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arXiv:1507.08468 · Physical review. B./Physical review. B

Long-range photon-mediated gate scheme between nuclear spin qubits in diamond

Adrian Auer, Guido Burkard

Published Jan 4, 2016• 12 citations
arXivHTMLPDF

Abstract

Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this process depends on the nuclear spin state of the nitrogen atom. If two NV centers are simultaneously coupled to a common cavity mode and individually excited, virtual cavity photon exchange can mediate an effective interaction between the nuclear spin qubits, conditioned on the spin state of both nuclei, which implements a universal controlled-$\mathit{Z}$ gate. We predict operation times below $10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which is four orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.

DOI
10.1103/physrevb.93.035402

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Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this process depends on the nuclear spin state of the nitrogen atom. If two NV centers are simultaneously coupled to a common cavity mode and individually excited, virtual cavity photon exchange can mediate an effective interaction between the nuclear spin qubits, conditioned on the spin state of both nuclei, which implements a universal controlled-Z\mathit{Z}Z gate. We predict operation times below 10\ensuremathμs10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}10\ensuremathμs, which is four orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.
While long spin coherence times and efficient single-qubit quantum control have been implemented successfully in nitrogen-vacancy (NV) centers in diamond, the controlled coupling of remote NV spin qubits remains challenging. Here, we propose and analyze a controlled-phase (cphase) gate for the spins of two NV centers embedded in a common optical cavity and driven by two off-resonant lasers. In combination with previously demonstrated single-qubit gates, cphase allows for arbitrary quantum computations. The coupling of the NV spin to the cavity mode is based upon Raman transitions via the NV excited states and can be controlled with the laser intensities and relative phase. We find characteristic laser frequencies at which the scattering amplitude of a laser photon into the cavity mode is strongly dependent on the NV center spin. A scattered photon can be reabsorbed by another selectively driven NV center and can generate a conditional phase (cphase) gate. Gate times around 200 ns are within reach, nearly two orders of magnitude shorter than typical NV spin coherence times of around 10 $\ensuremath{\mu}\mathrm{s}$. The separation between the two interacting NV centers is limited only by the extension of the cavity.
We propose a scheme to achieve nuclear-nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy (NV) center in diamond. Here we demonstrate two-qubit entangling gates and quantum-state transfer between two carbon nuclei in diamond. In such a system, the NV center interacts with a nearby nuclear spin via a dipole-dipole interaction. Under the quantum Zeno condition, the scheme is robust against decoherence caused by coupling between the NV center (nuclear spins) and the environment. Conveniently, precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center. Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication in a polygon geometry with each vertex occupied by a nuclear spin.
Motivated by the recent experimental progress in exploring the use of a nitrogen-vacancy (NV) center in diamond as a quantum computing platform, we propose schemes for fast and high-fidelity entangling gates on this platform. Using both analytical and numerical calculations, we demonstrate that synchronization effects between resonant and off-resonant transitions may be exploited such that spin-flip errors due to strong driving may be eliminated by adjusting the gate time or the driving field. This allows for fast, high-fidelity entangling operations between the electron spin and one or several nuclear spins. We investigate a two-qubit system where the NV center comprises a N 15 atom and a qubit-qutrit system for the case of a N 14 atom. In both cases, we predict a complete suppression of off-resonant driving errors for two-qubit gates when addressing the NV electron spin conditioned on states of nuclear spins of the nitrogen atom of the defect. Additionally, we predict fidelities > 0.99 for multiqubit gates when including the surrounding C 13 atoms in the diamond lattice in the conditioned logic.
This thesis describes a series of experiments on the control of the optical properties of the nitrogen-vacancy (NV) center in diamond, and on control of the electron and nuclear spin states associated with the NV center. The NV center is a fluorescing atomic defect center in diamond, consisting of a substitutional nitrogen atom adjacent to a vacancy in the diamond carbon lattice. The electron spin of the NV center can be initialized and read out optically, and coherently manipulated with high fidelity even at room temperature. This unique combination of properties has attracted much attention to the NV center in recent years for application in quantum information technologies. The experiments in this work focus on exploiting the intrinsic hybrid nature of the NV center. The NV center forms a hybrid spin register, as its electron spin is always coupled to the nuclear spin of its own nitrogen nucleus, and can furthermore be coupled to additional nuclear carbon-13 spins in the diamond. In addition, the electronic spin state can be mapped onto the state of a photon, in principle allowing long range transmission of quantum information and measurement-based entanglement of distant NV center registers. The long-term goal is to achieve a large scale quantum network where the different constituents each perform the task they are most well suited for: the stable nuclear spins store the quantum information, photons transfer quantum information over long distances, and the fast electron spin interfaces between spin and photon states. For measurement-based entanglement of distant NV centers it is of primary importance to maximize the emission and detection of coherent photons emitted by the NV center. Spontaneous emission can be controlled and enhanced by coupling an emitter to a photonic cavity. Chapters 3, 4, and 5 of this thesis describe experiments aimed at maximizing the coherent photon emission rate of an NV center by coupling the NV center to a photonic crystal cavity. One of the main challenges is to position a single NV center into the nanometer-sized cavity mode. Chapter 3 describes the development of a nanopositioning technique, which allows diamond nanocrystals ~50 nm in size containing single NV centers to be placed at arbitrary locations on a chip, with nanometer precision. By using a sharp etched tungsten tip, individual nanocrystals can be picked up, moved and placed under real-time imaging with an electron microscope. We explicitly demonstrate that the unique optical and spin properties of the NV center are conserved by the nanopositioning process. In chapter 4, we apply the nanopositioning technique to couple single NV centers contained in a diamond nanocrystals to gallium phosphide photonic crystal cavities. These cavities resonate in the visible with high quality factors, and are designed to have the lowest energy mode coincide with the zero-phonon line of the NV center. Efficient coupling is evidenced by a strong enhancement of NV center emission at the cavity wavelength. The high quality factor of a photonic crystal cavity is a result of careful design and fabrication. The introduction of a nanocrystal may therefore be expected to have a detrimental effect on the optical properties of a cavity. In chapter 5 we investigate the effect of a nanocrystal on the optical properties of photonic crystal cavities. Our simulations and measurements show that the effect of a nanocrystal is in fact only minor, a promising result for future work on cavity-QED systems in the solid state and with diamond defect centers in particular. Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Chapter 6 describes experiments that exploit quantum control of the NV center and recently developed dynamical decoupling techniques to study the properties of the surrounding bath of spins belonging to single substitutional nitrogen atoms. The coherence properties of a single NV center are affected by changes in the state of the bath spins, allowing a single NV center to be used as a probe to detect bath spin resonances and study the quantum dynamics of the spin bath. We use quantum control of the spin bath to extend the dephasing time of the NV center, important for the application of the NV center in DC magnetometry. In chapter 7 we describe the development and implementation of decoherence protected quantum gates for the hybrid spin register formed by the NV center electron spin that is coupled to the nuclear spin of its own nitrogen atom. Electron and nuclear spins evolve and decohere at vastly different rates, making it challenging to use such a hybrid system as a fully functional quantum register. We create a universal set of two-qubit quantum gates by integrating dynamical decoupling techniques into the gate operation. We demonstrate the power of our gate design by implementing for the first time Grover's quantum search algorithm on a solid-state spin register.
Abstract We propose a scheme to achieve nuclear–nuclear indirect interactions mediated by a mechanically driven nitrogen-vacancy (NV) center in a diamond. Here we demonstrate two-qubit entangling gates and quantum-state transfer between two carbon nuclei. When the dipole–dipole interaction strength is much larger than the driving field strength, the scheme is robust against decoherence caused by coupling between the NV center (nuclear spins) and the environment. Conveniently, precise control of dipole coupling is not required so this scheme is insensitive to fluctuating positions of the nuclear spins and the NV center. Our scheme provides a general blueprint for multi-nuclear-spin gates and for multi-party communication.
We propose efficient schemes for universal quantum gates with the photon polarization states and electron spin states of nitrogen-vacancy (NV) centers in diamond embedded in optical microcavity. A hybrid polarization-spin controlled-NOT gate and a two-qubit controlled phase gate between NV centers in separated cavities are demonstrated in the weak-coupling regime without complex devices or interaction. The gates presented here are deterministic and can be applied directly to a variety of quantum information processing tasks. The feasibility analyses show that our schemes can be accomplished with high fidelity under current technologies and have wide potential applications in quantum communication and computation fields.