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arXiv:quant-ph/0411099

Efficient decoupling and recoupling in solid state NMR for quantum computation

Fumiko Yamaguchi, Thaddeus D. Ladd, Cyrus P. Master, Y. Yamamoto, Navin Khaneja

Published Nov 15, 2004• 3 citations
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Abstract

A scheme for decoupling and selectively recoupling large networks of dipolar-coupled spins is proposed. The scheme relies on a combination of broadband, decoupling pulse sequences applied to all the nuclear spins with a band-selective pulse sequence for single spin rotations or recoupling. The evolution-time overhead required for selective coupling is independent of the number of spins, subject to time-scale constraints, for which we discuss the feasibility. This scheme may improve the scalability of solid-state-NMR quantum computing architectures.

DOI
10.48550/arxiv.quant-ph/0411099

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A scheme for decoupling and selectively recoupling large networks of dipolar-coupled spins is proposed. The scheme relies on a combination of broadband, decoupling pulse sequences applied to all the nuclear spins with a band-selective pulse sequence for single spin rotations or recoupling. The evolution-time overhead required for selective coupling is independent of the number of spins, subject to time-scale constraints, for which we discuss the feasibility. This scheme may improve the scalability of solid-state-NMR quantum computing architectures.
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Decoupling the interactions in a spin network governed by a pair-interaction Hamiltonian is a well-studied problem. Combinatorial schemes for decoupling and for manipulating the couplings of Hamiltonians have been developed which use selective pulses. In this paper we consider an additional requirement on these pulse sequences: as few {\em different} control operations as possible should be used. This requirement is motivated by the fact that optimizing each individual selective pulse will be expensive, i. e., it is desirable to use as few different selective pulses as possible. For an arbitrary ddd-dimensional system we show that the ability to implement only two control operations is sufficient to turn off the time evolution. In case of a bipartite system with local control we show that four different control operations are sufficient. Turning to networks consisting of several ddd-dimensional nodes which are governed by a pair-interaction Hamiltonian, we show that decoupling can be achieved if one is able to control a number of different control operations which is logarithmic in the number of nodes.
Proposals for scalable quantum computing devices suffer not only from decoherence due to the interaction with their environment, but also from severe engineering constraints. Here we introduce a practical solution to these major concerns, addressing solid-state proposals in particular. Decoherence is first reduced by encoding a logical qubit into two qubits, then completely eliminated by an efficient set of decoupling pulse sequences. The same encoding removes the need for single-qubit operations, which pose a difficult design constraint. We further show how the dominant decoherence processes can be identified empirically, in order to optimize the decoupling pulses.
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling,'' is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature (London) 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the S\o{}rensen-M\o{}lmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed 1/f1/f1/f spectrum of the vibrational bath.