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arXiv:quant-ph/0009122

Quantum computation in a one-dimensional crystal lattice with NMR force microscopy

Thaddeus D. Ladd, J. R. Goldman, Aykutlu Dâna, Fumiko Yamaguchi, Y. Yamamoto

Published Sep 28, 2000• 8 citations
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Abstract

A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.

DOI
10.48550/arxiv.quant-ph/0009122

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A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.
A quantum computer can be constructed from nuclear spins in a crystal lattice of a rare-earth monophosphide such as cerium-monophosphide (CeP). The 12 spin of a 31P nucleus can be used to represent a quantum bit (‘qubit’) with a relatively long relaxation time. In a CeP crystal lattice, 31P nuclei are periodically situated in three dimensions at distances of about 12Å. The application of a static magnetic field gradient in one direction causes differences in the Zeeman frequencies of separate nuclei. This allows thousands of distinct qubits to be individually addressed. Initializations of the qubits can be done efficiently by the Pound-Overhauser double resonance effect on the nuclear spins and the antiferromagnetically ordered 4f electron spins of cerium ions. Logic operations can be performed by simple pulse sequences, and computational results after logic operations can be measured by the nuclear magnetic resonance of neighboring nuclei, or the electron resonance of neighboring 4f electrons of cerium ions.
Nuclear magnetic resonance offers an appealing prospect for implementation of quantum computers, because of the long coherence times associated with nuclear spins, and extensive laboratory experience in manipulating the spins with radio frequency pulses. Existing proposals, however, suffer from a signal-to-noise ratio that decays exponentially in the number of qubits in the quantum computer. This places a severe limit on the size of the computations that can be performed by such a computer; estimates of that limit are well within the range in which a conventional computer taking exponentially more steps would still be practical. We give an NMR implementation in which the signal-to-noise ratio depends only on features of NMR technology, not the size of the computer. This provides a means for NMR computation techniques to scale to sizes at which the exponential speedup enables quantum computation to solve problems beyond the capabilities of classical computers.
We propose a scalable design for a solid-state spin-based quantum computer. It uses endohedral fullerenes like N@C60\mathrm{N}@{\mathrm{C}}_{60}N@C60​ or P@C60,\mathrm{P}@{\mathrm{C}}_{60},P@C60​, which can be positioned on Si surfaces with a scanning tunneling microscope. Each logical qubit is stored in two physical qubits, corresponding to the nuclear and electronic spins. We discuss the addressing of individual qubits by a magnetic field gradient, and the implementation of one- and two-qubit quantum gates by sequences of radio-frequency and microwave pulses.