Coherent Control of an NV - center and a nearby 13 C nuclear spin
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Coherent Control of an NV- center and a nearby 13C nuclear spin Burkhard Scharfenberger1, William J. Munro2,1 and Kae Nemoto1 1
National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan. 2 NTT Basic Research Labs, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan. ABSTRACT In this work, we numerically investigated the achievable fidelities when controlling an effective three-qubit system consisting of a NV- color center in diamond with a nearby strongly coupled 13C nuclear spin by means of microwave- and radio-frequency pulses in the experimentally attractive low magnetic field regime. We find that gates with straightforward square driving pulses do not achieve the fidelity currently required for the fault-tolerant quantum computing models. INTRODUCTION
While having been discovered much earlier, it is only in the last ten years or so, that negatively charged vacancy centers in diamond (NV-) have been under intense theoretical and experimental study, especially in the context of quantum information processing (QIP). Their main virtues are twofold: first, their energy level structure makes it possible to initialize and read out its spin degree of freedom by optical means (optical polarizability and spin-dependent fluorescence [1]) and second, they exhibit long decoherence times of the electronic spin [2], the longest of any currently known solid state system [3]. A further benefit making them interesting for QIP purposes is the presence of nuclear spin qubits in the vicinity coupling via hyperfine interaction to the electronic spin of the vacancy. It was recognized early on that they could be utilized as a quantum register [4], which since then has been realized in many experiments [5-10]. However, even though their dynamics are understood well enough on a theoretical level and they have been used in numerous proof-of-principle experiments, there is still no clear idea of the ultimate limits to their controllability in practice. Such knowledge would be of great value in order to properly assess NV centers’ use in applications such as quantum computing (QC), where a per-gate error rate on the order of 0.1% is targeted to be achieved. With this aim in mind, we numerically investigated the achievable fidelities under simulated microwave- and radio-frequency driving in an effective three-qubit system consisting of an NVcenter (vacancy electron and nitrogen nuclear spin) plus a nearby carbon 13C, where the vacancy spin remains in its ground state manifold during our operations. We studied two different strongly coupled 13C positions in a weak magnetic field of B=10-20G. This paper is structured as follows. In the theory section we will briefly introduce our model for the coherent as well as incoherent evolution of the system, we then describe the details of our study and present the main results before concluding in the last section.
THEORY The free time evolution of the system can be well described by the following effective spin model [11,12,13]: H NVC = SDS + B
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