Adiabatic evolution of a coupled-qubit Hamiltonian

TL;DR

This paper introduces a method for analyzing adiabatic evolution in coupled qubits, focusing on a two-qubit Hamiltonian suitable for quantum CNOT gates, with practical considerations for SQUID-based implementations.

Contribution

It provides a general approach for studying adiabatic processes in coupled qubits and identifies parameters for implementing a quantum CNOT gate with low dissipation.

Findings

Identified parameters for CNOT implementation

Determined conditions for adiabatic evolution

Supported feasibility of fast adiabatic operations with low dissipation

Abstract

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 Schroedinger 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 SQUIDs, we determine reasonable parameters for experimental purposes. The dissipation for SQUIDs 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.