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arXiv:1908.08443 · Physical review. B./Physical review. B

All-microwave holonomic control of an electron-nuclear two-qubit register in diamond

V. O. Shkolnikov, Roman Mauch, Guido Burkard

Published Apr 20, 2020• 11 citations
arXivHTMLPDF

Abstract

We present a theoretical scheme that allows one to perform a universal set of holonomic gates on a two-qubit register, formed by a $^{13}\mathrm{C}$ nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of $^{13}\mathrm{C}$ atoms allows one to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.

DOI
10.1103/physrevb.101.155306

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We present a theoretical scheme that allows one to perform a universal set of holonomic gates on a two-qubit register, formed by a 13C^{13}\mathrm{C}13C nuclear spin coupled to the electron spin of a nitrogen-vacancy center in diamond. Strong hyperfine interaction between the electron spin and the spins of the first three shells of 13C^{13}\mathrm{C}13C atoms allows one to operate the state of the register on the submicrosecond timescale using microwave pulses only. We describe the system and the operating regime analytically and numerically, as well as simulate the initialization protocols.
Abstract Spins in diamond are ideal for large-scale quantum processors and memories. Localized laser field offers spatial selectivity for electron spin manipulation through spin-obit coupling. However, it has been difficult to simultaneously achieve the precise and universal manipulation by itself. Here, we demonstrate microwave-driven holonomic quantum gates on an optically selected electron spin in a nitrogen-vacancy (NV) center in diamond. The electron spin is precisely manipulated with global microwave tuned to the frequency shift induced by the local optical Stark effect. We show the universality of the operations, including state initialization, preparation, readout, and echo. We also generate optically addressable entanglement between the electron and adjacent nitrogen nuclear spin, thus satisfying the scalability requirement of qubits. High fidelity operations are achieved by amplitude-alternating pulse, which are tolerant to fluctuations in microwave intensity and detuning. These techniques enable site-selective quantum teleportation transfer from a photon to a nuclear spin memory, paving the way for the realization of distributed quantum computers and the quantum Internet with large-scale quantum storage.
The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. In light of this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (about 80%) of 3-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate dark state with the qubits initial state hence decoherence of the multi-qubit system is well-controlled through a 0.33pi rotation. The electron return probability can exhibit spin-orbit coupling-like behavior as observed in topological materials based on the extra geometric phase.
The key challenge in experimental quantum information science is to identify isolated quantum mechanical systems with long coherence times that can be manipulated and coupled together in a scalable fashion. We describe the coherent manipulation of an individual electron spin and nearby individual nuclear spins to create a controllable quantum register. Using optical and microwave radiation to control an electron spin associated with the nitrogen vacancy (NV) color center in diamond, we demonstrated robust initialization of electron and nuclear spin quantum bits (qubits) and transfer of arbitrary quantum states between them at room temperature. Moreover, nuclear spin qubits could be well isolated from the electron spin, even during optical polarization and measurement of the electronic state. Finally, coherent interactions between individual nuclear spin qubits were observed and their excellent coherence properties were demonstrated. These registers can be used as a basis for scalable, optically coupled quantum information 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.
We show that arbitrary NNN-qubit interactions among nuclear spins can be achieved efficiently in solid state quantum platforms, such as nitrogen vacancy centers in diamond, by exerting control only on the electron spin coupled to the nuclei. This allows to exploit nuclear spins as robust quantum registers and the direct measurement of nuclear many-body correlators. The method takes advantage of recently introduced dynamical decoupling techniques and avoids the necessity of external, slow, control on the nuclei. Our protocol is general, being applicable to other nuclear spin-based platforms with electronic spin defects acting as mediators as silicon carbide.
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.