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Chinese Physics Letters

Liquid Nuclear Magnetic Resonance Implementation of Quantum Computation in Subspace

Yao Xi-Wei, Xue Fei, Pang Wen-Min, Jiangfeng Du, Zhou Xian-Yi, Rongdian Han

Published Jul 21, 2006• 6 citations
Publisher

Abstract

Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch–Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch–Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch–Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.

DOI
10.1088/0256-307x/23/8/010

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Based on the logical labelling method, we prepare an effective pure state in a subsystem of a three spin system via liquid nuclear magnetic resonance technique. Then with this subspace effective pure state we implement the Deutsch–Jozsa algorithm. The tomography for the subspace effective pure state and the corresponding spectrum of the output for the Deutsch–Jozsa algorithm agree with theoretical predictions, which shows that we have successfully implemented the Deutsch–Jozsa algorithm in a subsystem of a nuclear spin system and demonstrated a subspace quantum computation.
We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and that can be identified by labelling it based on logical (spin), temporal, or spatial degrees of freedom. This permits quantum computation to be realized with bulk ensembles far from the ground state. Experimental results are presented for quantum gates and circuits implemented with liquid nuclear magnetic resonance techniques and verified by quantum state tomography.
We report the first use of ``logical labeling'' to perform a quantum computation with a room-temperature bulk system. This method entails the selection of a subsystem that behaves as if it were at zero temperature---except for a decrease in signal strength---conditioned upon the state of the remaining system. No averaging over differently prepared molecules is required. In order to test this concept, we execute a quantum search algorithm in a subspace of two nuclear spins, labeled by a third spin, using solution nuclear magnetic resonance and employing a novel choice of reference frame to uncouple nuclei.
A new approach to the implementation of a quantum computer by high-resolution nuclear magnetic resonance (NMR) is described. The key feature is that two or more line-selective radio-frequency pulses are applied simultaneously. A three-qubit quantum computer has been investigated using the 400 MHz NMR spectrum of the three coupled protons in 2,3-dibromopropanoic acid. It has been employed to implement the Deutsch-Jozsa algorithm for distinguishing between constant and balanced functions. The extension to systems containing more coupled spins is straightforward and does not require a more protracted experiment.
This article reviews recent work done by us an some initial steps towards the implementation of quantum computation using liquid state NMR. We describe how special kinds of states required for such computation (called pseudo-pure states) can be created from a thermal ensemble of spins. We demonstrate the implementation of several quantum logic gates through one- and two-dimensional NMR methods, using transition- and spin- selective pulses. Finally, we discuss the implementation of the Deutsch-Jozsa algorithm using NMR.
An alternative method for preparing an effective-pure state in a subsystem of a three-spin system for quantum information processing(QIP) in liquid-state nuclear magnetic resonance(NMR) was demonstrated experimentally.With the aid of numerical search methods,strongly modulating pulses(SMP) scheme was obtained and can perform accurate,arbitrary,selective gates on a three-qubit system.Compared with low-power(nuclear-selective) pulse scheme,the number of shaped pulses and the width of each pulse were both reduced.A pair of two-qubit subspace effective-pure states within a three-spin system was acquired simultaneously.The tomography for the spin system agreed with theoretical predictions,which shows that the experiments were successfully implemented.The short pulse-width of SMP substantially reduced the effects of relaxation within the period of pulse.This is very useful for NMR QIP involving larger numbers of qubits.