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International Journal of Quantum Information

SILICON-BASED NUCLEAR SPIN QUANTUM COMPUTER

Hsi‐Sheng Goan

Published Nov 1, 2005• 11 citations
Publisher

Abstract

We review the basic physics and operation principles of the silicon-based quantum computer proposed by Kane, one of the most promising solid-state quantum computer proposals. We describe in some details how single- and two-qubit operations and readout measurements can, in principle, be performed for the Kane quantum computer. In addition, we also mention briefly its recent theoretical progress and development.

DOI
10.1142/s0219749905001225

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We review the basic physics and operation principles of the silicon-based quantum computer proposed by Kane, one of the most promising solid-state quantum computer proposals. We describe in some details how single- and two-qubit operations and readout measurements can, in principle, be performed for the Kane quantum computer. In addition, we also mention briefly its recent theoretical progress and development.
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.
Spin is a quantum mechanical property that describes the magnetic orientation of elementary and composite particles such as electrons and nuclei. For spin-half particles placed in a magnetic field, two states with differing energies are defined. Proposals exist for developing a revolutionary kind of computer that encodes bits of information on the states of a simple quantum two-level system - like those of a spin in a magnetic field. These quantum computers exploit the fundamental principles of quantum mechanics in order to perform certain calculations exponentially faster than their classical counterparts. Key to the development of such a device is the identification of potential systems that are suitable for employment as a quantum bit (qubit). This thesis explores quantum bits constructed from the spin states of single atoms hosted in silicon semiconductor devices. Silicon is an exceptional platform for spin-based quantum computing - in addition to being the dominant material in the microelectronic industry, it is also predominantly composed of nuclear spin-zero isotopes, providing very little background magnetic disturbance. The donor-atom phosphorus (31P) is investigated here. It possesses a nucleus that binds an additional electron to its positive charge, providing two distinct spin qubits. Here, several world-first experimental milestones in spin-based quantum information processing are reported. First, the readout of the electron spin is demonstrated in single-shot, using a silicon device which combines implanted phosphorus donors with a sensitive nanoscale electrometer. Then, the electron spin is coherently operated as a qubit by delivering on-chip microwave excitations. Combining the electron spin detection and control capabilities enables a quantum non-demolition measurement of the single 31P nuclear spin. Experiments yield exceptional nuclear readout fidelities - the highest for any solid-state qubit. Through an application of nuclear magnetic resonance, high-fidelity quantum control of the nuclear spin qubit is demonstrated. Finally, a single spin-bearing silicon nucleus (29Si) coupled to the electron spin is detected in single-shot and operated as a qubit. These results, along with the clear pathways identified for improving device performance, illustrate that single-atom electron and nuclear spin qubits in silicon constitute an excellent basis on which to construct a quantum computer.
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.
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.
The discovery of the quantum factorization algorithm more than a decade ago triggered intense interest in exploring possible physical realizations of quantum computers. Among the many solid state proposals, electron and nuclear spins in Si and group IV related materials have long coherence times and the capability of state preparation, gating and read-out using electric, magnetic and optical fields. Proposals involving silicon seek to take advantage of an existing mature technology and the implicit promise of scalability from solid state materials. Nevertheless, building such quantum systems depends in many cases on the development of fabrication techniques with nearly atomic precision. Managing decoherence, initialization and read-out in any quantum computer remains a daunting task. In this review we summarize proposals and recent developments relevant to the possible realization of a quantum computer constructed out of Si (or group IV) materials.
There is a worldwide race to build a computer which exploits the counterintuitive principles of quantum mechanics. Silicon is one of the most promising platforms for emerging quantum information technologies for two reasons: one, it possesses many of the key desirable criteria for low-error quantum information processing, and two, the microelectronics industry has decades of experience with producing ultrapure silicon and nanoscale silicon devices, which makes silicon-based quantum devices attractive for future commercial integration. This paper reviews a selection of silicon-based quantum computer design proposals, their technological requirements, and explores recent experimental progress towards their realisation.