Exploiting Movable Logical Qubits for Lattice Surgery Compilation

2025-12-03

AI Summary

Conventional lattice-surgery compilation statically assigns logical qubits to fixed spatial locations, limiting the efficiency of fault-tolerant quantum computation. Method: We propose a teleportation-based scheme for mobile logical qubits and, for the first time, integrate it into lattice-surgery compilation for two-dimensional color codes—enabling dynamic logical routing optimization on physically static superconducting hardware. Our approach leverages entanglement distribution and logical teleportation to reconstruct CNOT gate scheduling, thereby breaking the static-layout paradigm. Contribution/Results: Numerical simulations demonstrate substantial reduction in post-routing circuit depth. An open-source compiler implementing this framework is publicly available on GitHub. This work establishes a hardware-efficient, fault-tolerant compilation pathway tailored to superconducting platforms and represents a significant advance toward dynamic lattice surgery.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

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.

Problem

• Reduces circuit depth in lattice surgery compilation via movable logical qubits.
• Enables teleportation-based qubit movement in superconducting quantum hardware.
• Optimizes fault-tolerant quantum computation without requiring physically movable qubits.

Innovation

• Introduces movable logical qubits via teleportation in lattice surgery
• Reduces circuit depth compared to static place-and-route compilation
• Applies to superconducting hardware without requiring physically movable qubits