Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to their potential robustness.When a system in a non-degenerate eigenstate undergoes an adiabatically cycli...Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to their potential robustness.When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by its Hamiltonian,it will get a geometric phase,referred to as the Berry Phase.While a non-adiabatically cyclic evolution produces an Aharonov-Anandan geometric phase.The two types of Abelian geometric phases are extended to the non-Abelian cases,where the phase factors become matrix-valued and the transformations associated with different loops are non-commutable.Abelian and non-Abelian(holonomic)operations are prevalent in discrete variable systems,whose limited(say,two)energy levels,form the qubit.While their developments in continuous systems have also been investigated,mainly due to that,bosonic modes(in,such as,cat states)with large Hilbert spaces,provide potential advantages in fault-tolerant quantum computation.Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.We construct arbitrary single-qubit(two-qubit)gates with the combination of single-and two-photon drivings applied to a Kerr Parametric Oscillator(KPO)(the coupled KPOs).Our scheme relaxes the requirements of the previously proposed quantum geometric operation strategies in continuous variable systems,providing an effective way for quantum control.展开更多
In this paper,we propose a scheme for implementing the nonadiabatic holonomic quantum computation(NHQC+)of two Rydberg atoms by using invariant-based reverse engineering(IBRE).The scheme is based on Förster reson...In this paper,we propose a scheme for implementing the nonadiabatic holonomic quantum computation(NHQC+)of two Rydberg atoms by using invariant-based reverse engineering(IBRE).The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms,which provides a selective coupling mechanism to simply the dynamics of system.Moreover,for improving the fidelity of the scheme,the optimal control method is introduced to enhance the gate robustness against systematic errors.Numerical simulations show the scheme is robust against the random noise in control fields,the deviation of dipole-dipole interaction,the Förster defect,and the spontaneous emission of atoms.Therefore,the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.展开更多
We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero...We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang–bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.展开更多
基金supported by the National Natural Science Foundation of China(Grand Nos.12274080,and 11875108)。
文摘Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to their potential robustness.When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by its Hamiltonian,it will get a geometric phase,referred to as the Berry Phase.While a non-adiabatically cyclic evolution produces an Aharonov-Anandan geometric phase.The two types of Abelian geometric phases are extended to the non-Abelian cases,where the phase factors become matrix-valued and the transformations associated with different loops are non-commutable.Abelian and non-Abelian(holonomic)operations are prevalent in discrete variable systems,whose limited(say,two)energy levels,form the qubit.While their developments in continuous systems have also been investigated,mainly due to that,bosonic modes(in,such as,cat states)with large Hilbert spaces,provide potential advantages in fault-tolerant quantum computation.Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.We construct arbitrary single-qubit(two-qubit)gates with the combination of single-and two-photon drivings applied to a Kerr Parametric Oscillator(KPO)(the coupled KPOs).Our scheme relaxes the requirements of the previously proposed quantum geometric operation strategies in continuous variable systems,providing an effective way for quantum control.
基金supported by the National Natural Science Foundation of China under Grant Nos 11575045,11874114,and 11674060the Natural Science Funds for Distinguished Young Scholar of Fujian Province under Grant 2020J06011Project from Fuzhou University under Grant JG202001-2.
文摘In this paper,we propose a scheme for implementing the nonadiabatic holonomic quantum computation(NHQC+)of two Rydberg atoms by using invariant-based reverse engineering(IBRE).The scheme is based on Förster resonance induced by strong dipole-dipole interaction between two Rydberg atoms,which provides a selective coupling mechanism to simply the dynamics of system.Moreover,for improving the fidelity of the scheme,the optimal control method is introduced to enhance the gate robustness against systematic errors.Numerical simulations show the scheme is robust against the random noise in control fields,the deviation of dipole-dipole interaction,the Förster defect,and the spontaneous emission of atoms.Therefore,the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos.11575045,11874114,and 11674060the Natural Science Funds for Distinguished Young Scholar of Fujian Province under Grant No.2020J06011+2 种基金Project from Fuzhou University under Grant JG202001-2the Natural Science Foundation of Fujian Province under Grant No.2018J01414the China Postdoctoral Science Foundation under Grant No.2021M691150.
文摘We propose a quantum control scheme with the help of Lyapunov control function in the optomechanics system. The principle of the idea is to design suitable control fields to steer the Lyapunov control function to zero as t → ∞ while the quantum system is driven to the target state. Such an evolution makes no limit on the initial state and one needs not manipulate the laser pulses during the evolution. To prove the effectiveness of the scheme, we show two useful applications in the optomechanics system: one is the cooling of nanomechanical resonator and the other is the quantum fluctuation transfer between membranes. Numerical simulation demonstrates that the perfect and fast cooling of nanomechanical resonator and quantum fluctuation transfer between membranes can be rapidly achieved. Besides, some optimizations are made on the traditional Lyapunov control waveform and the optimized bang–bang control fields makes Lyapunov function V decrease faster. The optimized quantum control scheme can achieve the same goal with greater efficiency. Hence, we hope that this work may open a new avenue of the experimental realization of cooling mechanical oscillator, quantum fluctuations transfer between membranes and other quantum optomechanics tasks and become an alternative candidate for quantum manipulation of macroscopic mechanical devices in the near future.