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arXiv:2503.17147 · Applied Physics Letters

Suppression of coherent errors during entangling operations in NV centers in diamond

Regina Finsterhoelzl, Guido Burkard

Published Aug 18, 2025• 0 citations
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Abstract

We consider entangling operations in a single nitrogen-vacancy center in diamond where the hyperfine-coupled nuclear spin qubits are addressed with radio frequency pulses conditioned on the state of the central electron spin. Limiting factors for the gate fidelity are coherent errors due to off-resonant driving of neighboring transitions in the dense, hyperfine-split energy spectrum of the defect and non-negligible perpendicular hyperfine tensor components that narrow the choice of 13C nuclear spin qubits. We address these issues by presenting protocols based on synchronization effects that allow for a complete suppression of both error sources in state-of-the-art CNOT gate schemes. This is possible by a suitable choice of parameter sets that incorporate the error into the scheme instead of avoiding it. These results contribute to the recent progress toward scalable quantum computation with defects in solids.

DOI
10.1063/5.0268962

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We consider entangling operations in a single nitrogen-vacancy center in diamond where the hyperfine-coupled nuclear spin qubits are addressed with radio frequency pulses conditioned on the state of the central electron spin. Limiting factors for the gate fidelity are coherent errors due to off-resonant driving of neighboring transitions in the dense, hyperfine-split energy spectrum of the defect and non-negligible perpendicular hyperfine tensor components that narrow the choice of 13C nuclear spin qubits. We address these issues by presenting protocols based on synchronization effects that allow for a complete suppression of both error sources in state-of-the-art CNOT gate schemes. This is possible by a suitable choice of parameter sets that incorporate the error into the scheme instead of avoiding it. These results contribute to the recent progress toward scalable quantum computation with defects in solids.
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.
Individual nuclear spins in diamond can be optically detected through hyperfine couplings with the electron spin of a single nitrogen-vacancy (NV) center; such nuclear spins have outstandingly long coherence times. Among the hyperfine couplings in the NV center, the nearest neighbor 13C nuclear spins have the largest coupling strength. Nearest neighbor 13C nuclear spins have the potential to perform fastest gate operations, providing highest fidelity in quantum computing. Herein, we report on the control of coherences in the NV center where all three nearest neighbor carbons are of the 13C isotope. Coherence among the three and four qubits are generated and analyzed at room temperature.
Nitrogen-vacancy (NV) centers in diamond provide room-temperature electron-nuclear spin registers for quantum sensing and quantum information processing, with surrounding 13C nuclear spins serving as long-lived quantum memories. However, coherent control of large nuclear-spin registers is limited by finite electron-spin coherence and spectral addressability. Existing approaches follow two complementary strategies: dynamical-decoupling (DD) gates exploit filter-function resonances to realize selective conditional evolution but permit only discrete rotation angles, whereas dynamical-decoupling radio-frequency (DDrf) control restores continuous tunability at the cost of stringent hyperfine-geometry and RF-power requirements. Here, we introduce hybrid dynamical-decoupling and radio-frequency (H-DDrf) control, which preserves the DD-induced conditional evolution and employs a geometrically phase-matched RF drive to complete the target operation. This approach reduces both RF power and gate duration while maintaining high-fidelity control, thereby expanding the accessible 13C nuclear-spin register for room-temperature NV-based quantum memories and quantum processors.
Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid-state systems. Here we present a protocol that achieves a complete set of selective electron-nuclear gates and single nuclear rotations in such an ensemble in diamond facilitated by a nearby nitrogen-vacancy (NV) center. The protocol suppresses internuclear interactions as well as unwanted coupling between the NV center and other spins of the ensemble to achieve quantum gate fidelities well exceeding 99%. Notably, our method can be applied to weakly coupled, distant spins representing a scalable procedure that exploits the exceptional properties of nuclear spins in diamond as robust quantum memories.
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.
Abstract Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of CPMG and Uhrig sequences improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We provide analytical expressions for the sequence protocols and also show numerically the efficacy of our method on nitrogen-vacancy centers in diamond. Our results are broadly applicable to color centers weakly coupled to a small number of nuclear spin qubits.