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arXiv:2604.14296

Scalable quantum error correction tailored for a heavy-hex qubit array

Seok-Hyung Lee, Xanda C. Kolesnikow, Jun Zen, Evan T. Hockings, Campbell K. McLauchlan, Georgia M. Nixon, Thomas R. Scruby, Stephen D. Bartlett, Robin Harper, Benjamin J. Brown

quant-phSubmitted Apr 15, 2026• Announced Apr 17, 2026• 0 citations
v1 · Apr 15, 2026v2 · May 20, 2026
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Abstract

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3\% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.

Comments
15 pages; 7 figures; comments welcome

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To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.
Large quantum computations require high-fidelity error-corrected memory and fault-tolerant logical operations. To achieve these with superconducting circuits, quantum processors will need many components operating with low error rates. In practice, fabrication of monolithic superconducting devices produces unavoidable heterogeneity in component performance, which the quantum computer must accommodate. We implement strategies to operate a large dynamic compass code on an array of 156 superconducting qubits arranged on a heavy-hexagonal lattice, making use of the entire monolithic quantum processor and redesigning our measurement schedule to exclude underperforming components. We demonstrate improvements of up to 35%35\%35% in logical error probabilities for a memory experiment by using a noise-informed decoder combined with strategies to exclude the worst-performing qubits and couplers, along with post-selecting on shots with a low probability of leakage errors. In addition to these memory results, we also observe performance gains of up to 56%56\%56% when these strategies are applied to measurement-based logic, demonstrated by stability experiments. We furthermore demonstrate high-fidelity fault-tolerant logic through lattice surgery. Through pre-selection filtering techniques, we can obtain Bell fidelities above 77%77\%77%, and further logical gap post-selection using exclusive decoding increases these fidelities to above 97%97\%97%. Our experiments demonstrate that high performance can be maintained in key elements of fault-tolerant quantum memory and logic when working on monolithic superconducting quantum processors with underperforming components, by using a suite of noise-informed quantum error correction strategies.
The ongoing development of hardware that is capable of reliably executing general quantum algorithms requires quantum error-correcting codes that are both practical for realisation and rapidly reduce logical error rates as they are scaled up. Here we introduce the dynamic compass code, a code that can be implemented with a modest footprint on the heavy-hex lattice while also demonstrating a threshold. The dynamic code is obtained by choosing a novel measurement schedule for the syndrome extraction circuit of the heavy-hex subsystem code. We numerically evaluate its performance and observe that different choices of schedule can provide a trade-off in protection against logical errors in the XXX vs ZZZ basis. We also demonstrate that this new measurement schedule provides the code with a threshold for stability experiments. We finally show how the dynamic compass code could be used for fault-tolerant logic by illustrating lattice surgery between code patches.
Noise is the fundamental challenge to quantum computation. Large-scale quantum computers will overcome this challenge with fault-tolerant architectures that leverage quantum error correction. This thesis introduces and investigates a scalable noise characterisation protocol suited to this key context. First, we introduce this protocol by building upon averaged circuit eigenvalue sampling (ACES), a framework for noise characterisation experiments that simultaneously estimates the Pauli error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise characterisation procedure. Then we demonstrate in circuit-level numerical simulation that this protocol is practically capable of calibrating a fast correlated matching decoder, enabling noise-aware decoding. We find that noise-aware decoding increases the error suppression factor of the code, leading to reductions in the logical error rate that increase exponentially with the code distance. Finally, we present several results obtained from experimentally implementing this protocol. We use the noise characterisation results to design an improved syndrome extraction circuit for a heavy hexagon memory that is adapted to the noise characteristics of the quantum device. The model error of our noise characterisation results suggests that the circuit-level Pauli noise model estimated by ACES can describe the essential features of quantum noise. We also operate a heavy hexagon memory and use noise estimates to predict performance and inform decoding. These results demonstrate that Pauli noise estimates can calibrate decoders to enable noise-aware decoding and inform the co-design of quantum error correcting codes, decoders, fault-tolerant circuits, and quantum devices.
Characterizing the performance of noisy quantum circuits is central to the production of prototype quantum computers and can enable improved quantum error correction that exploits noise biases identified in a quantum device. We develop a scalable noise-characterization protocol suited to characterizing the syndrome-extraction circuits of quantum error-correcting codes, a key component of fault-tolerant architectures. Our protocol builds upon averaged circuit eigenvalue sampling (ACES), a framework for noise-characterization experiments that simultaneously estimates the Pauli-error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. By rigorously analyzing the performance of noise-characterization experiments in the ACES framework, we derive a figure of merit for their expected performance, allowing us to optimize their experimental design and improve the precision to which we estimate noise given fixed experimental resources. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise-characterization procedure for the syndrome-extraction circuit of a distance- 25 surface code with over 1000 qubits. Our results indicate that detailed noise-characterization methods are scalable to near-term quantum devices.
Building reliable quantum computers requires protecting fragile quantum states from inevitable environmental noise and operational errors. While quantum error correction codes like the Steane [ ⁣[7,1,3] ⁣][\![7,1,3]\!][[7,1,3]] code provide elegant theoretical solutions, their practical success hinges critically on how we measure errors - a process called syndrome extraction. The challenge lies in the ancilla qubits used for measurement: when they fail, errors can cascade across the entire quantum system, destroying the very information we're trying to protect. We address this fundamental problem by implementing and comparing three sophisticated syndrome measurement strategies: Shor's cat-state approach, which distributes measurements across multiple entangled ancillas achieving 85-92% preparation success; Steane's encoded-ancilla method using complete error-corrected logical qubits reaching 97.8% syndrome fidelity; and a flexible unified framework that adapts strategies based on hardware capabilities. Through extensive simulations using IBM's Qiskit platform spanning randomized benchmarking and T-heavy circuits, we demonstrate that intelligent ancilla management improves error suppression by up to 2.4×\times× compared to standard approaches. Our implementations achieve logical error rates as low as 5.1×10−55.1 \times 10^{-5}5.1×10−5 under realistic noise conditions with physical error rates of 10−310^{-3}10−3, while maintaining near-unity logical fidelity (0.99997) even for deep circuits. The threshold analysis reveals robust performance across distance-3 to distance-13 codes with characteristic threshold curves showing exponential error suppression below the critical physical error rate. These results provide immediately deployable tools for near-term quantum devices and establish practical design principles for scaling toward fault-tolerant quantum computers.
A solid-state quantum-computing architecture will require the fabrication of arrays of many coupled qubits. It is inevitable that this process will produce qubits and couplers with varying performance, with some components underperforming due to imperfect fabrication. Quantum error-correction requires high-performing components and hence these defects must be dealt with, either by adapting the code to exclude the defects, or by informing the decoder to accommodate defects in post-processing. Here we implement and compare strategies to operate distance-5 surface codes on a quantum processor consisting of a square-lattice array of 120 superconducting qubits. We demonstrate a dramatic reduction in the probability of a logical error in a memory experiment by excluding underperforming components, compared with both a standard approach of ignoring defects, and a defect-aware decoding approach. We observe up to 2.8X improvement in logical errors per round when excluding defects compared with the standard defect-ignorant approach (1.62% compared to 4.49%). In contrast, defect-aware decoding gives only modest gains. Defects are also expected to be particularly harmful for measurement-based logical operations. Using a stability experiment we show that excluding defects resurrects measurement-based logic gate performance, observing a 6.3% per-round suppression of failure rate when excluding defects, compared to zero suppression otherwise. Furthermore, we show a further substantial decrease in logical errors when using leakage post-selection in combination with our defect exclusion strategies, resulting in a distance-5 code outperforming the best distance-3 in one basis. Our experiments therefore give a proof-of-principle demonstration of the essential utility of defect exclusion methods in the scale-up of solid-state quantum computing approaches.