Parallel Quantum Gates via Scalable Subsystem-Optimized Robust Control

TL;DR

This work reduces the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost and effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates.

Abstract

Accurate and efficient implementation of parallel quantum gates is crucial for scalable quantum information processing. However, the unavoidable crosstalk between qubits in current noisy processors impedes the achievement of high gate fidelities and renders full Hilbert-space control optimization prohibitively difficult. Here, we overcome this challenge by reducing the full-system optimization to crosstalk-robust control over constant-sized subsystems, which dramatically reduces the computational cost. Our method effectively eliminates the leading-order gate operation deviations induced by crosstalk, thereby suppressing error rates. Within this framework, we construct analytical pulse solutions for parallel single-qubit gates and numerical pulses for parallel multi-qubit operations. We validate the proposed approach numerically across multiple platforms, including coupled nitrogen-vacancy centers, a nuclear-spin processor, and superconducting-qubit arrays with up to 200 qubits. As a result, the noise scaling is reduced from exponential to linear for parallel single-qubit gates, and an order-of-magnitude reduction is achieved for parallel multi-qubit gates. Moreover, our method does not require precise knowledge of crosstalk strengths and makes no assumption about the underlying qubit connectivity or lattice geometry, thereby establishing a scalable framework for parallel quantum control in large-scale quantum architectures.

Figures (4)

• Figure 1: Schematic diagram of the subsystem-optimized robust control for designing parallel quantum gates. (a) Physically, it is reasonable to assume that each quantum gate acts on a single subsystem, with weak crosstalk between subsystems. The system can thus be divided into $L$ subsystems (blue shaded), each governed by a Hamiltonian $H_{S_k}$, with inter-subsystem crosstalk described by $H_{S_kS_j}$. (b) Subsystem-optimized robust control performs pulse optimization on each subsystem pair $S_k$ and $S_j$ for realizing $\bar{U}_{S_k}\otimes \bar{U}_{S_j}$, rather than the full system. Specifically, it maximizes the crosstalk-free fidelity $f_{S_k}f_{S_j}$ while minimizing the directional derivative $f_{S_k S_j}$ associated with the variation in $H_{S'_k}+H_{S'_j}$ along the direction $H_{S_k S_j}$.
• Figure 2: Implementation of parallel single-qubit $R_y(\pi)$ gates on coupled NV centers. (A) Dipolar coupled NV centers with homogeneous coupling strengths $g$. (B) Geometric trajectories $\theta_k, \theta_j$ and the corresponding robust control fields $u_k, u_j$ for each subsystem pair $(k,j)$. For $N$ coupled NV centers, $u_k$ and $u_j$ are applied in an alternating manner to the electron spins. For comparison, the primitive rectangular pulse $u_p$ (blue lines) is also demonstrated, which is applied to each electron spin identically. (C) Gate fidelities $F$ versus the coupling strength $g$ for different number of subsystems $L$. The dashed lines indicate the fidelity threshold of 0.99. (D) Gate fidelities $F$ as a function of the number of repeated parallel gates $M$. The pentagon markers denote the linear-fit results, while the square markers represent the exponential-fit results.
• Figure 3: Implementation of parallel single-qubit $R_x(\pi/2)$ and parallel CNOT gates on a 12-qubit NMR processor. (A) Molecular structure of the NMR sample, divided into four yellow-shaded subsystems, each containing three spins. (B) Representative quantum circuit with parallel single-qubit and parallel CNOT gates acting on designated spins. (C) Gate fidelities $F$ versus the number of subsystems $L$, comparing our robust pulse (red lines) with the primitive pulse (blue lines) that does not account for crosstalk between subsystems. The dashed lines indicate the fidelity threshold of 0.99. (D) Gate fidelities $F$ versus the number of repeated parallel gates $M$. Both of the pentagon and square markers denote the exponential-fit results.
• Figure 4: Implementation of parallel CZ gates on superconducting qubit arrays. (A) Schematic and coupling types of the qubit arrays. The qubit idling frequencies are set to a high band (red, $\omega_{ki}/2\pi \approx 6.15~\mathrm{GHz}$) or a low band (orange, $\omega_{ki}/2\pi \approx 5.85~\mathrm{GHz}$), each with variations within $\pm 0.15~\mathrm{GHz}$. The anharmonicity is set to $\alpha_{ki}/2\pi\approx -265~\mathrm{MHz}$ with small device-level variations (within $\pm10~\mathrm{MHz}$). The intra-subsystem coupling is fixed at $J_k/2\pi\approx 24~\mathrm{MHz}$ with fluctuations below $\pm2~\mathrm{MHz}$. Nearest-neighbor couplings are sampled within $2|g_{\max}|~\mathrm{MHz}$, while next-nearest and more distant couplings lie within $|g_{\max}|~\mathrm{MHz}$. These parameter ranges follow typical values reported in the literature google2023suppressingPhysRevX.11.021058PhysRevApplied.16.054020PRXQuantum.3.020301. (B) Fidelity $F$ of parallel CZ gates as a function of the maximum coupling strength $g_{\max}$ under primitive (blue lines) and robust (red lines) pulses. The dashed lines indicate the fidelity threshold of 0.99. (C) Corresponding control waveforms applied to each subsystem for the case $L=4$. (D) Block fidelity $F_4$ versus the number of CZ gates $L$ under different control pulses, where $g_{\max}=0.8~$MHz. The dotted reference line corresponds to assumed subsystem fidelities of 0.998. For all the cases, the creation and annihilation operators are truncated to the lowest two energy levels. All error bars show variability across twenty independent runs of random coupling fluctuations.