We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
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.
A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multiloop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum gates. More intriguingly, we here illustrate in detail how to use a special single-loop method to remove the dynamical phase and thus to construct a set of universal quantum gates based on the nonadiabatic geometric phase shift. The present scheme is applicable to NMR systems and may be feasible in other physical systems.
Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, which greatly shortens the gate time. And also, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency error and qubit frequency shift-induced error, compared to the conventional dynamical gates, by using the randomized benchmarking method. Moreover, this scheme can be utilized to construct two-qubit geometric operations, while the generation of the maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.
A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance (NMR) under adiabatic conditions. However, in quantum computation, everything must be completed within the decoherence time. The adiabatic condition makes any fast conditional Berry phase (cyclic adiabatic geometric phase) shift gate impossible. Here we show that by using a newly designed sequence of simple operations with an additional vertical magnetic field, the conditional geometric phase shift gate can be run nonadiabatically. Therefore geometric quantum computation can be done at the same rate as usual quantum computation.
Recently, geometric phases, which is fault tolerate to certain errors intrinsically due to its geometric property, are getting considerable attention in quantum computing theoretically. So far, only one experiment about adiabatic geometric gate with NMR through Berry phase has been reported. However, there are two drawbacks in it. First, the adiabatic condition of Berry phase makes such gate very slowly. Second, the extra operation to eliminate the dynamic phase. As we know, geometric phase can exist both adiabatic(Berry phase) and nonadiabatic(Aharonov-Anandan phase). In this letter, we reports the first experimental realization of nonadiabatic geometric gate with NMR through conditional-AA phase. In our experiment the gates can be made faster and more easily, and the two drawbacks mentioned above are removed.
Quantum gates based on geometric phases possess intrinsic noise-resilience features and attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, significantly shortening the gate time. Moreover, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency and the qubit frequency shift-induced error, compared with the conventional dynamical gates, using the randomized benchmarking method. This scheme can also be utilized to construct two-qubit geometric operations while the generation of maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.