Exploiting Movable Logical Qubits for Lattice Surgery Compilation

TL;DR

This paper introduces a novel approach to lattice surgery in quantum computing by using movable logical qubits via teleportation, significantly reducing circuit depth and applicable to various hardware architectures.

Contribution

It proposes a new compilation scheme leveraging movable logical qubits during lattice surgery, contrasting with traditional static placement methods.

Findings

Substantial reduction in routed circuit depth demonstrated through simulations.

Movable logical qubits approach is applicable beyond architectures with physically movable qubits.

Open-source implementation available for further research and validation.

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.