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 (32)

• Unpaired Majorana fermions in quantum wires
• Cold bosonic atoms in optical lattices
• Quantum information with Rydberg atoms
• Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
• Fast quantum gates for neutral atoms
• 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
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Quantum Simulators: Architectures and Opportunities
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
• Non-Hermitian Linear Response Theory
• Digitized-counterdiabatic quantum approximate optimization algorithm
• Quasi-Topological Phases of Matter and Topological Protection
• Poor man's topological quantum gate based on the Su-Schrieffer-Heeger model
• Fast adiabatic evolution by oscillating initial Hamiltonians
• Accelerating adiabatic protocols for entangling two qubits in circuit QED
• Ultrafast creation of overlapping Rydberg electrons in an atomic BEC and Mott-insulator lattice
• 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
• Counterdiabatic Driving with Performance Guarantees
• Universal Counterdiabatic Driving
• A numerical approach for calculating exact non-adiabatic terms in quantum dynamics
• Calibrating quantum gates up to 52 qubits in a superconducting processor
• Topological charge pumping with subwavelength Raman lattices
• 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