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Physical Review A

Method for effective pure states with any number of spins

Ushio Sakaguchi, Hiroshi Ozawa, Toshio Fukumi

Published Mar 17, 2000• 18 citations
Publisher

Abstract

A method is proposed to prepare an effective pure state corresponding to the pure state $|0〉|0〉\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}|0〉$ for any number of spins on a nuclear magnetic resonance quantum computer, where $|0〉$ stands for the spin-up state of a nuclear spin. The method is based on the spatial labeling proposed by Cory et al. [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)].

DOI
10.1103/physreva.61.042313

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Preparation of effective pure states ∣00⋯0⟩\mid 00 \cdots 0 \rangle∣00⋯0⟩ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)
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Abstract In nuclear magnetic resonance (NMR) quantum computing systems, it is very important to prepare an effective pure state rather than a true pure state. Our main objective is to present a general algorithm that provides quantum circuits for preparing an effective pure state from any mixed state, consisting only of controlled‐not (CNOT) quantum gates for homonuclear spin systems. Our algorithm is based on the product operator approach and could be applicable to NMR quantum computing systems with more than eight qubits. Optimization of the number of controlled‐not quantum gates is discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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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.