Simulation of some quantum gates, with decoherence

TL;DR

This paper presents numerical simulations of rf-Squid quantum gates, analyzing their static and dynamic properties, including decoherence effects, to assess the feasibility of implementing quantum logic gates like CNOT.

Contribution

The study introduces high-accuracy numerical methods for simulating rf-Squid systems and explores the parameter ranges for effective two-state models and adiabatic gate operations.

Findings

Effective two-state approximation holds within specific parameter ranges.

Decoherence effects can be mitigated with certain device parameters.

A formula relating noise to decoherence rate was derived and validated.

Abstract

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 Schroedinger 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 1/2'' 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 beta slightly above one. It appears that with values of beta close to one, 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.