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arXiv:2305.13132 · Quantum Science and Technology

Neural-network-designed three-qubit gates robust against charge noise and crosstalk in silicon

David W. Kanaar, J. P. Kestner

Published Apr 10, 2024• 6 citations
arXivHTMLPDF

Abstract

Abstract Spin qubits in semiconductor quantum dots are a promising platform for quantum computing, however, scaling to large systems is hampered by crosstalk and charge noise. Crosstalk here refers to the unwanted off-resonant rotation of idle qubits during the resonant rotation of the target qubit. For a three-qubit system with crosstalk and charge noise, it is difficult to analytically create gate protocols that produce three-qubit gates, such as the Toffoli gate, directly in a single shot instead of through the composition of two-qubit gates. Therefore, we numerically optimize a physics-informed neural network to produce theoretically robust shaped pulses that generate a Toffoli-equivalent gate. Additionally, robust π 2 X and Controlled-Z gates are also presented in this work to create a universal set of gates robust against charge noise. The robust pulses maintain an infidelity of 10−3 for average quasistatic fluctuations in the voltage of up to a few mV instead of tenths of mV for non-robust pulses.

DOI
10.1088/2058-9565/ad3d06

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Abstract Spin qubits in semiconductor quantum dots are a promising platform for quantum computing, however, scaling to large systems is hampered by crosstalk and charge noise. Crosstalk here refers to the unwanted off-resonant rotation of idle qubits during the resonant rotation of the target qubit. For a three-qubit system with crosstalk and charge noise, it is difficult to analytically create gate protocols that produce three-qubit gates, such as the Toffoli gate, directly in a single shot instead of through the composition of two-qubit gates. Therefore, we numerically optimize a physics-informed neural network to produce theoretically robust shaped pulses that generate a Toffoli-equivalent gate. Additionally, robust π 2 X and Controlled-Z gates are also presented in this work to create a universal set of gates robust against charge noise. The robust pulses maintain an infidelity of 10−3 for average quasistatic fluctuations in the voltage of up to a few mV instead of tenths of mV for non-robust pulses.
The fidelity of two-qubit gates using silicon spin qubits is limited by charge noise. When attempting to dynamically compensate for charge noise using single-qubit echo pulses, crosstalk can cause complications. We present a method of using a deep neural network to optimize the components of an analytically designed composite pulse sequence, resulting in a two-qubit gate robust against charge noise errors while also taking crosstalk into account. We analyze two experimentally motivated scenarios. For a scenario with strong electron dipole spin resonance driving and negligible crosstalk, the composite pulse sequence yields up to an order of magnitude improvement over a simple cosine pulse. In a scenario with moderate electron spin resonance driving and appreciable crosstalk such that simple analytical control fields are not effective, optimization using the neural network approach allows one to maintain order-of-magnitude improvement despite the crosstalk.
The potential of quantum computing is constrained by the susceptibility of qubits to noise and crosstalk during multi-qubit gate operations. Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, feasibility, and robustness against complex noise sources. Here we show a physics-guided neural control framework that generates robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation. By combining a hardware-aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, the framework steers the search toward smooth and physically realizable pulses while exploring high-dimensional control landscapes. Numerical simulations for the controlled-Z gate demonstrate superior fidelity and pulse smoothness compared to the Krotov and GRAPE baselines under matched constraints. The results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting physics-guided neural control as a route to robust control on near-term transmon devices. Quantum computers are highly sensitive to unwanted crosstalk between qubits, especially during multi-qubit gate operations. Here, the authors show that physics-guided neural control can generate smooth, hardware-compatible pulses that make two-qubit gates more robust against crosstalk.
The potential of quantum computing is fundamentally constrained by the inherent susceptibility of qubits to noise and crosstalk, particularly during multi-qubit gate operations. Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, experimental feasibility, and robustness against complex noise sources. In this manuscript, we propose a physics-guided neural control (PGNC) framework to generate robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation. By combining a hardware aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, PGNC steers the search toward smooth and physically realizable pulses while efficiently exploring high dimensional control landscapes. Numerical simulations for the CZ gate demonstrate superior fidelity and pulse smoothness compared to a Krotov baseline under matched constraints. Taken together, the results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting PGNC as a viable route to robust control on near-term transmon devices.
Semiconductor quantum dots provide a promising platform for spin qubit manipulation and quantum logic gate implementation, which are essential for scalable quantum computing architectures. In this work we utilize a variational quantum compiling algorithm to design efficient three-qubit gates using a time-independent Hamiltonian composed of only physical interaction terms. The resulting gates, including the Toffoli and Fredkin gates, demonstrate high fidelity and robustness against both coherent and incoherent noise sources, including charge and nuclear spin noise. This method is applicable to a wide range of physical systems, such as superconducting qubits and trapped ions, paving the way for more resilient and universal quantum computing architectures.
Exchange-only (EO) spin qubits in silicon realise all-electrical qubit control through pairwise Heisenberg exchange interactions, making them attractive for scalable quantum computation. Their principal vulnerability is charge noise, which couples multiplicatively to the exchange coupling and degrades gate fidelity. We present a \emph{two-stage} Physics-Informed Neural Network (PINN) framework for per-gate pulse optimisation. In \textbf{Stage~I} (iterations~1--100) the PINN maximises the noise-averaged gate fidelity toward a threshold of $\Fth=0.99$; the pulse duration is held fixed at its nominal hardware value. Once the threshold is crossed, \textbf{Stage~II} (iterations~101--250) progressively compresses the total pulse time while maintaining $F\geq\Fth$ via continuous fine-tuning of the pulse-shape parameters. The cost function is a Monte-Carlo ensemble mean-squared error (MSE) averaged over Nreal=2000N_{\rm real}=2000Nreal​=2000 quasi-static Gaussian noise realisations drawn fresh at every iteration. We benchmark the framework on the single-qubit gate set {X,Y,Z,H}\{X,Y,Z,H\}{X,Y,Z,H} and the two-qubit set {X,Y,Z,H,CX}\{X,Y,Z,H,\mathrm{CX}\}{X,Y,Z,H,CX} at noise levels $\sigmaJ/J\in\{1\%,5\%,10\%\}$. All single-qubit gates cross $\Fth$ within the first 100 iterations across all noise levels; Stage~II then reduces pulse durations by 20--40\% from their nominal values. The two-qubit gates follow the same two-phase behaviour, with the CX gate compressing from its nominal \SI{31}{\nano\second} to $\approx\SI{22}{\nano\second}$ at 1\% noise.
Composite pulses are essential for universal manipulation of singlet-triplet spin qubits. In the absence of noise, they are required to perform arbitrary single-qubit operations due to the special control constraint of a singlet-triplet qubit, while in a noisy environment, more complicated sequences have been developed to dynamically correct the error. Tailoring these sequences typically requires numerically solving a set of nonlinear equations. Here we demonstrate that these pulse sequences can be generated by a well-trained, double-layer neural network. For sequences designed for the noise-free case, the trained neural network is capable of producing almost exactly the same pulses known in the literature. For more complicated noise-correcting sequences, the neural network produces pulses with slightly different line shapes, but the robustness against noises remains comparable. These results indicate that the neural network can be a judicious and powerful alternative to existing techniques in developing pulse sequences for universal fault-tolerant quantum computation.