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arXiv:2512.05322

Highly resilient, error-protected quantum gates in a solid-state quantum network node

E. Poem, M. I. Cohen, S. Blum, D. Minin, D. Korn, O. Heifler, S. Maayani, A. Hamo, I. Bayn, N. Bar-Gill, M. Tordjman

quant-phSubmitted Dec 4, 2025• Announced Dec 8, 2025• 0 citations
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Abstract

High-fidelity quantum gates are a cornerstone of any quantum computing and communications architecture. Realizing such control in the presence of realistic errors at the level required for beyond-threshold quantum error correction is a long-standing challenge for all quantum hardware platforms. Here we theoretically develop and experimentally demonstrate error-protected quantum gates in a solid-state quantum network node. Our work combines room-temperature randomized benchmarking with a new class of composite pulses that are simultaneously robust to frequency and amplitude, affecting random and systematic errors. We introduce Power-Unaffected, Doubly-Detuning-Insensitive Gates (PUDDINGs) -- a theoretical framework for constructing conditional gates with immunity to both amplitude and frequency errors. For single-qubit and two-qubit CNOT gate demonstrations in a solid-state nitrogen-vacancy (NV) center in diamond, we systematically measure an improvement in the error per gate up to a factor of 9. By projecting the application of PUDDING to cryogenic temperatures we show a record two-qubit error per gate of $1.2 \times 10^{-5}$, corresponding to a fidelity of $99.9988\%$, far below the thresholds required by surface and color code error correction. These results present viable building blocks for a new class of fault-tolerant quantum networks and represent the first experimental realization of error-protected conditional gates in solid-state systems.

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35 pages, 9 figures

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High-fidelity quantum gates are a cornerstone of any quantum computing and communications architecture. Realizing such control in the presence of realistic errors at the level required for beyond-threshold quantum error correction is a long-standing challenge for all quantum hardware platforms. Here we theoretically develop and experimentally demonstrate error-protected quantum gates in a solid-state quantum network node. Our work combines room-temperature randomized benchmarking with a new class of composite pulses that are simultaneously robust to frequency and amplitude, affecting random and systematic errors. We introduce Power-Unaffected, Doubly-Detuning-Insensitive Gates (PUDDINGs) -- a theoretical framework for constructing conditional gates with immunity to both amplitude and frequency errors. For single-qubit and two-qubit CNOT gate demonstrations in a solid-state nitrogen-vacancy (NV) center in diamond, we systematically measure an improvement in the error per gate up to a factor of 9. By projecting the application of PUDDING to cryogenic temperatures we show a record two-qubit error per gate of 1.2×10−51.2 \times 10^{-5}1.2×10−5, corresponding to a fidelity of 99.9988%99.9988\%99.9988%, far below the thresholds required by surface and color code error correction. These results present viable building blocks for a new class of fault-tolerant quantum networks and represent the first experimental realization of error-protected conditional gates in solid-state systems.
Quantum computation provides great speedup over its classical counterpart for certain problems. One of the key challenges for quantum computation is to realize precise control of the quantum system in the presence of noise. Control of the spin-qubits in solids with the accuracy required by fault-tolerant quantum computation under ambient conditions remains elusive. Here, we quantitatively characterize the source of noise during quantum gate operation and demonstrate strategies to suppress the effect of these. A universal set of logic gates in a nitrogen-vacancy centre in diamond are reported with an average single-qubit gate fidelity of 0.999952 and two-qubit gate fidelity of 0.992. These high control fidelities have been achieved at room temperature in naturally abundant (13)C diamond via composite pulses and an optimized control method.
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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.
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Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
Quantum computing has the potential to transform information technology by offering algorithms for certain tasks, such as quantum simulation, that are vastly more efficient than what is possible with any classical device. But experimentally implementing practical quantum information processing is a very difficult task. Here we study two important, and closely related, aspects of this challenge: architectures for quantum computing, and quantum error correction Exquisite quantum control has now been achieved in small ion traps, in nitrogen-vacancy centres and in superconducting qubit clusters, but the challenge remains of how to scale these systems to build practical quantum devices. In Part I of this thesis we analyse one approach to building a scalable quantum computer by networking together many simple processor cells, thus avoiding the need to create a single complex structure. The difficulty is that realistic quantum links are very error prone. Here we describe a method by which even these error-prone cells can perform quantum error correction. Groups of cells generate and purify shared resource states, which then enable stabilization of topologically encoded data. Given a realistically noisy network (10% error rate) we find that our protocol can succeed provided that all intra-cell error rates are below 0.8%. Furthermore, we show that with some adjustments, the protocols we employ can be made robust also against high levels of loss in the network interconnects. We go on to analyse the potential running speed of such a device. Using levels of fidelity that are either already achievable in experimental systems, or will be in the near-future, we find that employing a surface code approach in a highly noisy and lossy network architecture can result in kilohertz computer clock speeds. In Part II we consider the question of quantum error correction beyond the surface code. We consider several families of topological codes, and determine the minimum requirements to demonstrate proof-of-principle error suppression in each type of code. A particularly promising code is the gauge color code, which admits a universal transversal gate set. Furthermore, a recent result of Bombin shows the gauge color code supports an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a decoder and investigating its performance. We simulate fault-tolerant error correction with the gauge color code, and estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.