Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2411.18450 · Physical review. B./Physical review. B

Towards quantum error correction with two-body gates for quantum registers based on nitrogen-vacancy centers in diamond

Daniel Dulog, Martin Bodo Plenio

Published Feb 5, 2026• 0 citations
arXivHTMLPDF

Abstract

Color centers in diamond provide a possible hardware for quantum computation, where the most basic quantum information processing unit are nitrogen-vacancy (NV) centers, each in contact with adjacent carbon nuclear spins. With specifically tailored dynamical decoupling sequences, it is possible to execute selective, high-fidelity two-body gates between the electron spin of the NV center and a targeted nuclear spin. In this work, we present a method to determine the optimal execution time that balances the trade-off between fidelity and execution speed for gates generated by adaptive XY sequences. With these optimized gates, we use the nuclear spin environment as a code space for quantum error correction within a color center register.

DOI
10.1103/1fh4-l1g8

Related papers

Optimal control of fast and high-fidelity quantum gates with electron and nuclear spins of a nitrogen-vacancy center in diamond

Yi Chou, Shang‐Yu Huang, Hsi‐Sheng Goan

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.

arXiv:1504.06385•Physical Review A•May 15, 2015•40 citations

Universal high-fidelity quantum gates for spin qubits in diamond

Hans P. Bartling, Jiwon Yun, Kai-Niklas Schymik +8 more

Spins associated to solid-state color centers are a promising platform for investigating quantum computation and quantum networks. Recent experiments have demonstrated multiqubit quantum processors, optical interconnects, and basic quantum error-correction protocols. One of the key open challenges towards larger-scale systems is to realize high-fidelity universal quantum gates. In this work, we design and demonstrate a complete high-fidelity gate set for the two-qubit system formed by the electron and nuclear spin of a nitrogen-vacancy center in diamond. We use gate set tomography (GST) to systematically optimize the gates and demonstrate single-qubit gate fidelities of up to 99.999 ( 1 ) % and a two-qubit gate fidelity of 99.93 ( 5 ) % . Our gates are designed to decouple unwanted interactions and can be extended to other electron-nuclear spin systems. The high fidelities demonstrated provide opportunities towards larger-scale quantum processing with color-center qubits.

arXiv:2403.10633•Physical Review Applied•Mar 21, 2025•34 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

Noise-Resilient Quantum Computing with a Nitrogen-Vacancy Center and Nuclear Spins

Jorge Casanova, Z.-Y. Wang, Martin Bodo Plenio

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.

arXiv:1602.06862•Physical Review Letters•Sep 20, 2016•47 citations

Precise high-fidelity electron–nuclear spin entangling gates in NV centers via hybrid dynamical decoupling sequences

Wenzheng Dong, F A Calderon-Vargas, Sophia E Economou

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.

arXiv:2002.01480•New Journal of Physics•Jun 11, 2020•14 citations

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
Color centers in diamond provide a possible hardware for quantum computation, where the most basic quantum information processing unit are nitrogen-vacancy (NV) centers, each in contact with adjacent carbon nuclear spins. With specifically tailored dynamical decoupling sequences, it is possible to execute selective, high-fidelity two-body gates between the electron spin of the NV center and a targeted nuclear spin. In this work, we present a method to determine the optimal execution time that balances the trade-off between fidelity and execution speed for gates generated by adaptive XY sequences. With these optimized gates, we use the nuclear spin environment as a code space for quantum error correction within a color center register.
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.
Spins associated to solid-state color centers are a promising platform for investigating quantum computation and quantum networks. Recent experiments have demonstrated multiqubit quantum processors, optical interconnects, and basic quantum error-correction protocols. One of the key open challenges towards larger-scale systems is to realize high-fidelity universal quantum gates. In this work, we design and demonstrate a complete high-fidelity gate set for the two-qubit system formed by the electron and nuclear spin of a nitrogen-vacancy center in diamond. We use gate set tomography (GST) to systematically optimize the gates and demonstrate single-qubit gate fidelities of up to 99.999 ( 1 ) % and a two-qubit gate fidelity of 99.93 ( 5 ) % . Our gates are designed to decouple unwanted interactions and can be extended to other electron-nuclear spin systems. The high fidelities demonstrated provide opportunities towards larger-scale quantum processing with color-center qubits.
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.
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.
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.
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.