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Physical Review A

Implementation of parallel search algorithms using spatial encoding by nuclear magnetic resonance

Rangeet Bhattacharyya, Ranabir Das, K. V. Ramanathan, Anil Kumar

Published May 11, 2005• 9 citations
Publisher

Abstract

Information storage and database search are attractive areas in the field of nuclear magnetic resonance. Among the notable works reported earlier, an implementation of a parallel search algorithm in a dipolar coupled spin cluster has gained considerable attention [A. Khitrin, V. L. Ermakov, and B. M. Fung, Phys. Rev. Lett. 89, 277902 (2002)]. In this paper, we propose and exemplify that spatial encoding can be successfully utilized in realizing such parallel algorithms. We also introduce an improved protocol of the parallel search algorithm, which can be realized using spatial encoding. The methods have been demonstrated to perform a search operation using 215 bits.

DOI
10.1103/physreva.71.052313

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Information storage and database search are attractive areas in the field of nuclear magnetic resonance. Among the notable works reported earlier, an implementation of a parallel search algorithm in a dipolar coupled spin cluster has gained considerable attention [A. Khitrin, V. L. Ermakov, and B. M. Fung, Phys. Rev. Lett. 89, 277902 (2002)]. In this paper, we propose and exemplify that spatial encoding can be successfully utilized in realizing such parallel algorithms. We also introduce an improved protocol of the parallel search algorithm, which can be realized using spatial encoding. The methods have been demonstrated to perform a search operation using 215 bits.
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An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of NNN items with O(phN)O(\sqrt{\mathit{ph}N})O(phN​) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
Abstract Nuclear magnetic resonance imaging (MRI) at the atomic scale offers exciting prospects for determining the structure and function of individual molecules and proteins. Quantum defects in diamond have recently emerged as a promising platform towards reaching this goal, and allowed for the detection and localization of single nuclear spins under ambient conditions. Here, we present an efficient strategy for extending imaging to large nuclear spin clusters, fulfilling an important requirement towards a single-molecule MRI technique. Our method combines the concepts of weak quantum measurements, phase encoding and simulated annealing to detect three-dimensional positions from many nuclei in parallel. Detection is spatially selective, allowing us to probe nuclei at a chosen target radius while avoiding interference from strongly-coupled proximal nuclei. We demonstrate our strategy by imaging clusters containing more than 20 carbon-13 nuclear spins within a radius of 2.4 nm from single, near-surface nitrogen–vacancy centers at room temperature. The radius extrapolates to 5–6 nm for 1H. Beside taking an important step in nanoscale MRI, our experiment also provides an efficient tool for the characterization of large nuclear spin registers in the context of quantum simulators and quantum network nodes.
Nowadays, there is a growing emphasis on the advances in computing based on quantum mechanics, which is accelerating not only the process of building quantum computers and quantum simulators, but also the parallel process of quantum metrology and communication. To communicate on future quantum internet, we need an essential element, the storage of the quantum information in a physical qubit. Nuclear Magnetic Resonance arises as an excellent tool to demonstrate and study the concept of quantum information storage. We first manipulate nuclei with half spin of water molecules to generate quantum bits. To do this, we used appropriately selected NMR pulses and then used quantum tomography to generate the density matrix to obtain the quantum state. We have found that the inhomogeneity of the magnetic field greatly affects the high-fidelity storage time of the quantum state. We have used various error correction algorithms to eliminate this.