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arXiv:1303.0021 · Physical Review B

Two-qubit quantum gates for defect qubits in diamond and similar systems

Dmitry Solenov, Sophia E. Economou, T. L. Reinecke

Published Oct 15, 2013• 6 citations
arXivHTMLPDF

Abstract

We propose a fast, scalable all-optical design for arbitrary two-qubit operations for defect qubits in diamond (nitrogen-vacancy centers) and in silicon carbide, which are promising candidates for room temperature quantum computing. The interaction between qubits is carried out by microcavity photons. The approach uses constructive interference from higher energy excited states activated by optical control. In this approach the cavity mode remains off-resonance with the directly accessible optical transitions used for initialization and readout. All quantum operations are controlled by near-resonant narrow-bandwidth optical pulses. We perform full quantum numerical modeling of the proposed gates and show that high-fidelity operations can be obtained with realistic parameters.

DOI
10.1103/physrevb.88.161403

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We propose a fast, scalable all-optical design for arbitrary two-qubit operations for defect qubits in diamond (nitrogen-vacancy centers) and in silicon carbide, which are promising candidates for room temperature quantum computing. The interaction between qubits is carried out by microcavity photons. The approach uses constructive interference from higher energy excited states activated by optical control. In this approach the cavity mode remains off-resonance with the directly accessible optical transitions used for initialization and readout. All quantum operations are controlled by near-resonant narrow-bandwidth optical pulses. We perform full quantum numerical modeling of the proposed gates and show that high-fidelity operations can be obtained with realistic parameters.
Defect based qubit systems like the nitrogen vacancy center in diamond have recently emerged as promising candidates for quantum technologies due to their combination of long coherence times, room temperature operation, and robust optical interface. In order to realize many of their proposed applications, defect qubits must be incorporated into scalable devices architectures consisting of photonic, mechanical, or electrical degrees of freedom. Despite much recent progress, many challenges remain for diamond growth and device fabrication. As an alternate approach, we engaged in a search for nitrogen vacancy center analogues in alternative materials with the hope of obtaining a greater degree of control over defect and material properties. Ultimately, we discovered that divacancy-related point defects in all three of the most common forms of silicon carbide- termed 4H, 6H, and 3C- act as analogues to the nitrogen vacancy center in diamond. We chose to focus our research primarily on defects in 3C silicon carbide (termed 'Ky5' defects) because of its availability as a single crystal heteroepitaxial thin film grown on silicon, an advantage that greatly facilitates the fabrication of functional devices. We characterized the spin and optical properties of Ky5 defects in thin film geometries and observed many similarities to the nitrogen vacancy center. We performed the first measurements of spin dynamics in 3C silicon carbide and demonstrate coherent control of defect spins up to room temperature and observe coherence times of up to 22 microseconds. To demonstrate their use in real devices, we designed, fabricated, and characterized photonic crystal cavities in 3C silicon carbide thin films with mode volumes of less than (lambda/n)^3 and Q's as high as 1,500 with integrated Ky5 defects. Additionally, we performed simulations and analysis of the fabricated structures using observed structural imperfections to determine that the Q's are likely limited primarily by the non-vertical structure sidewall angle. Despite the modest Q's of these structures, they can be utilized to generate large local field intensities to enhance optical interactions with Ky5 qubit states within the cavities. We accomplish this by performing cavity enhanced photoluminescence excitation spectroscopy on cavity modes tuned to the zero phonon line of the defects and observe large (as high as 30 times) increases in the luminescence and optically detected magnetic resonance signals originating from the defect states and approximately 2x faster rates of ground state spin initialization. In addition, we use these techniques to probe the photoluminescence dynamics of the Ky5 defects' optical pumping cycle, perform excitation wavelength dependent studies of spin and spectral inhomogeneity, and use the small mode volume and narrowband photoluminescence enhancements of the cavities to observe spectrally distinct subensembles of defects with linewidths as narrow as 25 GHz within the inhomogeneously broadened zero phonon line. Although much is still unknown regarding the properties of these defects, they show great promise as a candidate system for defect qubit based quantum devices and technologies.
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.
Implementations for quantum computing require fast single- and multiqubit quantum gate operations. In the case of optically controlled quantum dot qubits, theoretical designs for long-range two- or multiqubit operations satisfying all the requirements in quantum computing are not yet available. We have developed a design for a fast, long-range two-qubit gate mediated by a photonic microcavity mode using excited states of the quantum-dot-cavity system that addresses these needs. This design does not require identical qubits, it is compatible with available optically induced single-qubit operations, and it advances opportunities for scalable architectures. We show that the gate fidelity can exceed 90% in experimentally accessible systems.
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 $10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which is four orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.
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.
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.