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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fast donor-based electron spin quantum computing

Charles D. Hill, Lloyd C. L. Hollenberg, Austin G. Fowler, Cameron J. Wellard, Andrew D. Greentree, Hsi‐Sheng Goan

Published Feb 23, 2005• 0 citations
Publisher

Abstract

We propose a scheme for electron spin quantum computing based on electron spin in semiconductors. This scheme shares many similarities with the existing Kane nuclear spin proposal. We show how quantum computation may be carried out in this proposal, including single qubit rotations and CNOT gate. We show how this control can potentially lead to gate speeds 100-1000 times faster than the existing nuclear spin proposal, and up to 106 times faster than a typical electron spin dephasing time, T2(e).

DOI
10.1117/12.583200

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We propose a scheme for electron spin quantum computing based on electron spin in semiconductors. This scheme shares many similarities with the existing Kane nuclear spin proposal. We show how quantum computation may be carried out in this proposal, including single qubit rotations and CNOT gate. We show how this control can potentially lead to gate speeds 100-1000 times faster than the existing nuclear spin proposal, and up to 106 times faster than a typical electron spin dephasing time, T2(e).
We propose a scheme for quantum information processing based on donor electron spins in semiconductors, with an architecture complementary to the original Kane proposal. We show that a na\"{\i}ve implementation of electron spin qubits provides only modest improvement over the Kane scheme, however through the introduction of global gate control we are able to take full advantage of the fast electron evolution timescales. We estimate that the latent clock speed is 100--1000 times that of the nuclear spin quantum computer with the ratio T2∕Tops{T}_{2}∕{T}_{\mathrm{ops}}T2​∕Tops​ approaching the 106{10}^{6}106 level.
We combine elements of the 1998 quantum computing proposals by Privman, Vagner and Kventsel, and by Kane, with the new idea of nuclear-spin qubit interactions mediated indirectly via the bound outer electrons of impurity atoms whose nuclear spins 1/2 are the qubits. These electrons, in turn, interact via the two-dimensional electron gas in the quantum Hall effect regime. The resulting quantum computing scheme retains all the gate-control and measurement aspects of the proposal by Kane, but allows qubit spacing at distances of order 100 nm, attainable with the present-day semiconductor-heterostructure device technologies.
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.
Quantum physics governs the world at the microscopic scale and determines the properties of matter. While classical computers exploit quantum phenomena passively by relying on transistor technology, the concept of a quantum computer with active control over quantum states promises unprecedented possibilities for information encoding and processing. Already developed quantum algorithms are known to perform certain tasks faster than any existing classical algorithms, and quantum computers also promise the possibility for precise simulations of complex quantum systems, a task infeasible for classical computers. These points emphasize the need for the development of quantum computers. Considering quantum computers, the fundamental unit of information is a qubit, a two-level quantum system. Qubits, in contrast to classical bits which are either in state 0 or 1, can exist in quantum superposition of the states 0 and 1, allowing for more complex and parallel computations. While there are many options to encode a logical qubit in a physical system, spin 1/2 particles are considered a natural choice because their spin degree of freedom defines a qubit intrinsically. Semiconductors are a promising platform for hosting spin qubits, as they enable the confinement of electrons with spin 1/2 either through gate-defined quantum dots (QDs) or donor atoms. Among the possible choices of donor atoms, phosphorous 31P is particularly noteworthy because its nucleus has nuclear spin 1/2. Nuclear spins are prime candidates for qubit implementation because they demonstrated exceptionally long coherence times, but the underlying good isolation from their environment is a challenge when it comes to readout and control. In this thesis, we face this challenge by proposing a hybrid quantum dot-donor (QDD) system consisting of a gate defined silicon (Si) QD and a thereto laterally displaced 31P phosphorous donor atom implanted in the Si host material. A single electron is presumed to be confined in the system, which can be moved between the QD and the donor on demand. If its wave function overlaps with the donor atom, electron spin and the donor nuclear spin interact via the hyperfine interaction and the electron can act as a mediator between the nuclear spin qubit and the environment for readout and control, whereas the nuclear spin qubit can be set in an idling mode by shifting the electron to the QD. Importantly, the proposed system can be embedded in circuit quantum electrodynamics (cQED) architectures enabling strong coupling between the system’s electron spin and microwave resonator photons. This coupling is fundamental for the research presented in this thesis. Analyzing the envisioned system, we first propose a novel method for nuclear-spin readout by probing the resonator transmission. This method is based on the observation that the signature of strong electron spin-photon coupling in the resonator transmission is altered due to the hyperfine interaction, in such a manner that well separated signatures for the electron spin-photon coupling conditioned on the state of the nuclear spin arise. As the next step, we turn our attention to the control of nuclear spin qubits and especially to the challenge of realizing a two-qubit gate between distant nuclear spins. In this course, we derive an effective nuclear spin-photon coupling. While expected to be weak, this interaction can be harnessed to couple the nuclear spins of two distant QDD systems dispersively to a microwave resonator resulting in an entangling nuclear spin two-qubit √iSWAP gate with a gate fidelity approaching 90%. These two key findings represent a significant and valuable contribution to the field of quantum information processing using nuclear spins.
Nuclear-spin qubit interactions in a heterostructure can be mediated via the bound outer electrons of impurity atoms whose nuclear spins 1/2 are the qubits. These outer electrons, in turn, interact via the two-dimensional electron gas in the quantum Hall effect regime. We devised a quantum computing scheme, based on this mechanism, with qubit separation of order 0.1 µm, attainable with the present-day semiconductor device technologies, and retaining all the gate-control and measurement aspects of earlier nuclear-spin quantum computing proposals.
We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broadband optical pulses to rotate electron spins and provide the clock signal to the system. Nonlocal two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.