Models of Quantum Computers and Decoherence Problem

TL;DR

This paper discusses mathematical models of quantum computers, explores the decoherence problem caused by environmental coupling, and proposes a control-based solution using analysis of the spin-boson Hamiltonian.

Contribution

It introduces a control method to mitigate decoherence in quantum computers based on analysis of the spin-boson Hamiltonian in the stochastic limit.

Findings

Mathematical models of quantum computers are described.

Decoherence due to environment coupling is analyzed.

A control-based solution for decoherence is proposed.

Abstract

Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one wants to build a quantum computer is the decoherence due to the coupling with the environment. We propose a possible solution of this problem by using a control of parameters of the system. This proposal is based on the analysis of the spin-boson Hamiltonian performed in the stochastic limit approximation.