Overcoming disorder in superconducting globally-driven quantum computing

TL;DR

The paper addresses the challenge of static disorder in a globally-controlled superconducting quantum computer implemented on a ladder architecture. It combines a detailed physical model of disorder in qubit frequencies and ZZ couplings with a GRAPE-based quantum optimal control framework to restore high-fidelity information flow and universal gate operations. The results show that optimized pulses can achieve fidelities exceeding 0.99 for single- and two-qubit gates and reliable information transport, even with realistic disorder, and that MPS-based GRAPE can substantially shorten operation times while maintaining accuracy. This work demonstrates the viability of globally-controlled superconducting processors and offers scalable control strategies that mitigate fabrication-induced imperfections.

Abstract

We study the impact of static disorder on a globally-controlled superconducting quantum computing architecture based on a quasi-two-dimensional ladder geometry [R. Menta et al., Phys. Rev. Research 7, L012065 (2025)]. Specifically, we examine how fabrication-induced inhomogeneities in qubit resonant frequencies and coupling strengths affect quantum state propagation and the fidelity of fundamental quantum operations. Using numerical simulations, we quantify the degradation in performance due to disorder and identify single-qubit rotations, two-qubit entangling gates, and quantum information transport as particularly susceptible. To address this challenge, we rely on pulse optimization schemes, and, in particular, on the GRAPE (Gradient Ascent Pulse Engineering) algorithm. Our results demonstrate that, even for realistic levels of disorder, optimized pulse sequences can achieve high-fidelity operations, exceeding 99.9% for the three quantum operations, restoring reliable universal quantum logic and robust information flow. These findings highlight pulse optimization as a powerful strategy to enhance the resilience to disorder of solid-state globally-driven quantum computing platforms.

Figures (11)

• Figure 1: Illustration of a 2D ladder globally driven quantum computing architecture. Three types of superconducting qubits, $A$, $B$, and $C$ (red, blue, and green squares), are driven by separate classical sources $V_{A,B,C}(t)$ (colored lines) and coupled via longitudinal ZZ interactions (black springs). Crossed squares indicate qubits with double Rabi frequency menta2024globallymenta2025building. Black triangles and circles denote local resonance frequency corrections. $B$- and $C$-type intra-row crossed qubits enable single-qubit gates, while the $A$-type inter-row crossed qubit enables two-qubit gates. The yellow-highlighted column marks the "information carrier column" (ICC), interfacing Néel ($|geg\rangle$) and Ferro ($|ggg\rangle$) phases. The first two columns form the initialization (INIT.) area and the last two form the read-out area. The figure corresponds to $N=2$ computational qubits quantum processor, and $15$ physical qubits.
• Figure 2: Fidelity w.r.t. disorder percentage:$\mathcal{F}(p,0) = \vert \langle \Psi_{\mathrm{target}}(p,0) | \Psi_{\mathrm{final}}(p,0) \rangle \vert$. Fidelity $\mathcal{F}(p, 0)$ as a function of static disorder percentage, computed using the RF+RWA drive Hamiltonian for $N = 2$ qubits and $\eta_{\rm BR} = 20$. Disorder is both in qubit frequencies ($\omega$) and couplings ($\zeta$), modeled as Gaussian noise with standard deviation $\epsilon \times \bar{\omega}$ and $\epsilon \times \bar{\zeta}$, respectively. The initial state is prepared on an $A$-type (solid blue) or $B$-type (solid green) ICC as $\vert \psi_{\mathrm{initial}} \rangle$. The solid pink line shows the fidelity under frequency disorder only. Results are averaged over $N_{\mathrm{samples}} \in \{200, 300\}$ disorder realizations. Due to the large energy scale separation, only the relative disorder percentage $\epsilon$ is plotted on the $x$-axis. ICC translation is performed using simultaneous $\pi$-pulses on $B$- and $C$-type qubits.
• Figure 3: Portions of the QPU simulated in the GRAPE setting. This figure illustrates the two architectures used for our GRAPE simulations. In the upper part (a), a single row of 7 qubits is shown, representing an $N=1$ QPU capable of executing both Information Flow protocols and single-qubit gates. In the lower part (b), the architecture for implementing a two-qubit gate is depicted. The two data qubits are shown in green, while the red crossed intrarow qubit is used to perform a Controlled-Z gate between them, following our protocol. Note that this portion of the QPU is quite similar to a 7 qubits IBM architecture called ibm_nairobiibm_nairobi.
• Figure 4: Resilience w.r.t. disorder perturbation. The $x$-axis represents the magnitude of the additional disorder applied to each resonant frequency (percentage of the perturbation w.r.t the static disorder $\delta\omega$ is in parentheses). For each point, we sample multiple disorder realizations and average the resulting fidelity. It is evident that even a small perturbation, on the order of $1$ MHz, leads to a dramatic drop in fidelity. Therefore, achieving high-resolution measurements of the static disorder within the chip is essential to obtain good fidelities.
• Figure 5: Summary plot. This plot shows the best result obtained for each operation. For improved resolution, we plot the infidelity $1-\overline{\mathcal{F}}$ on a logarithmic scale. The blue dots represent the fidelity error for the naive protocol in the presence of disorder, while the orange stars correspond to the error obtained using the pulse sequences optimized with the GRAPE algorithm. It is evident that GRAPE effectively mitigates the impact of static disorder, at least within our setting. Interestingly, the best fidelity is achieved for the two-qubit gate. This is because the protocol for this gate requires fewer pulses and only one species ($A$) is driven, making it less susceptible to static disorder.