The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed.We solve the Klein–Gor...The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed.We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function.We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues.We find that the energy eigenvalues depend on the quantum flux field that shows an analogue of the Aharonov–Bohm effect.Furthermore,we obtain the persistent currents,the magnetization,and the magnetic susceptibility at zero temperature in the quantum system defined in a state and show that these magnetic parameters are modified by various factors.展开更多
Recently,nonadiabatic geometric quantum computation has been received great attentions,due to its fast operation and intrinsic error resilience.However,compared with the corresponding dynamical gates,the robustness of...Recently,nonadiabatic geometric quantum computation has been received great attentions,due to its fast operation and intrinsic error resilience.However,compared with the corresponding dynamical gates,the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls,and the inherent geometric fault-tolerance characteristic is not fully explored.Here,we present an effective geometric scheme combined with a general dynamical-corrected technique,with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies,in terms of resisting the systematic error,i.e.,σ_(x)error.In addition,combined with the decoherence-free subspace(DFS)coding,the resulting geometric gates can also effectively suppress theσ_(z)error caused by the collective dephasing.Notably,our protocol is a general one with simple experimental setups,which can be potentially implemented in different quantum systems,such as Rydberg atoms,trapped ions and superconducting qubits.These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.展开更多
Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates hav...Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic nonAbelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with superconducting transmons, where the three lowest levels are all utilized in operation. However, the second excited state of transmons has a relatively short coherence time, which results in a decreased fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on the two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking.展开更多
We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in ...We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.展开更多
文摘The relativistic quantum motions of the oscillator field(via the Klein–Gordon oscillator equation)under a uniform magnetic field in a topologically non-trivial space-time geometry are analyzed.We solve the Klein–Gordon oscillator equation using the Nikiforov-Uvarov method and obtain the energy profile and the wave function.We discuss the effects of the non-trivial topology and the magnetic field on the energy eigenvalues.We find that the energy eigenvalues depend on the quantum flux field that shows an analogue of the Aharonov–Bohm effect.Furthermore,we obtain the persistent currents,the magnetization,and the magnetic susceptibility at zero temperature in the quantum system defined in a state and show that these magnetic parameters are modified by various factors.
基金supported by the Key-Area Research and Development Program of Guangdong Province (Grant No.2018B030326001)the National Natural Science Foundation of China (Grant No.12275090)+4 种基金Guangdong Provincial Key Laboratory (Grant No.2020B1212060066)the Quality Engineering Project of the Education Department of Anhui Province (No.2021cyxy046)the key Scientific Research Foundation of Anhui Provincial Education Department (KJ2021A0649)Outstanding Young Talents in College of Anhui Province (Grant No.gxyq2022059)the High-Level Talent Scientific Research Starting foundation (Grant No.2020rcjj14).
文摘Recently,nonadiabatic geometric quantum computation has been received great attentions,due to its fast operation and intrinsic error resilience.However,compared with the corresponding dynamical gates,the robustness of implemented nonadiabatic geometric gates based on the conventional single-loop geometric scheme still has the same order of magnitude due to the requirement of strict multi-segment geometric controls,and the inherent geometric fault-tolerance characteristic is not fully explored.Here,we present an effective geometric scheme combined with a general dynamical-corrected technique,with which the super-robust nonadiabatic geometric quantum gates can be constructed over the conventional single-loop geometric and two-loop composite-pulse geometric strategies,in terms of resisting the systematic error,i.e.,σ_(x)error.In addition,combined with the decoherence-free subspace(DFS)coding,the resulting geometric gates can also effectively suppress theσ_(z)error caused by the collective dephasing.Notably,our protocol is a general one with simple experimental setups,which can be potentially implemented in different quantum systems,such as Rydberg atoms,trapped ions and superconducting qubits.These results indicate that our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.
基金supported by the National Basic Research Program of China(Grant No.2015CB921004)the National Key Research and Development Program of China(Grant Nos.2019YFA0308602,and 2016YFA0301700)+3 种基金the National Natural Science Foundation of China(Grant Nos.11934010,and 11775129)the Fundamental Research Funds for the Central Universities in Chinathe Anhui Initiative in Quantum Information Technologies(Grant No.AHY080000)the funding support from Tencent Corporation。
文摘Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various quantum gates have been proposed, such as nonadiabatic geometric gates based on nonadiabatic Abelian geometric phases and nonadiabatic holonomic gates based on nonadiabatic nonAbelian geometric phases. Up to now, nonadiabatic holonomic one-qubit gates have been experimentally demonstrated with superconducting transmons, where the three lowest levels are all utilized in operation. However, the second excited state of transmons has a relatively short coherence time, which results in a decreased fidelity of quantum gates. Here, we experimentally realize Abelian-geometric-phase-based nonadiabatic geometric one-qubit gates with a superconducting Xmon qubit. The realization is performed on the two lowest levels of an Xmon qubit and thus avoids the influence from the short coherence time of the second excited state. The experimental result indicates that the average fidelities of single-qubit gates can be up to 99.6% and 99.7% characterized by quantum process tomography and randomized benchmarking.
文摘We obtained the ground-state energy level and associated geometric phase in the Dicke model with the dipoledipole interactions analytically by the Holstein-Primakoff transformation and the boson expansion approach in the thermodynamic limit. The nonadiabatic geometric phase induced by the photon field was derived with the time-dependent unitary transformation. It is shown that dipole-dipole interactions have a deep influence on scaled behavior of the geometric phase at the critical point.
