Geometric phases in quantum information

Abstract

The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by focusing on three main themes: the use of GPs to perform robust quantum computation, the development of GP concepts for mixed quantum states, and the discovery of a new type of topological phases for entangled quantum systems. We delineate the theoretical development as well as describe recent experiments related to GPs in the context of quantum information.

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Cited by in corpus (46)

• Entanglement generation in superconducting qubits using holonomic operations
• Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform
• Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers
• Composite nonadiabatic holonomic quantum computation
• Nonadiabatic noncyclic geometric quantum computation in Rydberg atoms
• Demonstration of an All-Microwave Controlled-Phase Gate between Far Detuned Qubits
• Doubly geometric quantum control
• High-fidelity geometric gate for silicon-based spin qubits
• Single-atom verification of the noise-resilient and fast characteristics of universal nonadiabatic noncyclic geometric quantum gates
• Superrobust Geometric Control of a Superconducting Circuit
• Quantumness and memory of one qubit in a dissipative cavity under classical control
• Accelerating geometric quantum gates through non-cyclic evolution and shortcut to adiabaticity
• Topological Uhlmann phase transitions for a spin-j particle in a magnetic field
• Geometric phases and the Sagnac effect: Foundational aspects and sensing applications
• All-microwave manipulation of superconducting qubits with a fixed-frequency transmon coupler
• Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
• Experimental observation of fractional topological phases with photonic qudits
• Investigation of the Aharonov-Bohm and Aharonov-Casher Topological Phases for Quantum Entangled States in 2+1 Dimensions
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness
• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
• Geometric phase of light-induced conical intersections: Adiabatic time-dependent approach
• Non-Abelian Geometric Phases Carried by the Spin Fluctuation Tensor
• Fast high-fidelity geometric gates for singlet-triplet qubits
• Optimizing nonadiabatic geometric quantum gates against off-resonance error by dynamical correction in a silicon-based spin qubit
• Coupling two charge qubits via a superconducting resonator operating in the resonant and dispersive regimes
• Implementation of geometric quantum gates on microwave-driven semiconductor charge qubits
• Geometric phase corrected by initial system-environment correlations
• Geometric Phase in Quantum Synchronization
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• Mixed state geometric phase for neutrino oscillations
• Optical control of the complex phase of a quantum ground state amplitude
• On the geometric phases in entangled states
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• Study of geometric phase using classical coupled oscillators
• Intrinsic bounds of a two-qudit random evolution
• Redshift as a stretching factor in rotating graphene wormholes
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• The Aharonov Casher phase of a bipartite entanglement pair traversing a quantum square ring
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• Robust composite two-qubit gates for silicon-based spin qubits
• Two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner
• Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond
• Geometric and holonomic quantum computation