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:2512.04169 · ACM/IEEE Design Automation Conference (DAC)

Exploiting Movable Logical Qubits for Lattice Surgery Compilation

Laura S. Herzog, Lucas Berent, Aleksander Kubica, Robert Wille

quant-phcs.ETSubmitted Dec 3, 2025• Announced Dec 5, 2025• 0 citations
arXivHTMLPDF

Abstract

Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation schemes, logical circuits are compiled following a place-and-route paradigm, where logical qubits remain statically fixed in space throughout the computation. In this work, we introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate. Focusing on lattice surgery with the color code, we propose a proof-of-concept compilation scheme that leverages this capability. Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth compared to standard place-and-route compilation techniques. Our results demonstrate that optimizations based on movable logical qubits are not limited to architectures with physically movable qubits, such as neutral atoms or trapped ions - they are also readily applicable to superconducting quantum hardware. An open-source implementation of our method is available on GitHub https://github.com/munich-quantum-toolkit/qecc.

DOI
10.1145/3770743.3804359

Related papers

Routing Techniques for Error-Corrected Silicon Spin Qubit Quantum Architectures

Julian Shen, Ludwig Schmid, Robert Wille

Silicon spin qubits have emerged as a promising qubit technology due to their favorable scaling and fabrication properties. However, efficiently compiling quantum circuits onto spin qubit platforms remains challenging, particularly when accounting for hardware constraints and the high sensitivity to static defects. Existing compilation approaches for spin qubits either largely ignore error correction, despite its critical role for large-scale quantum computation, or focus on low-level schedule constructions, missing a high-level compilation and routing for logical, error-corrected algorithms. To address this gap, we introduce a compilation framework for spin qubits based on the recent snakes on a plane model, which utilizes a 2D surface code and qubit teleportation to mitigate errors. Building on this model, we propose shortest-path and rotation-based algorithms as two novel classes of qubit-routing techniques, along with additional defect-handling and initial-mapping strategies. We evaluate both algorithms across diverse architectural settings and problem sizes, demonstrating that shortest-path methods excel in sparse, low-defect scenarios, while rotation-based approaches perform better in high-density environments. An open-source implementation of our framework is publicly available on GitHub as part of the Munich Quantum Toolkit (MQT) at https://github.com/munich-quantum-toolkit/spin-qubit-routing.

quant-pharXiv:2607.07822•Jul 10, 2026•0 citations

Lattice Surgery Compilation Beyond the Surface Code

Laura S. Herzog, Lucas Berent, Aleksander Kubica +1 more

Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery schemes. In this work, we broaden the scope by considering lattice surgery compilation for topological codes beyond the surface code. We begin by defining a code substrate-a blueprint for implementing topological codes and lattice surgery. We then abstract from the microscopic details and rephrase the compilation task as a mapping and routing problem on a macroscopic routing graph, potentially subject to substrate-specific constraints. We explore specific substrates and codes, including the color code and the folded surface code, providing detailed microscopic constructions. For the color code, we present numerical simulations analyzing how design choices at the microscopic and macroscopic levels affect the depth of compiled logical CNOT + T circuits. An opensource code is available on GitHub https://github.com/cda-tum/mqt-qecc.

arXiv:2504.10591•IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•1 citation

Transversality and lattice surgery: Exploring realistic routes toward coupled logical qubits with trapped-ion quantum processors

M. Gutiérrez, Markus Müller, A. Bermúdez

Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This midterm challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing the capability of current trapped-ion architectures in facing one of the most demanding parts of this quest: the implementation of an entangling controlled-NOT (CNOT) gate between encoded logical qubits. We present a detailed comparative study of two alternative strategies for trapped-ion topological color codes, either a transversal or a lattice-surgery approach, characterized by a detailed microscopic modeling of both current technological capabilities and experimental sources of noise afflicting the different operations. Our careful fault-tolerant design, together with a low-resource optimization, allows us to determine via exhaustive numerical simulations the experimental regimes where each of the approaches becomes favorable. We hope that our study thereby contributes to guiding the future development of trapped-ion quantum computers.

arXiv:1801.07035•Physical Review A•Feb 25, 2019•50 citations

Demand-Driven Routing Space for Lattice-Surgery Compilation

Hanyu Wang, Wan-Hsuan Lin, Zihan Chen +2 more

Lattice-surgery compilation places logical qubits on a grid of surface-code tiles and routes their interactions. Sparse static layouts limit routing contention but reserve space that often remains idle. Reducing this reservation requires balancing area savings against additional gate serialization and qubit movement. In this paper, we present a co-designed dynamic architecture and compiler that allocates routing space according to circuit demand. The architecture preserves a fixed virtual qubit floorplan while allowing its physical spacing to change between execution stages. The compiler coordinates placement, scheduling, and routing to implement lattice surgeries using fewer physical qubits. Across our application benchmarks, our method reduces space-time volume by 55.6% in geometric mean and compiles 75.5 times faster than the evaluated DasCot configuration. A circuit-synthesis case study shows how our compiler exposes optimization tradeoffs.

quant-pharXiv:2610.30747•Oct 23, 2026•0 citations

Lattice surgery for near-term experimental logical qubit entanglement creation in planar architectures

Lukas Bödeker, Áron Márton, Luis Colmenarez +3 more

In the era of early fault-tolerant quantum computing, basic demonstrations of entanglement operations between a few logical qubits are at the frontier of recent developments in quantum computing. In this work, we describe in detail, at both the logical and physical qubit levels, a logical teleportation protocol between two surface code logical qubits based on lattice surgery. We address several aspects of the teleportation protocol pertinent to superconducting qubit architectures. We explore the modularity constraints in the number and location of stabilizer readouts and compare variants of the teleportation protocol in this regard. Additionally, we investigate potential performance improvements related to in-sequence decision logic and the optimal size of the interface region between two surface code patches on a superconducting chip. Based on our simulations, we show possible near-term improvements in lattice surgery protocols that facilitate fault-tolerant quantum computing in superconducting circuit architectures.

quant-pharXiv:2606.15190•Jun 16, 2026•0 citations

High-fidelity and Fault-tolerant Teleportation of a Logical Qubit using Transversal Gates and Lattice Surgery on a Trapped-ion Quantum Computer

Ciarán Ryan-Anderson, Natalie C. Brown, Charles H. Baldwin +21 more

Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation circuit for a quantum error correction code - in particular, the planar topological [[7,1,3]] color code, or Steane code. The circuits use up to 30 trapped ions at the physical layer qubits and employ real-time quantum error correction - decoding mid-circuit measurement of syndromes and implementing corrections during the protocol. We conduct experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery protocols. Among the many measurements we report on, we measure the logical process fidelity of the transversal teleportation circuit to be 0.975(2) and the logical process fidelity of the lattice surgery teleportation circuit to be 0.851(9). Additionally, we run a teleportation circuit that is equivalent to Knill-style quantum error correction and measure the process fidelity to be 0.989(2).

arXiv:2404.16728•Apr 25, 2024•1 citation
Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation schemes, logical circuits are compiled following a place-and-route paradigm, where logical qubits remain statically fixed in space throughout the computation. In this work, we introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate. Focusing on lattice surgery with the color code, we propose a proof-of-concept compilation scheme that leverages this capability. Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth compared to standard place-and-route compilation techniques. Our results demonstrate that optimizations based on movable logical qubits are not limited to architectures with physically movable qubits, such as neutral atoms or trapped ions - they are also readily applicable to superconducting quantum hardware. An open-source implementation of our method is available on GitHub https://github.com/munich-quantum-toolkit/qecc.
Silicon spin qubits have emerged as a promising qubit technology due to their favorable scaling and fabrication properties. However, efficiently compiling quantum circuits onto spin qubit platforms remains challenging, particularly when accounting for hardware constraints and the high sensitivity to static defects. Existing compilation approaches for spin qubits either largely ignore error correction, despite its critical role for large-scale quantum computation, or focus on low-level schedule constructions, missing a high-level compilation and routing for logical, error-corrected algorithms. To address this gap, we introduce a compilation framework for spin qubits based on the recent snakes on a plane model, which utilizes a 2D surface code and qubit teleportation to mitigate errors. Building on this model, we propose shortest-path and rotation-based algorithms as two novel classes of qubit-routing techniques, along with additional defect-handling and initial-mapping strategies. We evaluate both algorithms across diverse architectural settings and problem sizes, demonstrating that shortest-path methods excel in sparse, low-defect scenarios, while rotation-based approaches perform better in high-density environments. An open-source implementation of our framework is publicly available on GitHub as part of the Munich Quantum Toolkit (MQT) at https://github.com/munich-quantum-toolkit/spin-qubit-routing.
Large-scale fault-tolerant quantum computation requires compiling logical circuits into physical operations tailored to a given architecture. Prior work addressing this challenge has mostly focused on the surface code and lattice surgery schemes. In this work, we broaden the scope by considering lattice surgery compilation for topological codes beyond the surface code. We begin by defining a code substrate-a blueprint for implementing topological codes and lattice surgery. We then abstract from the microscopic details and rephrase the compilation task as a mapping and routing problem on a macroscopic routing graph, potentially subject to substrate-specific constraints. We explore specific substrates and codes, including the color code and the folded surface code, providing detailed microscopic constructions. For the color code, we present numerical simulations analyzing how design choices at the microscopic and macroscopic levels affect the depth of compiled logical CNOT + T circuits. An opensource code is available on GitHub https://github.com/cda-tum/mqt-qecc.
Active quantum error correction has been identified as a crucial ingredient of future quantum computers, motivating the recent experimental efforts to encode logical quantum bits using small topological codes. In addition to the demonstration of the beneficial role of the encoding, a break-even point in the progress towards large-scale quantum computers will be the implementation of a universal set of gates. This midterm challenge will soon be faced by various quantum technologies, which urges the need of realistic assessments of their prospects. In this work, we pursue this goal by assessing the capability of current trapped-ion architectures in facing one of the most demanding parts of this quest: the implementation of an entangling controlled-NOT (CNOT) gate between encoded logical qubits. We present a detailed comparative study of two alternative strategies for trapped-ion topological color codes, either a transversal or a lattice-surgery approach, characterized by a detailed microscopic modeling of both current technological capabilities and experimental sources of noise afflicting the different operations. Our careful fault-tolerant design, together with a low-resource optimization, allows us to determine via exhaustive numerical simulations the experimental regimes where each of the approaches becomes favorable. We hope that our study thereby contributes to guiding the future development of trapped-ion quantum computers.
Lattice-surgery compilation places logical qubits on a grid of surface-code tiles and routes their interactions. Sparse static layouts limit routing contention but reserve space that often remains idle. Reducing this reservation requires balancing area savings against additional gate serialization and qubit movement. In this paper, we present a co-designed dynamic architecture and compiler that allocates routing space according to circuit demand. The architecture preserves a fixed virtual qubit floorplan while allowing its physical spacing to change between execution stages. The compiler coordinates placement, scheduling, and routing to implement lattice surgeries using fewer physical qubits. Across our application benchmarks, our method reduces space-time volume by 55.6% in geometric mean and compiles 75.5 times faster than the evaluated DasCot configuration. A circuit-synthesis case study shows how our compiler exposes optimization tradeoffs.
In the era of early fault-tolerant quantum computing, basic demonstrations of entanglement operations between a few logical qubits are at the frontier of recent developments in quantum computing. In this work, we describe in detail, at both the logical and physical qubit levels, a logical teleportation protocol between two surface code logical qubits based on lattice surgery. We address several aspects of the teleportation protocol pertinent to superconducting qubit architectures. We explore the modularity constraints in the number and location of stabilizer readouts and compare variants of the teleportation protocol in this regard. Additionally, we investigate potential performance improvements related to in-sequence decision logic and the optimal size of the interface region between two surface code patches on a superconducting chip. Based on our simulations, we show possible near-term improvements in lattice surgery protocols that facilitate fault-tolerant quantum computing in superconducting circuit architectures.
Quantum state teleportation is commonly used in designs for large-scale fault-tolerant quantum computers. Using Quantinuum's H2 trapped-ion quantum processor, we implement the first demonstration of a fault-tolerant state teleportation circuit for a quantum error correction code - in particular, the planar topological [[7,1,3]] color code, or Steane code. The circuits use up to 30 trapped ions at the physical layer qubits and employ real-time quantum error correction - decoding mid-circuit measurement of syndromes and implementing corrections during the protocol. We conduct experiments on several variations of logical teleportation circuits using both transversal gates and lattice surgery protocols. Among the many measurements we report on, we measure the logical process fidelity of the transversal teleportation circuit to be 0.975(2) and the logical process fidelity of the lattice surgery teleportation circuit to be 0.851(9). Additionally, we run a teleportation circuit that is equivalent to Knill-style quantum error correction and measure the process fidelity to be 0.989(2).