resistant quantum computing.

References in corpus (18)

• Strong quantum computational advantage using a superconducting quantum processor
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Suppressing quantum errors by scaling a surface code logical qubit
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Digitized-counterdiabatic quantum approximate optimization algorithm
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Accelerating adiabatic protocols for entangling two qubits in circuit QED
• Floquet engineering topological Dirac bands
• Efficient Paths for Local Counterdiabatic Driving
• Counterdiabatic Driving for Periodically Driven Systems
• Optimizing Counterdiabaticity by Variational Quantum Circuits
• Observation of dynamical topology in 1D
• Universal Counterdiabatic Driving
• Counterdiabatic Driving with Performance Guarantees
• A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
• Topological charge pumping with subwavelength Raman lattices
• Calibrating quantum gates up to 52 qubits in a superconducting processor
• Robust Nonadiabatic Holonomic Quantum Gates on Decoherence-Protected Qubits

Cited by in corpus (1)

• Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation