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Hu'nan Shifan Daxue xuebao. Ziran kexue ban

Nonadiabatic Controlled Geometric Phase for the Asymmetric dc-SQUID Charge States

Hao San

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

Introduced a physical model for the asymmetric dc SQUID(Superconducting QU antum Interference Device) system and given a simple scheme to control the fictitious magnetic fields of the charge qubits.We have also presented an easy scheme to make the geometric phase nonadiabaticaly,and obtained the geometric phase for the single qubit.We also showed that when the gate voltage and the externally applied current of the dc SQUID system satisfies an appropriate constraint condition,the charge state evolution can be controlled without the dynamic phase.

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Introduced a physical model for the asymmetric dc SQUID(Superconducting QU antum Interference Device) system and given a simple scheme to control the fictitious magnetic fields of the charge qubits.We have also presented an easy scheme to make the geometric phase nonadiabaticaly,and obtained the geometric phase for the single qubit.We also showed that when the gate voltage and the externally applied current of the dc SQUID system satisfies an appropriate constraint condition,the charge state evolution can be controlled without the dynamic phase.
We propose a method of controlling the dc-SQUID (superconducting quantum interference device) system by changing the gate voltages, which controls the amplitude of the fictitious magnetic fields , and the externally applied current that produces the piercing magnetic flux for the dc-SQUID system. We have also introduced a physical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phase gate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the two qubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies an appropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. The non-adiabatic evolution of the charge states is given as well.
We propose a method of controlling the dc-SQUID (superconducting quantum interference device) systemby changing the gate voltages, which controls the amplitude of the fictitious magnetic fields Bz, and the externallyapplied current that produces the piercing magnetic fiux φx for the dc-SQUID system. We have also introduced aphysical model for the dc-SQUID system. Using this physical model, one can obtain the non-adiabatic geometric phasegate for the single qubit and the non-adiabatic conditional geometric phase gate (controlled NOT gate) for the twoqubits. It is shown that when the gate voltage and the externally applied current of the dc-SQUID system satisfies anappropriate constraint condition, the charge state evolution can be controlled exactly on a dynamic phase free path. Thenon-adiabatic evolution of the charge states is given as well.
We have fabricated and studied a promising kind of direct current superconducting quantum interference device (dc-SQUID) in which the magnitude and sign of the critical current of the individual Josephson junctions can be controlled by additional voltage probes connected to the junctions. We show that the amplitude of the voltage oscillations of the SQUID as a function of the applied magnetic field can be tuned and that the phase of the oscillations can be switched between 0 and π in the temperature range of 0.1–4.2 K using a suitable control voltage. This is equivalent to the external application of (n+1/2) flux quantum.
Abstract Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are typically longer than conventional dynamical gates, resulting in weakening of robustness and more infidelities of the implemented geometric gates. Here, we propose a path-optimized scheme for geometric quantum computation (GQC) on superconducting transmon qubits, where high-fidelity and robust universal nonadiabatic geometric gates can be implemented, based on conventional experimental setups. Specifically, we find that, by selecting appropriate evolution paths, the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Numerical simulations show that the fidelities for single-qubit geometric phase, π /8 and Hadamard gates can be obtained as 99.93%, 99.95% and 99.95%, respectively. Remarkably, the fidelity for two-qubit control-phase gate can be as high as 99.87%. Therefore, our scheme provides a new perspective for GQC, making it more promising in the application of large-scale fault-tolerant quantum computation.
We present a theoretical analysis of a superconducting quantum circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc superconduction quantum intereference device (SQUID). Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc SQUID can be viewed as a tunable micrometer-sized resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regime. It describes very precisely the tunable coupling strength measured in this circuit [A. Fay et al., Phys. Rev. Lett. 100, 187003 (2008)] and explains the ``quantronium'' as well as the adiabatic quantum transfer readout.
We present a theoretical analysis of the quantum dynamics of a superconducting circuit based on a highly asymmetric Cooper pair transistor (ACPT) in parallel to a dc-SQUID. Starting from the full Hamiltonian we show that the circuit can be modeled as a charge qubit (ACPT) coupled to an anharmonic oscillator (dc-SQUID). Depending on the anharmonicity of the SQUID, the Hamiltonian can be reduced either to one that describes two coupled qubits or to the Jaynes-Cummings Hamiltonian. Here the dc-SQUID can be viewed as a tunable micron-size resonator. The coupling term, which is a combination of a capacitive and a Josephson coupling between the two qubits, can be tuned from the very strong- to the zero-coupling regimes. It describes very precisely the tunable coupling strength measured in this circuit and explains the 'quantronium' as well as the adiabatic quantum transfer read-out.