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arXiv:1509.07365 · Physical Review B

Exact magnetic field control of nitrogen-vacancy center spin for realizing fast quantum logic gates

Wen-Qi Fang, Bang‐Gui Liu

Published Nov 30, 2015• 2 citations
arXivHTMLPDF

Abstract

The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin $z$-components of +1, 0, and \ensuremath{-}1. Without external field, the +1 and \ensuremath{-}1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and antisymmetrical superpositions of the +1 and \ensuremath{-}1 states as our qubit basis, we obtain the exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-dependent quantum two-level systems with exact analytical solutions. With our exact evolution operator of the NV center spin including three levels, we show that arbitrary qubits can be prepared from the starting 0 state, and arbitrary rapid quantum logic gates of these qubits can be realized with magnetic fields. In addition, it is made clear that the typical quantum logic gates can be accomplished within a few nanoseconds and the fidelity can be very high because only magnetic field strength needs to be controlled in this approach. These results should be useful to realizing quantum computing with the NV center spin systems in diamond and exploring other effects and applications.

DOI
10.1103/physrevb.92.174423

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The negatively charged nitrogen-vacancy (NV) center spin in diamond can be used to realize quantum computation and to sense magnetic fields. Its spin triplet consists of three levels labeled with its spin zzz-components of +1, 0, and \ensuremath{-}1. Without external field, the +1 and \ensuremath{-}1 states are degenerate and higher than the 0 state due to the zero-field splitting. By taking the symmetrical and antisymmetrical superpositions of the +1 and \ensuremath{-}1 states as our qubit basis, we obtain the exact evolution operator of the NV center spin under time-dependent magnetic field by mapping the three-level system on time-dependent quantum two-level systems with exact analytical solutions. With our exact evolution operator of the NV center spin including three levels, we show that arbitrary qubits can be prepared from the starting 0 state, and arbitrary rapid quantum logic gates of these qubits can be realized with magnetic fields. In addition, it is made clear that the typical quantum logic gates can be accomplished within a few nanoseconds and the fidelity can be very high because only magnetic field strength needs to be controlled in this approach. These results should be useful to realizing quantum computing with the NV center spin systems in diamond and exploring other effects and applications.
Abstract Fast quantum spin manipulation is needed to design spin-based quantum logic gates and other quantum applications. Here, we construct the exact evolution operator of the nitrogen-vacancy-center (NV) spin in diamond under external magnetic fields, and investigate the nonadiabatic geometric phases—both cyclic and non-cyclic—in these fast-manipulated NV spin systems. It is believed that the nonadiabatic geometric phases can be measured in future experiments, and that these fast quantum manipulations can be useful in designing spin-based quantum applications.
The development of quantum information in the last decades has opened new horizons in science and technology.It turns out that quantum physics, apart from playing a fundamental role in the structure of matter, also opens new opportunities for computation and communication, if one can harness the quantum superposition and entanglement.This started a new scientific challenge to find the platform that can offer two well isolated discrete levels (a qubit), that are a standard building block for many quantum devices, like bits are those for a classical computer.In this thesis we focus on one such platform, the negatively charged nitrogen-vacancy (NV -) center in diamond.It uses the triplet states of two fermionic spin-1/2 particles (holes) to encode the information.In order to build a working device, be it a quantum computer or a communication hardware, one needs to have a very good control over the quantum system.Usually, the NV -centers are controlled with the microwave magnetic field of an antenna, that is placed in the vicinity of the NV -.One of the issues we address in this thesis is whether we can replace the magnetic field with electric field or strain to control the system.We derive the corresponding coupling Hamiltonian and discuss the schemes to measure its parameters.Another approach we are investigating to simplify the control of an NV -based device is replacing the antenna magnetic field with spin-waves, that couple to the NV -centers.We show that for a magnetic material with low damping, the spin waves can propagate over very long distances with no dissipation and can provide the control of NV -centers even if the microwave antenna is far away and can not reach the center.We develop the theoretical formalism that allows to calculate the coupling enhancement, offered with this approach with respect to a pure antenna driving.Another essential ingredient of a quantum device is the ability to generate state superpositions and entanglement between different qubits.This is done by means of quantum gates, that must be performed with extremely high fidelity in order for the system to work.We investigate the possibility to perform geometric quantum gates, that are tolerant to certain types of errors, on the spin of NV -centers in diamond.We are interested in both adiabatic and non-adiabatic geometric quantum computation.Inspired by a recent observation of Berry phase with NV -centers, we develop an effective Hamiltonian description of adiabatic geometric gates, alternative to conventional Berry connection approach.For non-adiabatic geometric gates, we analyze the fidelities and error channels, when the gates are performed optically through the orbital excited state of the NV -centers.We also develop a scheme to apply all-microwave universal non-adiabatic geometric gates on small registers of coupled NV -and nuclear spins.Finally, we develop an entanglement protocol, that generates a universal two-qubit gate on two NV -centers, coupled to a common mode of a high Q cavity.We show that it is possible to implement this gate fast and at a fidelity, that is high enough to apply error-correction protocols.
A negatively charged nitrogen-vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits, and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.
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.
The spin-1 carried by the nitrogen-vacancy (NV${}^{\ensuremath{-}}$) color center of a diamond is a promising candidate as a quantum bit (qubit) for the realization of a solid-state quantum computer. The interaction with the P1P1P1 center, which is a single substitutional nitrogen atom with spin-12\frac{1}{2}21​, converts the NV${}^{\ensuremath{-}}$ qubit to a multilevel system. The 18-level energy diagram of the NV${}^{\ensuremath{-}}$-P1P1P1 coupled defect pair exhibits several level anticrossings and the spin functions change sign at different values of the applied magnetic field. Beyond each resonance, the two electronic spins of the coupled triplet-doublet system flip individually or in concert, offering possibilities to implement quantum logic gates. Interlevel transitions are also possible. The transition probabilities can be predicted rigorously in the framework of the Landau-Zener theory. The spin flip occurs by quantum tunneling. It is also possible to introduce geometric phases, which can be useful for the realization of phase gates.
Abstract A nitrogen-vacancy (NV) center in a diamond enables the access to an electron spin, which is expected to present highly sensitive quantum sensors. Although exploiting a nitrogen nuclear spin improves the sensitivity, manipulating it using a resonant pulse requires a long gate time owing to its small gyromagnetic ratio. Another technique to control nuclear spins is a conditional rotation gate based on dynamical decoupling, which is faster but unavailable for nitrogen spins owing to the lack of transverse hyperfine coupling with the electron spin. In this study, we generated effective transverse coupling by applying a weak off-axis magnetic field. An effective coupling depends on the off-axis field; the conditional rotation gate on the nitrogen-14 spins of an NV center was demonstrated within 4.2 μs under an 1.8% off-axis field and a longitudinal field of approximately 280 mT. We estimated that a population transfer from the electron to nitrogen spins can be implemented with 8.7 μs. Our method is applicable to an ensemble of NV centers, in addition to a single NV center.