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arXiv:quant-ph/0211096 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Decoherence of quantum states and its suppression in ensemble large-scale solid state NMR quantum computers

Alexander A. Kokin

Published Jul 23, 2003• 1 citation
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Abstract

It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of 31P donor atoms having nuclear spin I=1/2. It is considered here, as main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity and of spin temperature whereby the required decoherence suppression is obtained. It is discussed the random phase error suppression in the ensemble quantum register basic states.

DOI
10.1117/12.517916

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It is discussed the decoherence problems in ensemble large-scale solid state NMR quantum computer based on the array of 31P donor atoms having nuclear spin I=1/2. It is considered here, as main mechanisms of decoherence for low temperature (<0.1K), the adiabatic processes of random modulation of qubit resonance frequency determined by secular part of nuclear spin interaction with electron spin of the basic atoms, with impurity paramagnetic atoms and also with nuclear spins of impurity and of spin temperature whereby the required decoherence suppression is obtained. It is discussed the random phase error suppression in the ensemble quantum register basic states.
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Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.
The problem of numerical simulation of NRM spectra of the donor impurity in silicon is solved in the context of the fact that the system of nuclear spins of 31 P is planned to be used to organize working registers of a solid-state quantum computer. The proposed simulation method is shown to be applicable in the case of a quantitative increase of the NMR register and its topological complication. A scheme of readout of the results of “quantum counting” at a level allowing determination (with the help of SQUID) of the state of an individual spin is proposed.
This study deals with the further development of nuclear spin model of scalable quantum register, which presents the one-dimensional chain of the magnetic atoms with nuclear spins 1/2, substituting the basic atoms in the plate of nuclear spin-free easy-axis 3D antiferromagnet. The decoherence rates of one qubit state and entanglement state of two removed qubits and longitudinal relaxation rates are caused by the interaction of nuclear spins-qubits with virtual spin waves in antiferromagnet ground state were calculated. It was considered also one qubit adiabatic decoherence, is caused by the interaction of nuclear spin of quantum register with nuclear spins of randomly distributed isotopes, substituting the basic nuclear spin-free isotopes of antiferromagnet. We have considered finally encoded DFS (Decoherence-Free Subspaces) logical qubits are constructed on clusters of the four-physical qubits, given by the two states with zero total angular momentum.