🔬 mesoscale physics

Micromagnet engineering for enhanced addressability of donor-cluster arrays in silicon

This paper presents a scalable silicon quantum processor architecture that integrates STM-defined phosphorus donor-cluster arrays with optimized on-chip micromagnets to generate magnetic field gradients, thereby enabling the independent frequency-addressing of over 120 atomic spin qubits via a single microwave antenna and overcoming the bottlenecks of hyperfine interaction randomness.

Original authors: Hao Wang, Baolong Zhao, Shihang Zhang, Ziliang Jin, Huan Shu, Peihao Huang, Guanyong Wang, Mingchao Duan, Tianluo Pan, Tao Xin, Guangchong Hu, Zhen Tian, Dapeng Yu, Yu He

Published 2026-10-06

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hao Wang, Baolong Zhao, Shihang Zhang, Ziliang Jin, Huan Shu, Peihao Huang, Guanyong Wang, Mingchao Duan, Tianluo Pan, Tao Xin, Guangchong Hu, Zhen Tian, Dapeng Yu, Yu He

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Building a computer that can solve problems beyond the reach of any machine today requires a fundamental shift in how we store and process information. Instead of using the binary switches of traditional electronics, these future devices rely on quantum bits, or qubits, which can exist in multiple states at once. One of the most promising ways to create these qubits is by trapping individual atoms of phosphorus inside a block of silicon. These atoms act as tiny, stable magnets that can hold quantum information for a remarkably long time. However, as scientists attempt to scale this technology from a few atoms to the millions needed for a powerful computer, they face a significant hurdle: how to speak to each atom individually without the signals getting crossed. In a crowded room of identical atoms, it is nearly impossible to tell one from another using only radio waves, because they all respond to the same frequency. If the signals overlap, the computer cannot perform the precise calculations required for complex tasks.

A team of researchers has proposed a solution to this problem by combining the precision of atomic engineering with the power of tiny, custom-built magnets. Their work focuses on a specific architecture where groups of phosphorus atoms are arranged in clusters on a silicon chip. While the natural differences between these atom groups provide some way to distinguish them, the researchers found that this natural variation is not enough to address the hundreds or thousands of qubits needed for a large-scale processor. To solve this, they designed a system that places microscopic magnets directly above the atom clusters. These magnets create a gentle slope in the magnetic field across the chip. Just as a hillside causes water to flow at different speeds depending on its position, this magnetic slope causes each atom cluster to resonate at a slightly different frequency based on where it sits. This allows a single control signal to be tuned to address specific groups of atoms without disturbing their neighbors, effectively giving each qubit a unique voice in a crowded chorus.

The researchers began by analyzing the limitations of relying solely on the natural properties of the atom clusters. They calculated that without external help, the natural variations in how the atoms interact would only allow for the independent control of about thirty qubits in a single module. This is far too few for a useful quantum computer. To push this number higher, they turned to computer simulations to design a new type of on-chip magnet. They modeled various shapes and sizes of cobalt magnets, testing how different dimensions would affect the magnetic field gradient they produced. The simulations revealed that a specific block-like shape, consisting of two rectangular pieces separated by a small gap, could generate a magnetic field slope strong enough to distinguish between many more atoms. By optimizing the length, width, and thickness of these magnets, the team determined that a single module could theoretically address over one hundred and twenty individual spin qubits using just one antenna. This represents a massive leap in capacity, turning a small experimental setup into a viable building block for a larger machine.

To prove that their computer models matched reality, the team fabricated actual samples of these cobalt magnets and measured their magnetic fields. They created the magnets using a process similar to the one used to make computer chips, depositing a thin layer of cobalt onto a silicon surface and shaping it with high-precision tools. They then used a specialized microscope equipped with a tiny magnetic sensor to map the field generated by the magnets. The measurements confirmed that the real-world magnets behaved very much like the ones in their simulations, producing the necessary magnetic slope across the chip. While the experimental magnets showed some small imperfections due to the natural roughness of the metal surface and the way the magnetic domains formed, the overall results aligned closely with the predictions. This validation is crucial because it shows that the theoretical design can be built and will function as intended in a physical device.

The significance of this work lies in its ability to solve the "addressability" problem, which has long been a bottleneck for scaling silicon-based quantum computers. By integrating these micromagnets with the atom clusters, the researchers have proposed a path forward where a single control line can manage a large array of qubits. This approach drastically reduces the complexity of the wiring needed to control the computer, as it eliminates the need for a separate wire for every single atom. The design also accounts for the fact that the natural arrangement of atoms is not perfectly uniform, using the magnetic slope to compensate for these variations. While the current study focuses on the design and initial validation of these magnets, the results suggest that this method could be the key to unlocking the potential of silicon quantum processors. By enabling the integration of over one hundred qubits in a single module through simulation and design, this engineering feat brings the dream of a fault-tolerant quantum computer built from silicon atoms one step closer to reality.

Technical Summary: Micromagnet Engineering for Enhanced Addressability of Donor-Cluster Arrays in Silicon

Problem Statement
Phosphorus donors in silicon represent a leading platform for fault-tolerant quantum computing due to their long coherence times and compatibility with CMOS technology. While recent advancements in scanning tunneling microscope hydrogen depassivation lithography (STM-HDL) have enabled the fabrication of multi-donor quantum clusters (e.g., 11-qubit processors), scaling this architecture faces a critical bottleneck: the independent addressability of individual spin qubits. In donor-cluster systems, qubit addressability relies on the distinct hyperfine (HF) interaction strengths between the shared electron and the nuclear spins. However, the random atomic configurations of phosphorus atoms within clusters—resulting from adsorption and overgrowth processes—lead to significant variations in HF coupling. As the number of qubits increases, these variations cause "frequency crowding," where the resonant frequencies of different qubits overlap, leading to crosstalk errors that prevent individual control. Current estimates suggest that relying solely on HF randomness limits the number of distinguishable clusters to approximately 10 units (30 qubits) before crosstalk becomes prohibitive.

Methodology
To overcome frequency crowding, the authors propose a scalable quantum processor architecture that integrates STM-defined phosphorus donor-cluster arrays with on-chip micromagnets. The core strategy involves generating a controlled magnetic field gradient across the donor array. This gradient superimposes on the external static magnetic field ( $B_0$ ), shifting the resonant frequency of each electron or nucleus based on its spatial position, thereby creating a unique addressable frequency for each qubit even if their intrinsic HF couplings are similar.

The study employs a multi-faceted approach:

Theoretical Analysis: The authors analyze the Hamiltonian of donor clusters to quantify the relationship between HF coupling variations and crosstalk errors. They establish a threshold for frequency separation ( $\Delta f_d \geq 10$ MHz) required to maintain crosstalk errors below 1%.
Micromagnetic Simulation: Using the Python package Magpylib, the authors simulate block-shaped Cobalt (Co) micromagnets to optimize their geometry (length $L$ , width $W$ , thickness $T$ , and gap $G$ ). The goal is to maximize the lateral range where the magnetic field gradient ( $\nabla_x B_y$ ) exceeds 0.45 mT/nm, a value sufficient to shift the Larmor frequency by the necessary amount between adjacent cluster units.
Fabrication and Characterization: Co micromagnet samples were fabricated using electron-beam lithography and lift-off processes. The magnetic properties were characterized using a commercial scanning nitrogen-vacancy center microscope (SNVM) via optically detected magnetic resonance (ODMR) to map the stray magnetic field components ( $B_x, B_y, B_z$ ).

Key Contributions and Results

Architectural Design: The paper presents a chip architecture where donor clusters are arranged in a "3+2+3+2" configuration within units, tiled periodically. A single microwave antenna is used to drive the entire array, with individual qubit selection achieved through frequency multiplexing enabled by the micromagnet-induced field gradient.
Simulation Optimization: Through geometric optimization, the authors determined that a micromagnet with dimensions $L=1.2$ µm, $W=0.8$ µm, $T=0.1$ µm, and $G=0.3$ µm generates an effective gradient range of approximately 222 nm along the x-axis. This range is more than four times the length of a 10-cluster unit, theoretically enabling the independent addressing of over 120 atomic spin qubits using a single antenna.
Experimental Validation: Experimental measurements of the fabricated Co micromagnets using SNVM showed general agreement with the micromagnetic simulations regarding the spatial distribution of magnetic field components. However, the experimental stray field strength was slightly lower than predicted. The authors attribute this discrepancy to non-ideal factors such as the formation of multi-domain structures (reducing remanent magnetization), the polycrystalline nature of the evaporated Co film, and surface oxidation or edge roughness.
Addressability Enhancement: By combining the micromagnet gradient with the intrinsic HF variations and potential Stark shifts from gate electrodes, the proposed design effectively expands the addressable frequency range, mitigating the frequency crowding issue inherent to random donor clusters.

Significance
The paper claims to establish a critical foundation for the development of scalable silicon quantum computing with atomic qubits. By demonstrating that micromagnet engineering can significantly enhance the addressability of donor-cluster arrays, the work offers a practical pathway to realizing large-scale quantum processors. The ability to integrate over 120 qubits into a single modular structure using a single control line greatly reduces the routing overhead (fan-out) typically associated with scaling quantum computers. While the authors acknowledge that further optimization of micromagnet materials and fabrication is needed to minimize field inhomogeneities, their results validate the feasibility of using on-chip micromagnets to solve the addressability bottleneck, paving the way for future integration with long-distance qubit-coupling techniques to achieve fault-tolerant quantum computation.

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