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arXiv:cond-mat/9905200

Dynamics of the Measurement of Nuclear Spins in a Solid-State Quantum Computer

G. P. Berman, David K Campbell, Gary D. Doolen, Kirill E. Nagaev

Published May 13, 1999• 4 citations
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Abstract

We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane by modeling the quantum dynamics of two coupled nuclear spins on $^{31}$P donors implanted in silicon. We estimate the minimum measurement time necessary for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. We also calculate the probability of error for typical values of the external noise.

DOI
10.48550/arxiv.cond-mat/9905200

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We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane by modeling the quantum dynamics of two coupled nuclear spins on 31^{31}31P donors implanted in silicon. We estimate the minimum measurement time necessary for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. We also calculate the probability of error for typical values of the external noise.
We study numerically the process of nuclear spin measurement in a solid-state quantum computer of the type proposed by Kane, by calculating the quantum dynamics of two coupled nuclear spins on 31 P donors implanted in 28 Si. We estimate the time of the `quantum swap operation' - the minimum measurement time required for the reliable transfer of quantum information from the nuclear spin subsystem to the electronic subsystem. Our calculations show that for realistic values of the parameters this time is of the order of swap ~5 × 10 -5 s. We also calculate the probability of error for typical values of the external noise.
The measurement of the nuclear spin state in the Kane's solid-state quantum computer was investigated for a simple two-qubit system. To simplify the calculations, the Hamiltonian matrix was divided into five invariant subspaces based on the projection of the total spins along the external magnetic field. The calculations analyzed the relations between the eigenvalues and eigenstates of the Hamiltonian matrix and the interactions between the two electrons. The results show that measurement of the nuclear spin state by exchanging the nuclear and election spin wave functions is restricted. Only four of the sixteen possible states in a two-qubit system can be measured using this method.
It has been over ten years since Kane's influential proposal for a silicon-based nuclear spin quantum computer using phosphorous donors. Since then, silicon-based architectures have been refined as the experimental challenges associated with the original proposal have become better understood, while simultaneously a number of powerful and generic models for quantum computation have emerged. Here, I discuss how the cluster state or "one-way" model for quantum computing might be advantageously applied to donors in silicon, with the potential to substantially reduce the practical requirements of a successful implementation. The essence of the scheme is to use the electron spin associated with a donor to weave an entangled network between 31P donor nuclear spins. This resource has been shown to have exceptional coherence times and supports universal quantum computation through local measurements on the nuclear spins. Some of the key ingredients, such as global spin manipulation, have been robustly established, while others, such as single spin measurement, have seen much progress in recent years. A key challenge will be the demonstration of electron transfer between donors that preserves spin coherence.
Nuclear spin registers in the vicinity of electron spins in solid state systems offer a powerful resource to address the challenge of scalability in quantum architectures. We investigate here the properties of 29 Si nuclear spins surrounding donor atoms in silicon, and consider the use of such spins, combined with the donor nuclear spin, as a quantum register coupled to the donor electron spin. We find the coherence of the nearby 29 Si nuclear spins is effectively protected by the presence of the donor electron spin, leading to coherence times in the second timescale—over two orders of magnitude greater than the coherence times in bulk silicon. We theoretically investigate the use of such a register for quantum error correction (QEC), including methods to protect nuclear spins from the ionisation/neutralisation of the donor, which is necessary for the re-initialisation of the ancillae qubits. This provides a route for multi-round QEC using donors in silicon.