We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU...We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.展开更多
By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the dege...By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis-Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In some special cases, the current solution can reduce to the results of the previous works.展开更多
Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of ...Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes Cummings system.展开更多
High-fidelity quantum gates are essential for large-scale quantum computation.However,any quantum manipulation will inevitably affected by noises,systematic errors and decoherence effects,which lead to infidelity of a...High-fidelity quantum gates are essential for large-scale quantum computation.However,any quantum manipulation will inevitably affected by noises,systematic errors and decoherence effects,which lead to infidelity of a target quantum task.Therefore,implementing high-fidelity,robust and fast quantum gates is highly desired.Here,we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity.In our proposal,the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally,leading to high-fidelity quantum gates in a simple setup.Besides,our scheme is readily realizable in physical system currently pursued for implementation of quantum computation.Therefore,our proposal represents a promising way towards fault-tolerant geometric quantum computation.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.
基金supported by the National Natural Science Foundation of China under Grant Nos.40674076 and 40474064the Hunan Natural Science Foundation of China under Grant No.07JJ3123the Scientific Research Fund of Hunan Provincial Education Department under Grant Nos.06C163,05B023,and 06B004
文摘By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis-Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In some special cases, the current solution can reduce to the results of the previous works.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘Based on the construction of supersymmetric generators, we use the Lewis-Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes-Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes Cummings system.
基金This work was supported by the Key R&D Program of Guangdong Province(Grant No.2018B030326001)the National Natural Science Foundation of China(Grant No.11874156)Science and Technology Program of Guangzhou(Grant No.2019050001).
文摘High-fidelity quantum gates are essential for large-scale quantum computation.However,any quantum manipulation will inevitably affected by noises,systematic errors and decoherence effects,which lead to infidelity of a target quantum task.Therefore,implementing high-fidelity,robust and fast quantum gates is highly desired.Here,we propose a fast and robust scheme to construct high-fidelity holonomic quantum gates for universal quantum computation based on resonant interaction of three-level quantum systems via shortcuts to adiabaticity.In our proposal,the target Hamiltonian to induce noncyclic non-Abelian geometric phases can be inversely engineered with less evolution time and demanding experimentally,leading to high-fidelity quantum gates in a simple setup.Besides,our scheme is readily realizable in physical system currently pursued for implementation of quantum computation.Therefore,our proposal represents a promising way towards fault-tolerant geometric quantum computation.
