Single-loop multiple-pulse nonadiabatic holonomic quantum gates

Abstract

Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. {\bf 14}, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\Lambda$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\Lambda$-coupling structure, by utilizing carefully chosen laser pulses.

Some amendments; journal reference added

References in corpus (20)

• Holonomic Quantum Computation
• Experimental Realization of Nonadiabatic Holonomic Quantum Computation
• Non-adiabatic holonomic quantum computation
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Experimental Realization of Non-Abelian Geometric Gates
• Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Quantum Holonomies for Quantum Computing
• Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits
• Robustness of non-adiabatic holonomic gates
• Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping
• Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies
• Experimental quantum state tomography of a solid state qubit
• Nonadiabatic holonomic single-qubit gates in off-resonant $\Lambda$ systems
• Nonadiabatic holonomic quantum computation with all-resonant control
• On the stability of quantum holonomic gates
• Noncyclic geometric changes of quantum states
• Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers
• Validity of rotating wave approximation in non-adiabatic holonomic quantum computation
• Realization of a holonomic quantum computer in a chain of three-level systems

Cited by in corpus (50)

• Single-loop realization of arbitrary non-adiabatic holonomic single-qubit quantum gates in a superconducting circuit
• Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
• Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace
• Nonadiabatic holonomic quantum computation with dressed-state qubits
• Nonadiabatic geometric quantum computation with parametrically tunable coupling
• Implementing universal nonadiabatic holonomic quantum gates with transmons
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates\\ with Optimal Control in a Trapped Ion
• Composite nonadiabatic holonomic quantum computation
• Fast holonomic quantum computation on superconducting circuits with optimal control
• General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation
• Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade
• Robust and Fast Holonomic Quantum Gates with Encoding on Superconducting Circuits
• Nonadiabatic holonomic quantum computation with Rydberg superatoms
• Path-shortening realizations of nonadiabatic holonomic gates
• Fast holonomic quantum computation based on solid-state spins with all-optical control
• Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutrit
• Nonadiabatic holonomic multiqubit controlled gates
• Dynamical-decoupling-protected nonadiabatic holonomic quantum computation
• Robust paths to realize nonadiabatic holonomic gates
• Composite Short-path Nonadiabatic Holonomic Quantum Gates
• Dynamically Corrected Nonadiabatic Holonomic Quantum Gates
• Superrobust Geometric Control of a Superconducting Circuit
• Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion
• Realizing nonadiabatic holonomic quantum computation beyond the three-level setting
• High-fidelity geometric quantum gates with short paths on superconducting circuits
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
• Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations
• Ultrafast Holonomic Quantum Gates
• Accelerated super-robust nonadiabatic holonomic quantum gates
• Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice
• Geometric quantum gates via dark paths in Rydberg atoms
• Nonadiabatic holonomic quantum computation based on commutation relation
• Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity
• Nonadiabatic Holonomic Quantum Computation via Path Optimization
• Dark path holonomic qudit computation
• Non-adiabatic holonomic quantum operations in continuous variable systems
• Holonomic swap and controlled-swap gates of neutral atoms via selective Rydberg pumping
• Robust pulses for high fidelity non-adiabatic geometric gate operations in an off-resonant three-level system
• One-step implementation of nonadiabatic geometric fSim gate in superconducting circuits
• Robust Nonadiabatic Holonomic Quantum Gates on Decoherence-Protected Qubits
• Nonadiabatic braiding of Majorana modes
• Parallel transport in rotating frames and projective holonomic quantum computation
• Time optimal holonomic quantum computation
• Robustness Enhancement of Universal Noncyclic Geometric Gates via Evolution Optimization
• Speeding up adiabatic holonomic quantum gates via $\pi$-pulse modulation
• Mitigation of systematic amplitude error in nonadiabatic holonomic operations
• Geometric and holonomic quantum computation
• Separation of quantum time evolution into holonomic and dynamical parts