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Journal of Materials Chemistry

Molecular electron-spin quantum computers and quantum information processing: pulse-based electron magnetic resonance spin technology applied to matter spin-qubits

Kazunobu Sato, Shigeaki Nakazawa, Robabeh Rahimi, Tomoaki Ise, Shinsuke Nishida, Tomohiro Yoshino, Nobuyuki Mori, Kazuo Toyota, Daisuke Shiomi, Yumi Yakiyama, Yasushi Morita, Masahiro Kitagawa, Kazuhiro Nakasuji, Mikio Nakahara, Hideyuki Hara, Patrick J. Carl, Peter Höfer, Takeji Takui

Published Jan 1, 2009• 152 citations
Publisher

Abstract

Pulse-based Electron–Nuclear and ELectron–electron DOuble Resonance (ENDOR/ELDOR) techniques have been applied to molecular spins in order to implement ensemble electron spin-qubit based quantum computers/computing (QC) and quantum information processing (QIP) in the solid state. Pulsed ENDOR-based QC/QIP experiments for super dense coding (SDC) have for the first time been carried out by the use of molecular electron- and nuclear-spin entities such as the stable malonyl radical as matter spin-qubits. The spin-qubit manipulation technology for quantum gate operations in this work is based on the time-proportional-phase-increment (TPPI) technique, enabling us to distinguish between the phases of spin-qubit based entangled states. The TPPI technique, as firstly applied by Mehring et al. (M. Mehring, J. Mende and W. Scherer, Phys. Rev. Lett., 2003, 90, 153001), has illustrated the establishment of quantum entanglement between electron- and nuclear-spin states and mutual interconversion between the electron–nuclear Bell states. The electron-spin 4π-periodicity in phase shows up in the QC/QIP experiments, explicitly and experimentally illustrating the electron-spin spinor nature for the first time. Tripartite QC experiments have been made, showing the occurrence of separable states. Also, the development of novel electron-spin technology to manipulate multi-electron spin-qubits is described. In this work, the pulsed coherent-dual ELDOR for QC/QIP has for the first time been implemented by invoking a novel microwave dual phase-rotation technique. Thus, applications of the coherent-dual ELDOR to molecular electron spin-qubit systems are also discussed, emphasising designing the molecular two electron-qubit systems appropriate for QC/QIP. g- and/or hyperfine A-tensor engineering approaches give us the two- and multi-electron-qubit systems, which have been a materials challenge to implement matter spin-qubit based QC/QIP. The targeted matter spin-qubits can be used to facilitate selective resonant microwave excitations achieved by the pulsed ELDOR technique. In addition to DiVincenzo's five criteria, general requisites for scalable electron spin-qubit systems as 1D periodic robust spin structures are described. According to the requisites, double- or triple-stranded helicates embedding open-shell metal cations are proposed instead of organic molecular spin-qubits.

DOI
10.1039/b819556k

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Pulse-based Electron–Nuclear and ELectron–electron DOuble Resonance (ENDOR/ELDOR) techniques have been applied to molecular spins in order to implement ensemble electron spin-qubit based quantum computers/computing (QC) and quantum information processing (QIP) in the solid state. Pulsed ENDOR-based QC/QIP experiments for super dense coding (SDC) have for the first time been carried out by the use of molecular electron- and nuclear-spin entities such as the stable malonyl radical as matter spin-qubits. The spin-qubit manipulation technology for quantum gate operations in this work is based on the time-proportional-phase-increment (TPPI) technique, enabling us to distinguish between the phases of spin-qubit based entangled states. The TPPI technique, as firstly applied by Mehring et al. (M. Mehring, J. Mende and W. Scherer, Phys. Rev. Lett., 2003, 90, 153001), has illustrated the establishment of quantum entanglement between electron- and nuclear-spin states and mutual interconversion between the electron–nuclear Bell states. The electron-spin 4π-periodicity in phase shows up in the QC/QIP experiments, explicitly and experimentally illustrating the electron-spin spinor nature for the first time. Tripartite QC experiments have been made, showing the occurrence of separable states. Also, the development of novel electron-spin technology to manipulate multi-electron spin-qubits is described. In this work, the pulsed coherent-dual ELDOR for QC/QIP has for the first time been implemented by invoking a novel microwave dual phase-rotation technique. Thus, applications of the coherent-dual ELDOR to molecular electron spin-qubit systems are also discussed, emphasising designing the molecular two electron-qubit systems appropriate for QC/QIP. g- and/or hyperfine A-tensor engineering approaches give us the two- and multi-electron-qubit systems, which have been a materials challenge to implement matter spin-qubit based QC/QIP. The targeted matter spin-qubits can be used to facilitate selective resonant microwave excitations achieved by the pulsed ELDOR technique. In addition to DiVincenzo's five criteria, general requisites for scalable electron spin-qubit systems as 1D periodic robust spin structures are described. According to the requisites, double- or triple-stranded helicates embedding open-shell metal cations are proposed instead of organic molecular spin-qubits.
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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.
The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.
The enormous theoretical potential of Quantum Information Processing (QIP) is driving the pursuit for its practical realization by various physical techniques. Currently Nuclear Magnetic Resonance (NMR) has been the forerunner by demonstrating a majority of quantum algorithms. In NMR, spin systems consisting of coupled nuclear spins are utilized as qubits. In order to carry out QIP, a spin system has to meet two major requirements: (i) qubit addressability and (ii) mutual coupling among the qubits. It has been demonstrated that the magnitude of the mutual coupling among qubits can be increased by orienting the spin-systems in a liquid crystal matrix and utilizing the residual dipolar couplings. While utilizing residual dipolar couplings may be useful to increase the number of qubits, nuclei of same species (homonuclei) might become strongly coupled. In strongly coupled spin-systems, spins loose their individual identity of being qubits. We propose that even such strongly coupled spin-systems can be used for QIP and the qubit-manipulation can be achieved by transition-selective pulses. We demonstrate experimental preparation of pseudopure states, creation of maximally entangled states, implementation logic gates and implementation of Deutsch-Jozsa (DJ) algorithm in strongly coupled 2,3 and 4 spin systems. The energy levels of the strongly coupled 3 and 4 spin systems were obtained by using a Z-COSY experiment.