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High-Fidelity Electron Spin Gates in a Scalable Diamond Quantum Registers

Timo Joas, Florian Ferlemann, Roberto Sailer, Philipp J. Vetter, J. Zhang, R. S. Said, Tokuyuki Teraji, Onoda Shinobu, Tommaso Calarco, G. Genov, Matthias M. Müller, Fedor Jelezko

Published May 1, 2025• 0 citations
OpenAlex

Abstract

Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen vacancy (NV) electron spins. Entanglement between dipolar-coupled NV spin pairs has been demonstrated, but with a limited entanglement fidelity and its error sources have not been characterized. Here, we design and implement a robust, easy to implement entangling gate between NV spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of F=(96.0±2.5) % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.

Related papers

High-Fidelity Electron Spin Gates for Scaling Diamond Quantum Registers

Timo Joas, Florian Ferlemann, Roberto Sailer +9 more

Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen-vacancy (NV) electron spins enabling scalable entanglement. Entanglement between dipolar-coupled NV spin pairs has been demonstrated but with a limited fidelity, and its error sources have not been characterized. Here, we design and implement a robust two-qubit gate between NV electron spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of F 2 q = ( 96.0 ± 2.5 ) % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.

arXiv:2406.04199•Physical Review X•May 27, 2025•11 citations

High-fidelity two-qubit gates in a 7-qubit register for quantum networks

Margriet van Riggelen, Jiwon Yun, H. Benjamin van Ommen +1 more

Quantum networks based on optically active solid-state spins may enable quantum technologies including long-range quantum communication and distributed quantum computing. Network nodes containing multiple high-fidelity qubits can facilitate large-scale fault-tolerant operation. However, the stringent error thresholds remain out of reach for multi-qubit registers. In this work, we demonstrate high-fidelity two-qubit gates in a 7-qubit register, based on nuclear spins coupled to a nitrogen-vacancy (NV) center in diamond. We analyze crosstalk in highly connected spin systems, develop an efficient optimization procedure, and characterize the gates using gate set tomography. The two-qubit gate fidelities (best: 99.61(5)%, average: 99.18(2)%) demonstrate a multi-qubit register at the threshold for distributed quantum computation. Finally, as an example application, we perform a variational quantum eigensolver (VQE) simulation of the ground-state energy of H2 and LiH molecules. These results demonstrate one of the key prerequisites for scalable quantum networks based on solid-state spins.

quant-pharXiv:2606.14847•Jun 16, 2026•0 citations

Quantum error correction with spins in diamond

Julia Cramer

Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.

•Jan 1, 2016•1 citation

High-fidelity entangling gates for electron and nuclear spin qubits in diamond

Regina Finsterhoelzl, Wolf-Rüdiger Hannes, Guido Burkard

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.

arXiv:2403.11553•Physical review. B./Physical review. B•Jun 3, 2025•6 citations

Efficient creation of dipolar coupled nitrogen-vacancy spin qubits in diamond

I Jakobi, S A Momenzadeh, F Fávaro de Oliveira +6 more

Coherently coupled pairs or multimers of nitrogen-vacancy defect electron spins in diamond have many promising applications especially in quantum information processing (QIP) but also in nanoscale sensing applications. Scalable registers of spin qubits are essential to the progress of QIP. Ion implantation is the only known technique able to produce defect pairs close enough to allow spin coupling via dipolar interaction. Although several competing methods have been proposed to increase the resulting resolution of ion implantation, the reliable creation of working registers is still to be demonstrated. The current limitation are residual radiation-induced defects, resulting in degraded qubit performance as trade-off for positioning accuracy. Here we present an optimized estimation of nanomask implantation parameters that are most likely to produce interacting qubits under standard conditions. We apply our findings to a well-established technique, namely masks written in electron-beam lithography, to create coupled defect pairs with a reasonable probability. Furthermore, we investigate the scaling behavior and necessary improvements to efficiently engineer interacting spin architectures.

arXiv:1610.00924•Journal of Physics Conference Series•Sep 1, 2016•29 citations

Single-gate, multipartite entanglement on a room-temperature quantum register

Joseph Minnella, Mathieu Ouellet, Amelia R. Klein +1 more

Multipartite entanglement is an essential aspect of quantum systems, needed to execute quantum algorithms, implement error correction and achieve quantum-enhanced sensing. In solid-state quantum registers such as nitrogen-vacancy centres in diamond, entangled states are typically created using sequential, pairwise gates between the central electron and individual nuclear qubits. This sequential approach is slow and suffers from crosstalk errors. Here we demonstrate a parallelized multi-qubit entangling gate to generate a four-qubit Greenberger-Horne-Zeilinger state using a room-temperature nitrogen-vacancy centre in only 14.8 μs-ten times faster than that using sequences of two-qubit gates and close to the fundamental limit set by the hyperfine coupling frequencies. Parallel three-qubit gates are also realized with all-nuclear-qubit subsets. The entangled states are verified by measuring multiple quantum coherences. The four-qubit parallel gate has a fidelity of 0.92(4), whereas the sequential four-qubit gate fidelity is only 0.69(3). The approach is generalizable to other solid-state platforms, and it lays the foundation for scalable generation and control of entanglement in practical devices.

arXiv:2508.08465•Nature Nanotechnology•Sep 14, 2026•1 citation
Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen vacancy (NV) electron spins. Entanglement between dipolar-coupled NV spin pairs has been demonstrated, but with a limited entanglement fidelity and its error sources have not been characterized. Here, we design and implement a robust, easy to implement entangling gate between NV spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of F=(96.0±2.5) % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.
Diamond is a promising platform for quantum information processing as it can host highly coherent qubits that could allow for the construction of large quantum registers. A prerequisite for such devices is a coherent interaction between nitrogen-vacancy (NV) electron spins enabling scalable entanglement. Entanglement between dipolar-coupled NV spin pairs has been demonstrated but with a limited fidelity, and its error sources have not been characterized. Here, we design and implement a robust two-qubit gate between NV electron spins in diamond and quantify the influence of multiple error sources on the gate performance. Experimentally, we demonstrate a record gate fidelity of F 2 q = ( 96.0 ± 2.5 ) % under ambient conditions. Our identification of the dominant errors paves the way towards NV-NV gates beyond the error correction threshold.
Quantum networks based on optically active solid-state spins may enable quantum technologies including long-range quantum communication and distributed quantum computing. Network nodes containing multiple high-fidelity qubits can facilitate large-scale fault-tolerant operation. However, the stringent error thresholds remain out of reach for multi-qubit registers. In this work, we demonstrate high-fidelity two-qubit gates in a 7-qubit register, based on nuclear spins coupled to a nitrogen-vacancy (NV) center in diamond. We analyze crosstalk in highly connected spin systems, develop an efficient optimization procedure, and characterize the gates using gate set tomography. The two-qubit gate fidelities (best: 99.61(5)%, average: 99.18(2)%) demonstrate a multi-qubit register at the threshold for distributed quantum computation. Finally, as an example application, we perform a variational quantum eigensolver (VQE) simulation of the ground-state energy of H2 and LiH molecules. These results demonstrate one of the key prerequisites for scalable quantum networks based on solid-state spins.
Digital information based on the laws of quantum mechanics promisses powerful new ways of computation and communication. However, quantum information is very fragile; inevitable errors continuously build up and eventually all information is lost. Therefore, realistic large-scale quantum information processing requires the protection of quantum bits (qubits) against errors. In this thesis we present the experimental implementation of quantum error correction protocols based on spins in diamond. In such protocols, a quantum state is protected against errors by encoding in multiple qubits. Errors can be detected and corrected by measurement of correlations, so-called stabilizer-measurements, on these qubits.The experimental work presented in this thesis employs multiple spins in diamond as qubits to explore and implement error correction protocols. The nitrogen-vacancy (NV) centre in diamond is a lattice defect consisting of a nitrogen atom (N) and a vacancy (V) on two adjacent diamond lattice sites. This defect effectively results in an electronic spin that can be addressed as a qubit. The spin state can be manipulated by microwave fields and optically read out. At liquid helium temperatures (cryogenic temperature, ~4 K = -269 C), the NV electron spin provides high-fidelity single-shot readout and long coherence times.The NV centre is surrounded by naturally available (1.1% abundance) nuclear C13 spins. As the number of spins that are close enough to the NV centre to be strongly coupled is limited, we employ the weakly coupled nuclear spins in the spin bath of the NV centre. Using dynamical decoupling techniques these nuclear spins can be detected via the NV electron spin through the hyperfine interaction. The nuclear spins are long-lived and robust against optical excitation of the NV electron spin, which can make these spins a robust quantum register for quantum error correction.In Ch. 4 we demonstrate universal control over multiple of such weakly coupled nuclear C13 spins in the environment of the NV centre at ambient temperatures. We demonstrate initialization, control and read-out of individual nuclear spins. Finally, we implement a quantum error correction protocol by encoding a quantum state in the NV electron spin and two nuclear spins. Errors are detected by un-encoding the quantum state back to the electron spin and correction via a double controlled operation.For universal fault-tolerant quantum computations it is essential that the quantum information remains encoded at all times. In Ch. 5 we present multiple rounds of quantum error correction and active feedback on a continuously encoded qubit at cryogenic temperatures. A quantum state is protected by encoding in three weakly coupled spins. Errors are detected via high-fidelity non-demolition readout of the NV electron spin and actively corrected using fast classical electronics. We demonstrate that an actively error-corrected qubit is robust against phase flip errors and show that a superposition state can live longer than the best physical qubit in the encoding.The presented methods and results can be extended to a range of future experiments. In Ch. 6 we propose the implementation of five-qubit quantum error correction, the smallest code to correct for general single-qubit errors on the physical qubits in the encoding, by extending the experimental methods as developed in Chs. 4&5. Besides the exploration and development of larger error correction protocols and fault-tolerant quantum computing, the presented quantum register based in spins in diamond can be employed as a quantum node and combined with recent advances in the realization of quantum entanglement over large distances to form quantum networks. These networks can be used to study both fundamental questions as well as future applications in quantum information technology.
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.
Coherently coupled pairs or multimers of nitrogen-vacancy defect electron spins in diamond have many promising applications especially in quantum information processing (QIP) but also in nanoscale sensing applications. Scalable registers of spin qubits are essential to the progress of QIP. Ion implantation is the only known technique able to produce defect pairs close enough to allow spin coupling via dipolar interaction. Although several competing methods have been proposed to increase the resulting resolution of ion implantation, the reliable creation of working registers is still to be demonstrated. The current limitation are residual radiation-induced defects, resulting in degraded qubit performance as trade-off for positioning accuracy. Here we present an optimized estimation of nanomask implantation parameters that are most likely to produce interacting qubits under standard conditions. We apply our findings to a well-established technique, namely masks written in electron-beam lithography, to create coupled defect pairs with a reasonable probability. Furthermore, we investigate the scaling behavior and necessary improvements to efficiently engineer interacting spin architectures.
Multipartite entanglement is an essential aspect of quantum systems, needed to execute quantum algorithms, implement error correction and achieve quantum-enhanced sensing. In solid-state quantum registers such as nitrogen-vacancy centres in diamond, entangled states are typically created using sequential, pairwise gates between the central electron and individual nuclear qubits. This sequential approach is slow and suffers from crosstalk errors. Here we demonstrate a parallelized multi-qubit entangling gate to generate a four-qubit Greenberger-Horne-Zeilinger state using a room-temperature nitrogen-vacancy centre in only 14.8 μs-ten times faster than that using sequences of two-qubit gates and close to the fundamental limit set by the hyperfine coupling frequencies. Parallel three-qubit gates are also realized with all-nuclear-qubit subsets. The entangled states are verified by measuring multiple quantum coherences. The four-qubit parallel gate has a fidelity of 0.92(4), whereas the sequential four-qubit gate fidelity is only 0.69(3). The approach is generalizable to other solid-state platforms, and it lays the foundation for scalable generation and control of entanglement in practical devices.