Universal quantum gates based on a pair of orthogonal cyclic states: Application to NMR systems
arXiv:quant-ph/0210027 · doi:10.1103/PhysRevA.67.022319
Abstract
We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In particular, geometric quantum computation may be achieved by eliminating the dynamic phase accumulated in the whole evolution. Therefore, both dynamic and geometric operations for quantum computation are workable in the present theory. Physical implementation of this set of gates is designed for NMR systems. Also interestingly, we show that a set of universal geometric quantum gates in NMR systems may be realized in one cycle by simply choosing specific parameters of the external rotating magnetic fields. In addition, we demonstrate explicitly a multiloop method to remove the dynamic phase in geometric quantum gates. Our results may provide useful information for the experimental implementation of quantum logical gates.
9 pages, language revised, the publication version
References in corpus (28)
- Mixed State Entanglement and Quantum Error Correction
- Quantum state engineering with Josephson-junction devices
- Coherent control of macroscopic quantum states in a single-Cooper-pair box
- The Physical Implementation of Quantum Computation
- Measurement of conditional phase shifts for quantum logic
- Noiseless Quantum Codes
- Reliable Quantum Computers
- Holonomic Quantum Computation
- Geometric quantum computation with NMR
- Geometric Manipulation of Trapped Ions for Quantum Computation
- Josephson-Junction Qubits with Controlled Couplings
- Preserving coherence in quantum computation by pairing quantum bits
- Quantum Manipulations of Small Josephson Junctions
- Detection of Geometric Phases in Superconducting Nanocircuits
- Implementation of universal quantum gates based on nonadiabatic geometric phases
- Universality in Quantum Computation
- Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a Nuclear Magnetic Resonance Quantum Computer
- Non-adiabatic conditional geometric phase shift with NMR
- Adiabatic quantum computation with Cooper pairs
- Efficient fault-tolerant quantum computing
- Optimal quantum codes for preventing collective amplitude damping
- Geometric phase shift in quantum computation using superconducting nanocircuits: nonadiabatic effects
- Nonadiabatic noncyclic geometric phase of a spin-1/2 particle subject to an arbitrary magnetic field
- Nonadiabatic noncyclic geometric phase and ensemble average spectrum of conductance in disordered mesoscopic rings with spin-orbit coupling
- Non-adiabatically detecting the geometric phase of the macroscopic quantum state with symmetric SQUID
- NMR C-NOT gate through Aharanov-Anandan's phase shift
- Dirac particles in a rotating magnetic field
- Geometric phases for neutral and charged particles in a time-dependent magnetic field
Cited by in corpus (45)
- Non-adiabatic holonomic quantum computation
- Unconventional geometric quantum computation
- Quantum Computing with NMR
- Plug-and-Play Approach to Non-adiabatic Geometric Quantum Gates
- Geometric quantum gates robust against stochastic control errors
- Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
- Critical Property of Geometric Phase in the Dicke Model
- Geometric phases in quantum information
- Nonadiabatic geometric quantum computation with parametrically tunable coupling
- Proposal for implementing universal superadiabatic geometric quantum gates in nitrogen-vacancy centers
- Experimental Realization of Asymmetric Phase-Covariant Quantum Cloning
- Experimental implementation of high-fidelity unconventional geometric quantum gates using NMR interferometer
- Superadiabatic Holonomic Quantum Computation in Cavity QED
- Composite pulses in NMR as non-adiabatic geometric quantum gates
- Universal, high-fidelity quantum gates based on superadiabatic, geometric phases on a solid-state spin-qubit at room temperature
- Nonadiabatic Geometric Quantum Computation Using A Single-loop Scenario
- Quantum information processing using Josephson junctions coupled through cavities
- Approach to realizing nonadiabatic geometric gates with prescribed evolution paths
- Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries
- Designing Robust Unitary Gates: Application to Concatenated Composite Pulse
- Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
- Conceptual aspects of geometric quantum computation
- Geometric Phase in Entangled Systems: A Single-Neutron Interferometer Experiment
- Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators
- Testing Bell's inequality and measuring the entanglement using superconducting nanocircuits
- Non-Adiabatic Universal Holonomic Quantum Gates Based on Abelian Holonomies
- State-independent Nonadiabatic Geometric Quantum Gates
- Nonadiabatic holonomic quantum computation based on commutation relation
- Realization of universal nonadiabatic geometric control on decoherence-free qubits in the XY model
- Universal quantum gates based on both geometric and dynamic phases in quantum dots
- Nonadiabatic geometric quantum gates with on-demand trajectories
- Robust nonadiabatic geometric quantum computation by dynamical correction
- Implementation of geometric quantum gates on microwave-driven semiconductor charge qubits
- Interplay between geometric and dynamic phases in a single spin system
- Implementing conventional and unconventional nonadiabatic geometric quantum gates via SU(2) transformations
- Decoherence induced by squeezing control errors in optical and ion trap holonomic quantum computations
- Decoherence induced by squeezing control errors in optical and ion trap holonomic quantum computations II
- Proper magnetic fields for nonadiabatic geometric quantum gates in NMR
- Nonadiabatic geometric rotation of electron spin in a quantum dot by 2Pi hyperbolic secant pulses
- Observable-geometric phases and quantum computation
- Entangling power of holonomic gates in atom-cavity systems
- iSWAP-type geometric gates induced by paths on Schmidt sphere
- Geometric and holonomic quantum computation
- Universal Non-adiabatic Holonomic Gates in Quantum Dots and Single-Molecule Magnets
- Scalable star-shape architecture for universal spin-based nonadiabatic holonomic quantum computation