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Physical Review A

Fullerene-based electron-spin quantum computer

Wolfgang Harneit

Published Feb 27, 2002• 322 citations
Publisher

Abstract

We propose an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes. The key advantages are that electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy. Qubits are set and read out via pulsed electron-spin resonance. Addressing is provided by local magnetic fields or field gradients $(A$ gate). The qubit-qubit interaction is mediated by magnetic dipolar coupling and can be controlled via the direction of the magnetic field with respect to the distance vector of the qubits $(J$ gate). Molecular as well as solid-state architectures are discussed.

DOI
10.1103/physreva.65.032322

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We propose an alternative concept for a scalable spin quantum computer that combines aspects of other proposals with the advantageous features of endohedral fullerenes. The key advantages are that electron spins instead of nuclear spins are used and that the manipulation of fullerene molecules is fairly easy. Qubits are set and read out via pulsed electron-spin resonance. Addressing is provided by local magnetic fields or field gradients (A(A(A gate). The qubit-qubit interaction is mediated by magnetic dipolar coupling and can be controlled via the direction of the magnetic field with respect to the distance vector of the qubits (J(J(J gate). Molecular as well as solid-state architectures are discussed.
We propose a scalable design for a solid-state spin-based quantum computer. It uses endohedral fullerenes like N@C60\mathrm{N}@{\mathrm{C}}_{60}N@C60​ or P@C60,\mathrm{P}@{\mathrm{C}}_{60},P@C60​, which can be positioned on Si surfaces with a scanning tunneling microscope. Each logical qubit is stored in two physical qubits, corresponding to the nuclear and electronic spins. We discuss the addressing of individual qubits by a magnetic field gradient, and the implementation of one- and two-qubit quantum gates by sequences of radio-frequency and microwave pulses.
We present a scheme to perform universal quantum computation using global addressing techniques as applied to a physical system of endohedrally doped fullerenes. The system consists of an ABAB\mathcal{ABAB}ABAB linear array of group-V endohedrally doped fullerenes. Each molecule spin site consists of a nuclear spin coupled via a hyperfine interaction to an electron spin. The electron spin of each molecule is in a quartet ground state S=3/2.S=3/2.S=3/2. Neighboring molecular electron spins are coupled via a magnetic dipole interaction. We find that an all-electron construction of a quantum cellular automaton is frustrated due to the degeneracy of the electronic transitions. However, we can construct a quantum-cellular-automata quantum computing architecture using these molecules by encoding the quantum information on the nuclear spins while using the electron spins as a local bus. We deduce the NMR and ESR pulses required to execute the basic cellular automaton operation and obtain a rough figure of merit for the number of gate operations per decoherence time. We find that this figure of merit compares well with other physical quantum computer proposals. We argue that the proposed architecture meets well the first four DiVincenzo criteria and we outline various routes toward meeting the fifth criterion: qubit readout.
Electron spin resonance (ESR) experiments are used to assess the possibilities for processing quantum information in the electronic and nuclear spins of endohedral fullerenes. It is shown that ¹⁵N@C₆₀ can be used for universal two-qubit quantum computing. The first step in this scheme is to initialize the nuclear and electron spins that each store one qubit. This was achieved with a magnetic field of 8.6 T at 3 K, by applying resonant RF and microwave radiation. This dynamic nuclear polarization technique made it possible to show that the nuclear T₁ time of ¹⁵N@C����� is on the order of twelve hours at 4.2 K. The electronic T₂ is the limiting decoherence time for the system. At 3.7 K, this can be extended to 215 μs by using amorphous sulphur as the solvent. Pulse sequences are described that could perform all single-qubit gates to the two qubits independently, as well as CNOT gates. After these manipulations, the value of the qubits should be measured. Two techniques are demonstrated for this, by measuring the nuclear spin. Sc@C₈₂ could also be useful for quantum computation. By comparing ESR measurements with density functional theory calculations, it is shown how the orientation of a Sc@C₈₂ molecule in an applied magnetic field affects the molecule's Zeeman and hyperfine coupling. Hence the g- and A-tensors are written in the coordinate frame of the molecule. Pulsed ESR measurements show that the decoherence time at 20 K is 13 μs, which is 20 times longer than had been previously reported. Carbon nanotubes have been filled with endohedral fullerenes, forming 1D arrays that could lead to a scalable quantum computer. N@C₆₀ and Sc@C₈₂ have been used for this filling in various concentrations. ESR measurements of these samples are consistent with simulations of the dipolar coupling.
We propose to carry out two-qubit quantum gates with only one-step operations on endohedral fullerenes N@C60N@C_{60}N@C60​ or P@C60P@C_{60}P@C60​. The qubits are stored in electronic spin degrees of freedom of the doped atom NNN or PPP. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate is performed by a selective microwave pulse, and the two-qubit conditional phase gate is done by simultaneous radiation by two detuned microwaves. We will show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.
We propose a scheme to implement the two-qubit gates between the nuclear spins of the encapsulated atoms in endohedral fullerenes 15N@C60^{15}\mathrm{N}@{\mathrm{C}}_{60}15N@C60​ or 31P@C60^{31}\mathrm{P}@{\mathrm{C}}_{60}31P@C60​, within today's magnetic resonance techniques. Since there is no interaction between the nuclear spins, this scheme employs the electronic spins as medium and two swap operations are proposed to transfer the information between the nuclear spin 12\frac{1}{2}21​ and the electronic spin 32\frac{3}{2}23​, and between two electronic spins 32\frac{3}{2}23​. These two-qubit gates, along with the single-qubit rotation gates, compose a universal set of quantum gates in fullerene-based quantum computation.
We propose two potentially practical schemes to carry out two-qubit quantum gates on endohedral fullerenes N@C60\mathrm{N}@{\mathrm{C}}_{60}N@C60​ or P@C60\mathrm{P}@{\mathrm{C}}_{60}P@C60​. The qubits are stored in electronic spin degrees of freedom of the doped atom N or P. By means of the magnetic dipolar coupling between two neighboring fullerenes, the two-qubit controlled-NOT gate and the two-qubit conditional phase gate are performed by selective microwave pulses assisted by the refocusing technique. We will discuss the necessary additional steps for the universality of our proposal. We will also show that our proposal is useful for both quantum gating and the readout of quantum information from the spin-based qubit state.