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理论物理通讯：英文版

Nonadiabatic Geometric Quantum Computation with Asymmetric Superconducting Quantum Interference Device

Yang Hao, San-Ru, Hou, Bo-Yu, Xi Xi, Xiaoqiang, Yue Yue, Rui-Hong

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

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.

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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 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.
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 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.
Based on superconducting quantum interference devices (SQUID's) coupled to a cavity, we propose a scheme for implementing a quantum phase-shift gate and generating a WWW state by an adiabatic evolution of dark eigenstates, without any contributions from dynamical and geometric gates. The Sole requirement is of adiabatically increasing or decreasing Rabi frequencies of classical microwave pluses. Thus, the manipulation is robust against certain types of errors. We also analyze the experimental possibility that identical coupling can be achieved between SQUID qubits and cavity fields, and the cavity decay can be ignored in certain conditions. Based on a simple operation, our scheme may be realized in this solid-state system.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
Recently, nonadiabatic geometric quantum computation has received much attention due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and special evolution paths have been proposed, which usually require longer gate-time and more operational steps, and thus lead to lower quality of the implemented quantum gates. Here, we present an effective scheme to find the shortest geometric path under conventional conditions of geometric quantum computation, where high-fidelity and robust geometric gates can be realized by only single-loop evolution, and the gate performances are better than the corresponding dynamical ones. Furthermore, we can optimize the pulse shapes in our scheme to further shorten the gate-time, which is determined by how fast the path is traveled. In addition, we also present its physical implementation on superconducting circuits, consisting of capacitively coupled transmon qubits, where fidelities of geometric single- and two-qubit gates can be higher than 99.95% and 99.80% within the current state-of-the-art experimental technologies, respectively. These results indicate that our scheme is promising for large-scale fault-tolerant quantum computation.