Molecular Realizations of Quantum Computing 2007

The following sections are included:

• PREFACE

• List of PARTICIPANTS

• CONTENTS

We review the working principle of a liquid-state Nuclear Magnetic Resonance (NMR) quantum computer where spins of nuclei in isolated molecules dissolved in a solvent work as qubits and they are controlled by radio frequency magnetic field pulses. Then, we show some of our recent experimental results, "generation and suppression of artificial decoherence" and "quantum teleportation without irreversible detection".

Superconducting flux qubits are attractive candidates for quantum bits because when properly operated they have quite good coherence properties. They are also flexible to fabricate. We describe how to achieve tunable coupling between such qubits in theory and experiment without sacrificing quantum coherence.

We discuss in detail the physics of single phase qubits, as well as building an elementary quantum information link between them by means of an on–chip transmission line cavity resonator. We present the experiment at NIST [Nature 449, 438 (2007)], where we experimentally demonstrated the ability to coherently transfer quantum states between two phase qubits through such a quantum bus.

Electrons with the spin quantum number 1/2, as physical qubits, have naturally been anticipated for implementing quantum computing and information processing (QC/QIP). Recently, electron spin-qubit systems in organic molecular frames have emerged as a hybrid spin-qubit system along with a nuclear spin-1/2 qubit. Among promising candidates for QC/QIP from the materials science side, the reasons for why electron spin-qubits such as molecular spin systems, i.e., unpaired electron spins in molecular frames, have potentialities for serving for QC/QIP will be given in the lecture (Chapter), emphasizing what their advantages or disadvantages are entertained and what technical and intrinsic issues should be dealt with for the implementation of molecular-spin quantum computers in terms of currently available spin manipulation technology such as pulse-based electron-nuclear double resonance (pulsed or pulse ENDOR) devoted to QC/QIP. Firstly, a general introduction and introductory remarks to pulsed ENDOR spectroscopy as electron-nuclear spin manipulation technology is given. Super dense coding (SDC) experiments by the use of pulsed ENDOR are also introduced to understand differentiating QC ENDOR from QC NMR based on modern nuclear spin technology. Direct observation of the spinor inherent in an electron spin, detected for the first time, will be shown in connection with the entanglement of an electron-nuclear hybrid system. Novel microwave spin manipulation technology enabling us to deal with genuine electron-electron spin-qubit systems in the molecular frame will be introduced, illustrating, from the synthetic strategy of matter spin-qubits, a key-role of the molecular design of g-tensor/hyperfine-(A-)tensor molecular engineering for QC/QIP. Finally, important technological achievements of recently-emerging CD ELDOR (Coherent-Dual ELectron-electron DOuble Resonance) spin technology enabling us to manipulate electron spin-qubits are described.

Fullerene C₆₀ is a molecule with a hollow space in its closed cage of sixty carbon atoms and able to accommodate atoms or molecules inside. Recently, the system of an electron spin coupled with a nuclear spin of a nitrogen atom trapped inside C₆₀ (N@C₆₀) has been demonstrated to be a possible qubit system for the implementation of quantum computation (QC) and quantum information processing (QIP). In the last decade, there has appeared an increasing number of reports for this molecule, on its magnetic properties, ideas for physical realization as quantum computers, and experimental approaches based on the magnetic resonance techniques. In this Chapter, the research areas on the topic on the fullerene-based QC/QIP are reviewed together with a relevant part of the fullerene stories. The production of N@C₆₀ in our research group is introduced.

We review recent progress in molecular magnets especially in the viewpoint of the application for quantum computing. After a brief introduction to single-molecule magnets (SMMs), a method for qubit manipulation by using non-equidistant spin sublevels of a SMM will be introduced. A weakly-coupled dimer of two SMMs is also a candidate for quantum computing, which shows no quantum tunneling of magnetization (QTM) at zero field. In the AF ring Cr₇Ni system, the large tunnel splitting is a great advantage to reduce decoherence during manipulation, which can be a possible candidate to realize quantum computer devices in future.

We reinvestigate a proposal for universal quantum gates in Kane's model, in which the assumption that electron spin is always downward. We demonstrate a considerable error appears in the spin-flip operations. The transition from the subspace for expressing a qubit to the irrelevant subspace occurs (i.e., a leakage error). We try to eliminate such an error by a composite pulse.

We introduce a conceptually reasonable framework of quantum simultaneous noncooperative bimatrix games with naturally-behaving game referees. Although an entangling operation arranged by a game referee is so far a commonly used tool to obtain an advantage over classical counterparts in the conventional formulation of quantum games, we should recall that the classical metagame theory introduced in 1960s resolves many dilemmas without introducing a special correlated system prepared by a game referee. We introduce a quantum metagame framework with which we can eliminate dilemmas under the metalevel one for certain games, without introducing an entangling operation.

The properties of continuous–variable teleportation of single–photon states are investigated. The output state is different from the input state due to the non–maximal entanglement in the EPR beams. The photon statistics of the teleportation output are determined and the correlation between the field information β obtained in the teleportation process and the change in photon number is discussed. The results of the output photon statistics are applied to the transmission of a qubit encoded in the polarization of a single photon. The information encoded in the polarization of a single photon can be transferred to a remote location by two–channel continuous variable quantum teleportation. However, the finite entanglement used in the teleportation causes random changes in photon number. If more than one photon appears in the output, the continuous variable teleportation accidentally produces clones of the original input photon. In this paper, it derives the polarization statistics of the N–photon output components and shows that they can be decomposed into an optimal cloning term and completely unpolarized noise. It is found that the accidental cloning of the input photon is nearly optimal at experimentally feasible squeezing levels, indicating that the loss of polarization information is partially compensated by the availability of clones.