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arXiv:quant-ph/0205135 · Physical Review A

Decoupling-free NMR quantum computer on a quantum spin chain

Atsushi Goto, Tadashi Shimizu, Kenjiro Hashi, Hideaki Kitazawa, Shinobu Ohki

Published Feb 28, 2003• 24 citations
arXivHTMLPDF

Abstract

We propose a decoupling-free nuclear-spin quantum computer installed on a quantum electron spin chain with a singlet ground state and a finite spin gap. Qubits are $I=1/2$ nuclear spins implanted periodically along the quantum spin chain. A magnetic field gradient is applied parallel to the chain, which allows individual access to each qubit. A single-qubit operation (rotation gate) is realized with the rf field tuned to the nuclear Larmor frequency at the qubit of interest, while a two-qubit operation (controlled-NOT gate) is achieved using the Suhl-Nakamura interaction through a packet of triplet magnons, which are excited by a microwave tuned to the spin gap energy $(SN$ gate). The interaction can be switched off by turning off the microwave, and a decoupling-free quantum computer is realized. The initialization is achieved with an optical pumping qubit initializer, which has a multilayered structure of the quantum spin chain and a semiconductor. Spin polarizations created by the optical pumping in the semiconducting layers are transferred to the spin chain layers through a cross polarization and a spin diffusion. The scheme allows us to separate the initialization process from the computation, enabling us to optimize the latter independently of the former.

DOI
10.1103/physreva.67.022312

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We propose a decoupling-free nuclear-spin quantum computer installed on a quantum electron spin chain with a singlet ground state and a finite spin gap. Qubits are I=1/2I=1/2I=1/2 nuclear spins implanted periodically along the quantum spin chain. A magnetic field gradient is applied parallel to the chain, which allows individual access to each qubit. A single-qubit operation (rotation gate) is realized with the rf field tuned to the nuclear Larmor frequency at the qubit of interest, while a two-qubit operation (controlled-NOT gate) is achieved using the Suhl-Nakamura interaction through a packet of triplet magnons, which are excited by a microwave tuned to the spin gap energy (SN(SN(SN gate). The interaction can be switched off by turning off the microwave, and a decoupling-free quantum computer is realized. The initialization is achieved with an optical pumping qubit initializer, which has a multilayered structure of the quantum spin chain and a semiconductor. Spin polarizations created by the optical pumping in the semiconducting layers are transferred to the spin chain layers through a cross polarization and a spin diffusion. The scheme allows us to separate the initialization process from the computation, enabling us to optimize the latter independently of the former.
A new NMR quantum computer scheme based on semiconductor nanostructures is discussed theoretically. We also propose using an infrared laser as a new independent instrument for manipulating qubits. Methods of single- and many-qubit gate realization are discussed. Resonant transfer of the electron to several quantum dots helps in implementing complex many-qubit gates. The energy spectrum of the spin-qubit system is obtained. This variant of a quantum computer is simpler to control and more coherent. The distance between qubits and hence the structural requirements are more achievable using modern nanotechnology.
Quantum computers are machines that exploit the quantum mechanical properties of physical systems to realize an exponential speed-up in problem-solving capability compared with existing computers. Existing schemes for the realization of such machines occur in diverse areas such as atomic physics, nuclear magnetic resonance, superconductivity, quantum optics and solid state physics. We are concerned here with the experimental realization of various elements needed for quantum information processing using nuclear spin immersed in a confined electronic system in the quantum Hall regime. Some distinguishing characteristics of this approach include the application of the Overhauser effect for dynamic nuclear polarization at relatively high temperatures, spin measurement using relatively simple electrical detection techniques, spin control with microwave/radio frequency methods, the utilization of the electronic spin exciton as a possible mobile spin transfer mechanism for the eventual realization of a logic gate, and the application of semiconductor technology to device integration. Concepts involved in this approach are also illustrated with experimental results.
Schemes for the nuclear spin quantum memory are proposed based on a system composed of two electrons or one electron coupled to a single nuclear spin in isotopically purified group-IV elemental and II-VI compound semiconductors. The qubit consists of the singlet state and one of the triplet states of two electrons or simply of an electron spin. These systems are free from the decoherence due to the nuclear dipole-dipole interaction and are advantageous for the long memory time. In the case of two electrons, the protocol for the quantum state transfer between the electron-spin qubit and the nuclear spin qubit is based on the magnetic or electric field tuning of the singlet-triplet state crossing and on the hyperfine coupling supplemented with a well-defined scheme to initialize the nuclear spin. In the case of a single-electron qubit, the quantum state transfer is driven by the hyperfine interaction itself without the need of the nuclear spin initialization. Many practical systems are considered, e.g., two electrons loaded on a Si or ZnSe quantum dot, a single-electron charged state in a Si quantum dot doped with a P atom, a single-electron charged 28Si^{28}\text{S}\text{i}28Si quantum dot doped with an isotope atom of 29Si^{29}\text{S}\text{i}29Si, and a localized electron system of Si:P and ZnSe:F in the bulk crystal. General aspects of these systems are investigated and a comparison of merits and demerits is made between the two-electron qubit and the single-electron qubit.
A solid-state quantum computer conventionally requires the control lines for each qubit to operate individually. This makes quantum circuits complicated, especially in multi-qubit systems. Here we propose a simple single-qubit operation in a superconducting flux-qubit chain without control lines in an analogy of the Nuclear Magnetic Resonance (NMR) imaging technique. A superconducting flux qubit can be regarded as an artificial atom with spin 1/2 that can be manipulated by an external magnetic field. To identify the location of each qubit in the qubit chain, a static field gradient is introduced along the qubit chain. This magnetic field gradient causes differences in the Zeeman frequencies of each separate qubit. This allows a large number of distinct qubits to be individually addressed. Single-qubit operations are then possible when the external electromagnetic frequency is adjusted to the resulting energy-level separation of the target qubit.