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arXiv:1808.10015 · Physical Review A

Single-photon heralded two-qubit unitary gates for pairs of nitrogen-vacancy centers in diamond

Chenxu Liu, M. V. Gurudev Dutt, David Pekker

Published Nov 27, 2018• 5 citations
arXivHTMLPDF

Abstract

The implementation of a high-fidelity two-qubit quantum logic gate remains an outstanding challenge for isolated solid-state qubits such as nitrogen-vacancy (NV) centers in diamond. In this work, we show that by driving pairs of NV centers to undergo photon scattering processes that flip their qubit states simultaneously, we can achieve a unitary two-qubit gate conditioned upon a single photon-detection event. Further, by exploiting quantum interference between the optical transitions of the NV centers' electronic states, we realize the existence of two special drive frequencies: a ``magic'' point where the spin-preserving elastic scattering rates are suppressed and a ``balanced'' point where the state-flipping scattering rates are equal. We analyzed four different gate operation schemes that utilize these two special drive frequencies, and various combinations of polarizations in the drive and collection paths. Our theoretical and numerical calculations show that the gate fidelity can be as high as 98%. The proposed unitary gate, combined with available single-qubit unitary operations, forms a universal gate set for quantum computing.

DOI
10.1103/physreva.98.052342

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The implementation of a high-fidelity two-qubit quantum logic gate remains an outstanding challenge for isolated solid-state qubits such as nitrogen-vacancy (NV) centers in diamond. In this work, we show that by driving pairs of NV centers to undergo photon scattering processes that flip their qubit states simultaneously, we can achieve a unitary two-qubit gate conditioned upon a single photon-detection event. Further, by exploiting quantum interference between the optical transitions of the NV centers' electronic states, we realize the existence of two special drive frequencies: a magic'' point where the spin-preserving elastic scattering rates are suppressed and a balanced'' point where the state-flipping scattering rates are equal. We analyzed four different gate operation schemes that utilize these two special drive frequencies, and various combinations of polarizations in the drive and collection paths. Our theoretical and numerical calculations show that the gate fidelity can be as high as 98%. The proposed unitary gate, combined with available single-qubit unitary operations, forms a universal gate set for quantum computing.
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.
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.
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.
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.
Heralded universal quantum gates can largely decrease the quantum resource consumed in the integration of a multiqubit quantum circuit. Here, we present a scheme for heralded universal quantum computing, including the construction of the CNOT gate, Fredkin gate, and Toffoli gate on the electron spins in diamond nitrogen-vacancy (NV) centers assisted by low- Q microtoroidal resonators. These quantum gates can achieve unity fidelity, as the infidelity induced by the imperfect input–output process is transferred into photon loss. The clicks on different single-photon detectors can either herald the success of the quantum gates or instruct an immediate recycling procedure, even without reinitializing the NV centers. Besides the heralding, this scheme is also more realistic, observing that the non-monochromatic auxiliary photon and the inhomogeneous NV centers have no adverse impact on fidelity. The high fidelity and efficiency with experimental parameters show that the scheme is feasible with current technology.
Hybrid quantum gates hold great promise for quantum information processing since they preserve the advantages of different quantum systems. Here we present compact quantum circuits to deterministically implement controlled-NOT, Toffoli, and Fredkin gates between a flying photon qubit and diamond nitrogen-vacancy (NV) centers assisted by microcavities. The target qubits of these universal quantum gates are encoded on the spins of the electrons associated with the diamond NV centers and they have long coherence time for storing information, and the control qubit is encoded on the polarizations of the flying photon and can be easily manipulated. Our quantum circuits are compact, economic, and simple. Moreover, they do not require additional qubits. The complexity of our schemes for universal three-qubit gates is much reduced, compared to the synthesis with two-qubit entangling gates. These schemes have high fidelities and efficiencies, and they are feasible in experiment.