Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2403.01353 · Quantum Science and Technology

Spatially parallel decoding for multi-qubit lattice surgery

Sophia Fuhui Lin, Eric Peterson, Krishanu Sankar, Prasahnt Sivarajah

Published Mar 28, 2025• 6 citations
arXivHTMLPDF

Abstract

Abstract Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery—possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput—a decision that should be influenced by the device’s physical noise.

DOI
10.1088/2058-9565/adc6b6

Related papers

Patchwork: automated lattice surgery and space-time partitioning for real-time decoding

Christopher Chamberland, Muyuan Li, Scott Thornton +3 more

We introduce patchwork, a lattice-surgery compiler for arbitrary multi-qubit Pauli measurements on a prescribed narrow-corridor two-dimensional surface-code layout. Systematic geometric rules simplify stabilizer placement and gate scheduling, including for logical $Y$ measurements implemented using twist defects. We introduce measurement circuits and schedules that, together with protruding lobes of $Y$-extension patches, preserve the full effective code distance for all numerically tested code distances. To support parallel decoding, we develop a wavefront algorithm that partitions merged lattice-surgery patches into space-time commit, buffer, and cleanup regions. Simulations of three sequential multi-qubit Pauli measurements acting on ten logical qubits show that staged decoding achieves total failure probabilities close to those of monolithic decoding over the parameters tested. These methods provide an automated framework for fault-tolerant lattice surgery and a route toward scalable, real-time decoding.

quant-pharXiv:2610.22112•Oct 16, 2026•0 citations

Low-overhead quantum computing with the color code

Felix Thomsen, Markus S. Kesselring, Stephen D. Bartlett +1 more

Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the rich structure of the color-code phase to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, and assuming the same amount of time is needed to complete a round of syndrome measurements, our approach yields about a 3 × improvement in the space-time overhead, obtained from a combination of a 1.5 × improvement in spatial overhead together with a 2 × speedup due to the parallelization of commuting logical measurements. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10% at a physical error rate of 10 − 3 and by 50% at 10 − 4 . Published by the American Physical Society 2024

arXiv:2201.07806•Physical Review Research•Nov 12, 2024•15 citations

A Syndrome-Extraction Framework for Distributed Lattice Surgery on Arbitrary Rotated Surface-Code Layouts

Pritesh Thakur, Daniel Dilley, Zain Saleem

Modular quantum computing is a leading candidate for scalable fault tolerant quantum computation. Performing lattice surgery using surface code patches in different modules requires the use of inter-module gates that are noisier than the local gates. Furthermore, the merged layouts during lattice surgery expose multiple directions in which hook errors can propagate to reduce the fault distance. Existing hook-avoiding schedules either increase the syndrome extraction circuit depth, or let link faults propagate into the bulk. We introduce a seam construction that allows splitting arbitrary merged rotated surface code layout into smaller patches with uniform boundaries that could keep their own hook-avoiding N/Z shaped schedule. At the seam we split weight-4 stabilizers into pairs of weight-2 stabilizers that are mediated through a Bell pair and measured within a CNOT depth of 4. We also employ the use of three-qubit $\texttt{CXX}$ gates for parity measurements at the seam to maintain the minimum CNOT depth. Through this seam construction, we confine the elevated link error at the seam, protecting the bulk from higher error rate. We also give a custom detector annotator for such seams that can find the detector space, annotate detectors in the Stim circuits, and ensure that they are suitable to use by matching decoders. We implement our construction for the logical Pauli-$XX$ measurement lattice surgery and a cross-shaped spatial junction and sweep the link error rate from $10$ times to $100$ times a fixed bulk error rate, and show that our construction gives the lowest and most stable logical error rate than the other frameworks compared here.

quant-pharXiv:2609.26736•Sep 23, 2026•0 citations

Parallel window decoding enables scalable fault tolerant quantum computation

Luka Skorić, Dan E. Browne, Kenton M. Barnes +2 more

Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 μs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today's leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.

arXiv:2209.08552•Nature Communications•Nov 3, 2023•81 citations

Network-Integrated Decoding System for Real-Time Quantum Error Correction with Lattice Surgery

Namitha Liyanage, Yue Wu, Emmet Houghton +1 more

Existing real-time decoders for surface codes are limited to isolated logical qubits and do not support logical operations involving multiple logical qubits. We present Deconet, a first-of-its-kind decoding system that scales to thousands of logical qubits and supports logical operations implemented through lattice surgery. Deconet organizes compute resources in a network-integrated hybrid tree-grid structure, which results in minimal latency increase and no throughput degradation as the system grows. Specifically, Deconet can be scaled to any arbitrary number of$l$logical qubits by increasing the compute resources by$O(l \times \log (l))$, which provides the required$O(l)$growth in I/O resources while incurring only an$O(\log (l))$increase in latency-a modest growth that is sufficient for thousands of logical qubits. Moreover, we analytically show that the scaling approach preserves throughput, keeping Deconet backlog-free for any number of logical qubits We report an exploratory prototype of Deconet, called Deconet/Helios, built with five VMK-180 FPGAs, that successfully decodes 100 logical qubits of distance five. For 100 logical qubits, under a phenomenological noise rate of$\mathbf{0. 1 \%}$, the Deconet/Helios has an average latency of$2.40 \mu ~\mathrm{s}$and an inverse throughput of 0.84$\mu$s per measurement round.

arXiv:2504.11805•IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•3 citations

Lattice Surgery for Dummies

Avimita Chatterjee, Subrata K. Das, Swaroop Ghosh

Quantum error correction (QEC) plays a crucial role in correcting noise and paving the way for fault-tolerant quantum computing. This field has seen significant advancements, with new quantum error correction codes emerging regularly to address errors effectively. Among these, topological codes, particularly surface codes, stand out for their low error thresholds and feasibility for implementation in large-scale quantum computers. However, these codes are restricted to encoding a single qubit. Lattice surgery is crucial for enabling interactions among multiple encoded qubits or between the lattices of a surface code, ensuring that its sophisticated error-correcting features are maintained without significantly increasing the operational overhead. Lattice surgery is pivotal for scaling QECCs across more extensive quantum systems. Despite its critical importance, comprehending lattice surgery is challenging due to its inherent complexity, demanding a deep understanding of intricate quantum physics and mathematical concepts. This paper endeavors to demystify lattice surgery, making it accessible to those without a profound background in quantum physics or mathematics. This work explores surface codes, introduces the basics of lattice surgery, and demonstrates its application in building quantum gates and emulating multi-qubit circuits.

arXiv:2404.13202•Sensors•Mar 17, 2025•1 citation
Abstract Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery—possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput—a decision that should be influenced by the device’s physical noise.
We introduce patchwork, a lattice-surgery compiler for arbitrary multi-qubit Pauli measurements on a prescribed narrow-corridor two-dimensional surface-code layout. Systematic geometric rules simplify stabilizer placement and gate scheduling, including for logical YYY measurements implemented using twist defects. We introduce measurement circuits and schedules that, together with protruding lobes of YYY-extension patches, preserve the full effective code distance for all numerically tested code distances. To support parallel decoding, we develop a wavefront algorithm that partitions merged lattice-surgery patches into space-time commit, buffer, and cleanup regions. Simulations of three sequential multi-qubit Pauli measurements acting on ten logical qubits show that staged decoding achieves total failure probabilities close to those of monolithic decoding over the parameters tested. These methods provide an automated framework for fault-tolerant lattice surgery and a route toward scalable, real-time decoding.
Fault-tolerant quantum computation demands significant resources: large numbers of physical qubits must be checked for errors repeatedly to protect quantum data as logic gates are implemented in the presence of noise. We demonstrate that an approach based on the color code can lead to considerable reductions in the resource overheads compared with conventional methods, while remaining compatible with a two-dimensional layout. We propose a lattice surgery scheme that exploits the rich structure of the color-code phase to perform arbitrary pairs of commuting logical Pauli measurements in parallel while keeping the space cost low. Compared to lattice surgery schemes based on the surface code with the same code distance, and assuming the same amount of time is needed to complete a round of syndrome measurements, our approach yields about a 3 × improvement in the space-time overhead, obtained from a combination of a 1.5 × improvement in spatial overhead together with a 2 × speedup due to the parallelization of commuting logical measurements. Even when taking into account the color code's lower error threshold using current decoders, the overhead is reduced by 10% at a physical error rate of 10 − 3 and by 50% at 10 − 4 . Published by the American Physical Society 2024
Modular quantum computing is a leading candidate for scalable fault tolerant quantum computation. Performing lattice surgery using surface code patches in different modules requires the use of inter-module gates that are noisier than the local gates. Furthermore, the merged layouts during lattice surgery expose multiple directions in which hook errors can propagate to reduce the fault distance. Existing hook-avoiding schedules either increase the syndrome extraction circuit depth, or let link faults propagate into the bulk. We introduce a seam construction that allows splitting arbitrary merged rotated surface code layout into smaller patches with uniform boundaries that could keep their own hook-avoiding N/Z shaped schedule. At the seam we split weight-4 stabilizers into pairs of weight-2 stabilizers that are mediated through a Bell pair and measured within a CNOT depth of 4. We also employ the use of three-qubit CXX\texttt{CXX}CXX gates for parity measurements at the seam to maintain the minimum CNOT depth. Through this seam construction, we confine the elevated link error at the seam, protecting the bulk from higher error rate. We also give a custom detector annotator for such seams that can find the detector space, annotate detectors in the Stim circuits, and ensure that they are suitable to use by matching decoders. We implement our construction for the logical Pauli-XXXXXX measurement lattice surgery and a cross-shaped spatial junction and sweep the link error rate from 101010 times to 100100100 times a fixed bulk error rate, and show that our construction gives the lowest and most stable logical error rate than the other frameworks compared here.
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 μs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today's leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.
Existing real-time decoders for surface codes are limited to isolated logical qubits and do not support logical operations involving multiple logical qubits. We present Deconet, a first-of-its-kind decoding system that scales to thousands of logical qubits and supports logical operations implemented through lattice surgery. Deconet organizes compute resources in a network-integrated hybrid tree-grid structure, which results in minimal latency increase and no throughput degradation as the system grows. Specifically, Deconet can be scaled to any arbitrary number ofllllogical qubits by increasing the compute resources byO(l×log⁡(l))O(l \times \log (l))O(l×log(l)), which provides the requiredO(l)O(l)O(l)growth in I/O resources while incurring only anO(log⁡(l))O(\log (l))O(log(l))increase in latency-a modest growth that is sufficient for thousands of logical qubits. Moreover, we analytically show that the scaling approach preserves throughput, keeping Deconet backlog-free for any number of logical qubits We report an exploratory prototype of Deconet, called Deconet/Helios, built with five VMK-180 FPGAs, that successfully decodes 100 logical qubits of distance five. For 100 logical qubits, under a phenomenological noise rate of0.1%\mathbf{0. 1 \%}0.1%, the Deconet/Helios has an average latency of2.40μ s2.40 \mu ~\mathrm{s}2.40μ sand an inverse throughput of 0.84μ\muμs per measurement round.
Quantum error correction (QEC) plays a crucial role in correcting noise and paving the way for fault-tolerant quantum computing. This field has seen significant advancements, with new quantum error correction codes emerging regularly to address errors effectively. Among these, topological codes, particularly surface codes, stand out for their low error thresholds and feasibility for implementation in large-scale quantum computers. However, these codes are restricted to encoding a single qubit. Lattice surgery is crucial for enabling interactions among multiple encoded qubits or between the lattices of a surface code, ensuring that its sophisticated error-correcting features are maintained without significantly increasing the operational overhead. Lattice surgery is pivotal for scaling QECCs across more extensive quantum systems. Despite its critical importance, comprehending lattice surgery is challenging due to its inherent complexity, demanding a deep understanding of intricate quantum physics and mathematical concepts. This paper endeavors to demystify lattice surgery, making it accessible to those without a profound background in quantum physics or mathematics. This work explores surface codes, introduces the basics of lattice surgery, and demonstrates its application in building quantum gates and emulating multi-qubit circuits.