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Modern Electronic Technique

Simulation of NMR Experiment for Quantum Logic Gates

Yanhua Zhong

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

At present, it is one of various effective approaches for quantum algorithm by using the nuclear magnetic resonance (NMR) experiment technology. In this paper, a NMR pulse array is described to realize various quantum logic gates, such as the CNOT and the Toffoli gate. Then an experiment about QCE is given.

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Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit (qubit) conditional on the state of the remaining qubits in the system. We show that such selective gates, termed $(\mathrm{controlled}{)}^{n}\ensuremath{-}\mathrm{NOT}$ gates, or ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for any number of control spins. In this work, a catalog of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for systems of as many as 16 spins is provided along with an experimental implementation of a ${\mathrm{c}}^{3}\ensuremath{-}\mathrm{N}\mathrm{O}\mathrm{T}$ gate on a four spin system, 13C{}^{13}\mathrm{C}13C alanine.
At present, it is one of various effective approaches for quantum algorithm to using the nuclear magnetic resonance (NMR) experiment technology. NMR uses radio frequency (RF) electromagnetic pulses to rotate the spins. By tuning the frequency of the RF-field to the precession frequency of a particular spin, the power of the applied pulse controls how much the spin will rotate. The axis of the rotation is determined by the direction of the applied RF-field. By selecting the appropriate RF pulses, arbitrary single-spin rotation can be carried out. In other words, using RF pulses we can perform any single-qubit operation. Communication between the qubits is accomplished through the spin-spin interaction in model. A simulation approach in this paper is described to realize quantum Fourier transform algorithm (QFT).
Currently,the NMR technology is one of the effective physical systems to realize quantum computation.As the multiple-quantum operator algebra theory mentions,any unitary transformation can be decomposed into a sequence of a limited number of one-qubit quantum gates and two-qubit diagonal gates.Based on these backgrounds,we propose a method to form NMR pulse sequences to realize the multi-qubit Grover quantum search algorithm.Experiments finish the algorithm with three-qubit,on a Quantum Computer Emulator.
Abstract It is shown theoretically how to use the EPR (electron paramagnetic resonance) technique, using electron spins as qubits, coupled with each other by the exchange interaction, to set the configuration of n qubits ( n = 1–4) at resonance, in conjunction with pulses, to construct the NOT (one qubit), CNOT (two qubits), CCNOT (three qubits), and CCCNOT (four qubits) Toffoli gates, which can be exploited to build a quantum computer. This is unique to EPR, wherein exchange‐coupled electron spins are used. This is different from NMR (Nuclear Magnetic Resonance), which uses nuclear spins as qubits, that do not couple with each other by the exchange interaction.