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Design of Adiabatic Logic for a Quantum CNOT Gate

Corato, V., P. Silvestrini, Leo Stodolsky, Wosiek, J.

Published Jan 1, 2003• 4 citations
OpenAlex

Abstract

We examine the realization of a quantum CNOT gate by adiabatic operations.The principles of such systems and their analysis are briefly discussed and a model consisting of two weakly coupled double- potential well qubits is studied numerically. Regions of the parameter space with suitable well-defined sets of wavefunctions are found, in which then an adiabatic sweep of an external bias produces the switching behavior of CNOT. Results are presented on the adiabatic condition and the identification with the parameters of a flux-coupled two-SQUID system is given.For typical parameters adiabatic times in the nanosecond regime are obtained.

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We examine the realization of a quantum CNOT gate by adiabatic operations.The principles of such systems and their analysis are briefly discussed and a model consisting of two weakly coupled double- potential well qubits is studied numerically. Regions of the parameter space with suitable well-defined sets of wavefunctions are found, in which then an adiabatic sweep of an external bias produces the switching behavior of CNOT. Results are presented on the adiabatic condition and the identification with the parameters of a flux-coupled two-SQUID system is given.For typical parameters adiabatic times in the nanosecond regime are obtained.
We present a general method for studying coupled qubits driven by adiabatically changing external parameters. Extended calculations are provided for a two-bit Hamiltonian whose eigenstates can be used as logical states for a quantum CNOT gate. From a numerical analysis of the stationary Schr\"odinger equation we find a set of parameters suitable for representing CNOT, while from a time-dependent study the conditions for adiabatic evolution are determined. Specializing to a concrete physical system involving superconducting quantum interference devices (SQUID's), we determine reasonable parameters for experimental purposes. The dissipation for SQUID's is discussed by fitting experimental data. The low dissipation obtained supports the idea that adiabatic operations could be performed on a time scale shorter than the decoherence time.
Methods and results for numerical simulations of one and two interacting rf-SQUID systems suitable for adiabatic quantum gates are presented. These are based on high accuracy numerical solutions to the static and time dependent Schr\"odinger equation for the full SQUID Hamiltonian in one and two variables. Among the points examined in the static analysis is the range of validity of the effective two-state or ``spin-12\frac{1}{2}21​'' picture. A range of parameters is determined where the picture holds to good accuracy as the energy levels undergo gate manipulations. Some general points are presented concerning the relations between device parameters and ``good'' quantum mechanical state spaces. The time dependent simulations allow the examination of suitable conditions for adiabatic behavior, and permits the introduction of a random noise to simulate the effects of decoherence. A formula is derived and tested relating the random noise to the decoherence rate. Sensitivity to device and operating parameters for the logical gates NOT and CNOT are examined, with particular attention to values of the tunnel parameter $\ensuremath{\beta}$ slightly above one. It appears that with values of $\ensuremath{\beta}$ close to 1, a quantum CNOT gate is possible even with rather short decoherence times. Many of the methods and results will apply to coupled double-potential well systems in general.
Quantum logic gate is indispensable to quantum computation. One of the important qubit operations is the quantum controlled-not (CNOT) gate that performs a NOT operation on a target qubit depending on the state of the control qubit. In this paper we present a scheme to realize the quantum CNOT gate between two spatially separated atoms via shortcuts to adiabatic passage. The influence of various decoherence processes on the fidelity is discussed. The strict numerical simulation results show that the fidelity for the CNOT gate is relatively high.
We propose a scheme for realizing quantum gates [controlled-NOT (CNOT) and Toffoli] using a two-level quantum system by means of a pulsed bias. We show how to realize a CNOT gate using a two-qubit, two-level coupled system and a Toffoli gate using a three-qubit, two-level coupled system. For the CNOT gate, we show how to reduce the $4\ifmmode\times\else\texttimes\fi{}4$ Hamiltonian of the coupled system to a $2\ifmmode\times\else\texttimes\fi{}2$ Hamiltonian in order to solve for parameter values of the system. When these values are substituted into the coupled system equations for the two-qubit system, the simulation results confirm the CNOT gate operation. We further demonstrate our proposed scheme for a CNOT gate operation using a multilevel system of two coupled superconducting quantum interference devices as a particular example. We next use the same approach to implement a Toffoli gate using a three-qubit system.
We present an approach to realize universal two-bit quantum gates using two SQUID flux qubits. In this approach the basic unit consists of two inductively coupled SQUIDs with realistic device parameters. Quantum logical gates are implemented by applying resonant microwave pulse to the qubits. This procedure is demonstrated by realizing a controlled-NOT (CNOT) gate and the maximally entangled states of the coupled qubits through highly accurate numerical solution of the time-dependent Schrodinger equation of the system. This coupling scheme is simple and can be readily extended to many-qubit circuits required for scalable quantum information processing.
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.