We investigate the theoretically achievable fidelities when coherently controlling an effective three-qubit system consisting of a negatively charged nitrogen vacancy ( 15 NV − ) center in diamond with an additional nearby carbon 13 C spin via square and two frequency component radio and microwave frequency pulses in different magnetic field regimes. Such a system has potentially interesting applications in quantum information-related tasks such as distributed quantum computation or quantum repeater schemes. We find that the best fidelities can be achieved in an intermediate magnetic field regime. However, with only square pulses it will be challenging to reach the fidelity threshold(s) predicted by current models of fault-tolerant quantum computing.
We investigate the theoretically achievable fidelities when coherently controlling an effective three-qubit system consisting of a negatively charged nitrogen vacancy ( 15 NV − ) center in diamond with an additional nearby carbon 13 C spin via square and two frequency component radio and microwave frequency pulses in different magnetic field regimes. Such a system has potentially interesting applications in quantum information-related tasks such as distributed quantum computation or quantum repeater schemes. We find that the best fidelities can be achieved in an intermediate magnetic field regime. However, with only square pulses it will be challenging to reach the fidelity threshold(s) predicted by current models of fault-tolerant quantum computing.
The NV-center in diamond is a promising system for quantum information processing. The typical qubits are the electron spin in the NV-center and the surrounding 13C nuclear spins. Fast and precise control of many 13C spins is desirable but challenging due to crosstalk. Crosstalk is the unwanted effect of a control pulse on the other qubits. The coupled NV-13C system is explored, and numerical techniques to optimize the control of multiple and single qubits are used. In this report the effect of the Bloch-Siegert shift in the weak driving regime is investigated first. This is done by studying the effect of a π-pulse when two carbon qubits are driven at the same time on resonance. It turns out that in this weak driving regime the effect of the off resonance is very small, and changes the fidelity not more than 0.3%. Furthermore the effect of a square πpulse on 4 nearby qubits is studied. If the pulse is not optimized (thus square), the pulse cannot be done in less than 100µs while retaining at least 99% fidelity. By optimizing the envelope of the driving field using constrained optimization the pulse can be done in 22µs while retaining at least 99% fidelity.
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.
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.
With its long coherence times and comparatively simple optical accessibility, already the `bare' NV-center has an interesting potential in quantum computing related applications. Although a number of experiments have already been conducted using NV centers with one or more13C nearby, fidelities achieved are limited not only by experimental inaccuracies but a lack of theoretical understanding of the system dynamics. We seek to redress this by fully modeling the NVC systems behaviour in the ground state manifold, including all hyperfine interactions (between N and V as well as C and V) and dissipation.
Microwave control of the negatively charged nitrogen-vacancy (NV) defect in diamond is usually based on a two-level approximation of its ground state that is only valid in the regime of high bias magnetic fields or low microwave power. We present the NV-ERC technique, which has demonstrated efficient initialization and readout of the double quantum transition with no leakage to any third level, thanks to an effective Raman coupling. The protocol may be used in the low-field regime and for high-frequency sensing. Furthermore, we propose a scheme to perform fast single-qubit gates in the double quantum transition, consisting of pulse trains of constant frequency and intensity. We analyze its robustness with respect to pulse-timing errors resulting from inaccurate identification of system parameters or phase-control limitations. We also demonstrate that the technique can be implemented in the presence of unknown electric or strain fields.
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.