Perturbation approach for nuclear magnetic resonance solid-state quantum computation
type: Item
instance of: scholarly article
title: Perturbation approach for nuclear magnetic resonance solid-state quantum computation
zbMATH Open document ID: 1031.81017
DOI: 10.1155/S1110757X03110182
author: Yanyan Li
published in: Journal of Applied Mathematics
publication date: 2003-03-18T00:00:00Z
full work available at URL: https://eudml.org/doc/50592
review text: Several solid state quantum systems are considered nowadays as candidates for quantum computers. In this paper the implementation of quantum logic gates by radio-frequency pulses in the nuclear-spin one-dimensional solid state system is considered. The dynamics of such a quantum computer with a large number \((L=1000)\) of qubits is studied using a perturbation approach. This approach allows estimation of errors in implementation of quantum logic operations without recourse to either exact solution of quantum dynamical equations or direct diagonalization of large matrices. Small parameters are introduced and used to compute the error in an implementation of an entanglement between remote qubits, using a sequence of radio-frequency pulses. The error is computed up to the different orders of the perturbation theory and tested using exact numerical solution. The procedure describes the behavior of the quantum system in large Hilbert space and predicts the final quantum state of the system after action of the sequence of pulses with different frequencies. This approach provides tools for choosing the optimal parameters for operation of the scalable quantum computer with a large number of qubits.
Mathematics Subject Classification ID: 81P68
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 82B20
zbMATH DE Number: 1884080
zbMATH Keywords: quantum computers
zbMATH Keywords: quantum logic gates
zbMATH Keywords: nuclear-spin one-dimensional solid state system
zbMATH Keywords: perturbation approach
zbMATH Keywords: entanglement
zbMATH Keywords: large number of qubits
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1884080