Geometric and holonomic quantum computation

Abstract

Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only on the evolution paths of quantum systems, quantum gates based on them possess built-in resilience to certain kinds of errors. This review provides an introduction to the topic as well as gives an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates and how to combine them with other error-resistant techniques.

arXiv commentadded a new section "experimental realizations and gates robustness", updated the section on "Combining GQC and HQC with other quantum technologies" with 80 more references

References in corpus (237)

• Quantum Computing in the NISQ era and beyond
• Fault-tolerant quantum computation by anyons
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Cavity Optomechanics
• Surface codes: Towards practical large-scale quantum computation
• Quantum Simulation
• Quantum computational advantage using photons
• Spin-orbit interactions of light
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Introduction to Quantum Noise, Measurement and Amplification
• Decoherence Free Subspaces for Quantum Computation
• Dynamical Decoupling of Open Quantum Systems
• Noisy intermediate-scale quantum (NISQ) algorithms
• Topological quantum memory
• Dynamical suppression of decoherence in two-state quantum systems
• Ultrastrong coupling between light and matter
• Coupling Superconducting Qubits via a Cavity Bus
• Quantum Error Correction for Quantum Memories
• Atomic physics and quantum optics using superconducting circuits
• Microwave photonics with superconducting quantum circuits
• Noiseless Quantum Codes
• NMR Techniques for Quantum Control and Computation
• Quantum computing with trapped ions
• Strong quantum computational advantage using a superconducting quantum processor
• Suppressing quantum errors by scaling a surface code logical qubit
• Quantum computation with ions in thermal motion
• Shortcuts to adiabaticity: concepts, methods, and applications
• Multi-particle entanglement of hot trapped ions
• Superconducting Circuits and Quantum Information
• Holonomic Quantum Computation
• A Theory of Quantum Error-Correcting Codes
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Geometric quantum computation with NMR
• Landau-Zener-Stuckelberg interferometry
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Entanglement and quantum computation with ions in thermal motion
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• Natural and artificial atoms for quantum computation
• Josephson-Junction Qubits with Controlled Couplings
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Geometric phases for mixed states in interferometry
• Preserving coherence in quantum computation by pairing quantum bits
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• Quantum Manipulations of Small Josephson Junctions
• Quantum Decoherence
• A microfabricated surface-electrode ion trap for scalable quantum information processing
• Experimental Realization of Nonadiabatic Holonomic Quantum Computation
• Quantum state engineering on an optical transition and decoherence in a Paul trap
• Non-adiabatic holonomic quantum computation
• Superconducting Quantum Computing: A Review
• Observation of Berry's Phase in a Solid State Qubit
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Detection of Geometric Phases in Superconducting Nanocircuits
• Implementation of universal quantum gates based on nonadiabatic geometric phases
• Experimental Realization of Non-Abelian Geometric Gates
• Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit
• Geometry and non-adiabatic response in quantum and classical systems
• Kinematic approach to the mixed state geometric phase in nonunitary evolution
• Non-Abelian Berry connections for quantum computation
• Nonperturbative theory of weak pre- and post-selected measurements
• Non-adiabatic conditional geometric phase shift with NMR
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• Geometric phase in open systems
• Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces
• Unconventional geometric quantum computation
• Quantum feedback: theory, experiments, and applications
• Dynamically Error-Corrected Gates for Universal Quantum Computation
• Experimental fault-tolerant universal quantum gates with solid-state spins under ambient conditions
• Optimal quantum control using randomized benchmarking
• Geometric Quantum Computation
• Quantum computation with trapped ions in an optical cavity
• Inconsistency in the application of the adiabatic theorem
• Plug-and-Play Approach to Non-adiabatic Geometric Quantum Gates
• Holonomic Quantum Control by Coherent Optical Excitation in Diamond
• Single-loop realization of arbitrary non-adiabatic holonomic single-qubit quantum gates in a superconducting circuit
• Optical holonomic single quantum gates with a geometric spin under a zero field
• Dynamical Generation of Noiseless Quantum Subsystems
• Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates
• Qiskit Pulse: Programming Quantum Computers Through the Cloud with Pulses
• Non-Abelian phases, charge pumping, and quantum computation with Josephson junctions
• Geometric quantum computation and multi-qubit entanglement with superconducting charge qubits inside a cavity
• Quantitative conditions do not guarantee the validity of the adiabatic approximation
• Holonomic quantum computation in decoherence-free subspaces
• Experimental demonstration of the stability of Berry's phase for a spin-1/2 particle
• Universal holonomic quantum gates in decoherence-free subspace on superconducting circuits
• Robustness of non-adiabatic holonomic gates
• Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm
• Controllable coherent population transfers in superconducting qubits for quantum computing
• Experimental implementation of universal nonadiabatic geometric quantum gates in a superconducting circuit
• Robust optimal quantum gates for Josephson charge qubits
• Frictionless dynamics of Bose-Einstein condensates under fast trap variations
• Geometric phases for non-degenerate and degenerate mixed states
• Multi-bit gates for quantum computing
• Semiconductor-based Geometrical Quantum Gates
• Robustness of non-abelian holonomic quantum gates against parametric noise
• Holonomic quantum computation with neutral atoms
• Preserving qubit coherence by dynamical decoupling
• Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
• Indirect Interaction of Solid-State Qubits via Two-Dimensional Electron Gas
• Holonomic quantum control with continuous variable systems
• Generalization of geometric phase to completely positive maps
• Single-loop multiple-pulse nonadiabatic holonomic quantum gates
• Exploring the Effect of Noise on the Berry Phase
• Spin electric effects in molecular antiferromagnets
• The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
• Unconventional geometric quantum phase gates with a cavity QED system
• Topological and holonomic quantum computation based on second-order topological superconductors
• Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems
• Geometric phases in quantum information
• Single-Loop and Composite-Loop Realization of Nonadiabatic Holonomic Quantum Gates in a Decoherence-Free Subspace
• Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit
• Nonadiabatic holonomic quantum computation with dressed-state qubits
• Off-diagonal geometric phase for mixed states
• Nonadiabatic geometric quantum computation with parametrically tunable coupling
• Quantum Computation in Noiseless Subsystems with Fast Non-Abelian Holonomies
• Nonadiabatic holonomic single-qubit gates in off-resonant $\Lambda$ systems
• Experimental quantum state tomography of a solid state qubit
• Decoherence of geometric phase gates
• Coherent pulsed excitation of degenerate multistate systems: Exact analytic solutions
• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Engineering of arbitrary U(N) transformations by quantum Householder reflections
• Nonadiabatic geometric quantum computation with cat qubits via invariant-based reverse engineering
• Realization of holonomic single-qubit operations
• Scalable quantum computer with superconducting circuits in the ultrastrong coupling regime
• Fault-tolerant holonomic quantum computation
• Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers
• Mixed state geometric phases, entangled systems, and local unitary transformations
• Experimental implementation of high-fidelity unconventional geometric quantum gates using NMR interferometer
• Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces
• Nonadiabatic holonomic quantum computation with all-resonant control
• Geometric phase distributions for open quantum systems
• Holonomic quantum computation in the presence of decoherence
• Holonomic Surface Codes for Fault-Tolerant Quantum Computation
• Effect of noise on geometric logic gates for quantum computation
• Composite nonadiabatic holonomic quantum computation
• Geometric Phase and Non-Adiabatic Effects in an Electronic Harmonic Oscillator
• Control-free control: manipulating a quantum system using only a limited set of measurements
• A scheme for unconventional geometric quantum computation in cavity QED
• Robust gates for holonomic quantum computation
• Geometric phases of light: insights from fibre bundle theory
• Geometric Phase Gates with Adiabatic Control in Electron Spin Resonance
• Non-adiabatic geometrical quantum gates in semiconductor quantum dots
• Superadiabatic Holonomic Quantum Computation in Cavity QED
• Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
• Holonomic quantum gates: A semiconductor-based implementation
• Transport quantum logic gates for trapped ions
• Geometric phase shift in quantum computation using superconducting nanocircuits: nonadiabatic effects
• Composite pulses in NMR as non-adiabatic geometric quantum gates
• Correlation-induced suppression of decoherence in capacitively coupled Cooper-pair boxes
• Noncyclic geometric changes of quantum states
• Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature
• Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit
• Adiabatic Approximation for weakly open systems
• Doubly geometric quantum control
• General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation
• Holonomic Quantum Computation with Electron Spins in Quantum Dots
• Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers
• Noncyclic geometric phase and its non-Abelian generalization
• Nonadiabatic geometric quantum computation in decoherence-free subspaces based on unconventional geometric phases
• High-fidelity and Robust Geometric Quantum Gates that Outperform Dynamical Ones
• Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade
• Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling
• Adiabatic Markovian Dynamics
• Non-Abelian adiabatic geometric transformations in a cold Strontium gas
• Nonadiabatic Geometric Quantum Computation Using A Single-loop Scenario
• Measuring the Berry Phase in a Superconducting Phase Qubit by a Shortcut to Adiabaticity
• Nonadiabatic holonomic quantum computation with Rydberg superatoms
• High-fidelity geometric gate for silicon-based spin qubits
• Path-shortening realizations of nonadiabatic holonomic gates
• Geometric phase for mixed states: a differential geometric approach
• Non-abelian superconducting pumps
• Environment-assisted holonomic quantum maps
• Validity of rotating wave approximation in non-adiabatic holonomic quantum computation
• Approach to realizing nonadiabatic geometric gates with prescribed evolution paths
• Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutrit
• Coherent evolution via reservoir driven holonomy
• Fault-tolerant multiqubit geometric entangling gates using photonic cat-state qubits
• Fidelity optimization for holonomic quantum gates in dissipative environments
• Electric nonadiabatic geometric entangling gates on spin qubits
• Non-Abelian Geometric Quantum Memory with Atomic Ensemble
• Dynamical-decoupling-protected nonadiabatic holonomic quantum computation
• Quantum state preparation of a mechanical resonator using an optomechanical geometric phase
• Super-robust nonadiabatic geometric quantum control
• Implementation of holonomic quantum computation through engineering and manipulating environment
• Geometric quantum gates with superconducting qubits
• Topological Features in Ion Trap Holonomic Computation
• Stability of holonomic quantum computations
• Superrobust Geometric Control of a Superconducting Circuit
• Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries
• Universal quantum computation by holonomic and nonlocal gates with imperfections
• Non-Abelian geometric phases in a system of coupled quantum bits
• Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
• Robustness against parametric noise of non ideal holonomic gates
• Conceptual aspects of geometric quantum computation
• Non-Abelian geometric phases in ground state Josephson devices
• Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field
• Higher-order exceptional point in a blue-detuned non-Hermitian cavity optomechanical system
• Holonomic quantum computation in subsystems
• Quantum holonomies with Josephson-junction devices
• Holonomic Quantum Computing Based on the Stark Effect
• All-electric qubit control in heavy hole quantum dots via non-Abelian geometric phases
• Non-adiabatic geometric quantum computation with trapped ions
• Geometric quantum computation using fictitious spin- 1/2 subspaces of strongly dipolar coupled nuclear spins
• Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators
• NMR C-NOT gate through Aharanov-Anandan's phase shift
• The non-Abelian geometric phase in the diamond nitrogen-vacancy center
• Refocusing schemes for holonomic quantum computation in presence of dissipation
• Realizing nonadiabatic holonomic quantum computation beyond the three-level setting
• Decoherence-induced geometric phase in a multilevel atomic system
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Ground-state geometric quantum computing in superconducting systems
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
• Environmental noise reduction for holonomic quantum gates
• Control aspects of holonomic quantum computation
• Realization of a holonomic quantum computer in a chain of three-level systems
• A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise
• Geometric Manipulation of Ensembles of Atoms on Atom Chip for Quantum Computation
• Mathematical Foundations of Holonomic Quantum Computer
• Leakage Suppression for Holonomic Quantum Gates
• Universal non-adiabatic geometric manipulation of pseudo-spin charge qubits
• Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model
• Universal quantum computation and quantum error correction using discrete holonomies
• Mixed state non-Abelian holonomy for subsystems
• Dark path holonomic qudit computation
• Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators
• Geometrical phases for the G(4,2) Grassmannian manifold
• Robust Hadamard gate for optical and ion trap holonomic quantum computers
• Geometric energy transfer in a Stückelberg interferometer of two parametrically coupled mechanical modes
• Ultrafast geometric manipulation of electron spin and detection of the geometric phase via Faraday rotation spectroscopy
• Implementation of holonomic quantum gates by an isospectral deformation of an Ising dimer chain
• Spin-electric Berry phase shift in triangular molecular magnets
• Decoherence induced by squeezing control errors in optical and ion trap holonomic quantum computations II
• Decoherence induced by squeezing control errors in optical and ion trap holonomic quantum computations
• Suppressing the geometric dephasing of Berry phase by using modified dynamical decoupling sequences
• Holonomy for Quantum Channels