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arXiv:2609.20183

Fast Unitary Preparation of Surface-Code Logical States on Neutral-Atom Hardware

Ludwig Schmid, Robert Wille

quant-phSubmitted Jul 27, 2026• Announced Jul 29, 2026• 0 citations
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Abstract

Preparing logical states is a constantly recurring primitive at the start of any surface-code-based quantum computation. The standard measurement-based protocol is expensive on neutral atoms, since measurements are orders of magnitude slower than gates and, on single-zone architectures, additionally require shuttling the atoms to a readout zone. In this work, we present a measurement-free, unitary preparation of surface-code Pauli eigenstates tailored to neutral atoms. A bidirectional stabilizer-expanding CNOT cascade grows the patch from its middle line outward in depth $(d{+}3)/2$, while retaining fault distance $d$ in the protected error direction. Each layer maps to one collective atom move followed by a single global Rydberg pulse, with about one row pickup per two layers. We compile and simulate the resulting schedules with the open-source bloqade toolchain under a hardware-calibrated, circuit-level neutral-atom noise model. The bidirectional cascade achieves the lowest logical error rate at every distance, and is the only construction tested that operates below threshold for both logical states at the considered device-level noise.

Comments
4 pages, 4 figures

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Preparing logical states is a constantly recurring primitive at the start of any surface-code-based quantum computation. The standard measurement-based protocol is expensive on neutral atoms, since measurements are orders of magnitude slower than gates and, on single-zone architectures, additionally require shuttling the atoms to a readout zone. In this work, we present a measurement-free, unitary preparation of surface-code Pauli eigenstates tailored to neutral atoms. A bidirectional stabilizer-expanding CNOT cascade grows the patch from its middle line outward in depth (d+3)/2(d{+}3)/2(d+3)/2, while retaining fault distance ddd in the protected error direction. Each layer maps to one collective atom move followed by a single global Rydberg pulse, with about one row pickup per two layers. We compile and simulate the resulting schedules with the open-source bloqade toolchain under a hardware-calibrated, circuit-level neutral-atom noise model. The bidirectional cascade achieves the lowest logical error rate at every distance, and is the only construction tested that operates below threshold for both logical states at the considered device-level noise.
In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable, distance-preserving encoding scheme for preparing Pauli eigenstates in surface codes. Unlike previous unitary approaches whose fault-distance remains constant with increasing code distance, our scheme ensures that the protection offered by the code is preserved during state preparation. Building on strategies discovered by reinforcement learning for the surface-17 code, we generalize the construction to arbitrary code distances and both rotated and unrotated surface codes. The proposed encoding relies only on geometrically local gates, and is therefore fully compatible with planar 2D qubit connectivity, and it achieves circuit depth scaling as O(d)\mathcal{O}(d)O(d), consistent with fundamental entanglement-generation bounds. We design explicit stabilizer-expanding circuits with and without ancilla-mediated connectivity and analyze their error-propagation behavior. Numerical simulations under depolarizing noise show that our unitary encoding without ancillas outperforms standard stabilizer-measurement-based schemes, reducing logical error rates by up to an order of magnitude. These results make the scheme particularly relevant for platforms such as trapped ions and neutral atoms, where measurements are costly relative to gates and idling noise is considerably weaker than gate noise. Our work bridges the gap between measurement-based and unitary encodings of surface-code states and opens new directions for distance-preserving state preparation in fault-tolerant quantum computation.
The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires: mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a 4×44 \times 44×4 rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold p⋆≈0.034p^\star \approx 0.034p⋆≈0.034. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.
Efficient quantum error correction and fault-tolerant quantum computing require scalable, high-fidelity long-range connectivity. In neutral-atom quantum computers, this is commonly achieved through atom transport, but shuttling introduces latency and motional heating that worsen with system size. Here, we introduce a neutral-atom architecture based on static atomic buses, in which auxiliary mediator atoms enable long-range entangling operations without qubit transport. The architecture naturally supports long-range stabilizer measurements in high-rate LDPC codes and transversal logical gates between neighboring surface-code patches, enabling a modular framework for efficient logical memories, Clifford computation, and magic-state distillation. To realize these capabilities, we co-design optimal-control protocols for bus-mediated controlled-Z gates that incorporate both microscopic neutral-atom dynamics and architectural constraints. We obtain smooth bus-mediated gates with fidelities approaching 99.9% and durations of a few hundred nanoseconds by combining time-optimal control with interaction-flatness and robustness constraints. Large-scale simulations of quantum error correction and logical entangling operations between neighboring surface-code patches predict more than an order-of-magnitude improvement in logical error rates compared with atom-shuttling architectures under realistic noise. The architecture achieves logical gate times of approximately 100 us and quantum-error-correction cycle times of about 1 ms for code distances d<12. These results establish static atomic buses as a practical alternative to atom shuttling for scalable fault-tolerant neutral-atom quantum computing.
Abstract The central prerequisite of any fault-tolerant quantum architecture is a quantum memory: a block of encoded physical qubits whose logical state is actively preserved against noise across many rounds of error correction. In neutral-atom Rydberg arrays, realizing such a memory is obstructed not by the entangling gates themselves, which are already fast and high-fidelity, but by the auxiliary operations that a conventional error-correction cycle requires — mid-circuit fluorescence measurement, inter-zone atom transport, and locally focused single-qubit addressing. Each of these introduces latency, atom loss, or optical crosstalk that exceeds the cost of the underlying gates by orders of magnitude. These costs accumulate cycle after cycle, progressively degrading the very logical information the code is meant to protect. Here we propose a protocol that stabilizes a toric-code quantum memory without moving, measuring or local addressing atoms. The key is to use a three-species Rydberg atom array for the complete stabilizer cycle, including syndrome extraction, coherent correction, and ancilla reset, under global, species-selective laser pulses. Numerical simulation of a 4 ⁣× ⁣44\!\times\!44×4 rotated toric code shows a longer qubit lifetime when the physical error rate is below a pseudo-threshold p⋆ ⁣≈ ⁣0.034p^\star\!\approx\!0.034p⋆≈0.034. The scheme offers a concrete, hardware-efficient route to topological quantum memory in neutral-atom platforms.
We consider stabilizer measurements for surface codes with neutral atoms and identify gate protocols that minimize logical error rates in the presence of a fundamental error source—spontaneous emission from Rydberg states. We demonstrate that logical error rates are minimized by protocols that prevent the propagation of Rydberg leakage errors and not by protocols that minimize the physical two-qubit error rate. We provide laser-pulse-level gate protocols to counter these errors. These protocols significantly reduce the logical error rate for implementations of surface codes involving one or two species of atoms. Our work demonstrates the importance of optimizing quantum gates for logical errors in addition to gate fidelities and opens the way to the efficient realization of surface codes with neutral atoms.
Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.