Robert Wille

Fault-tolerant quantum computation (FTQC) requires compiling logical quantum circuits encoded using a quantum error-correcting code into physical operations tailored to specific hardware architectures. Lattice surgery has emerged as a leading method to perform logical computation, initially motivated by superconducting qubit architectures with geometrically local connectivity. However, current lattice surgery techniques are limited due to certain paradigmatic assumptions that are widely regarded as standard. In our works we identify and address two of these limiting paradigms. First, prior work has predominantly focused on the surface code, even though other topological codes offer certain advantages. Second, compilation schemes usually follow a place-and-route paradigm where logical qubits remain fixed in space throughout the computation. We initiate a more flexible line of work that goes beyond both aforementioned paradigms. To address the first, we introduce the concept of a code substrate - a blueprint for realizing quantum error correction with topological quantum codes using lattice surgery. We formulate the problem using two layers of abstraction. The microscopic level specifies how lattice surgery operations are realized using distance-preserving ancilla regions, while the macroscopic level abstracts compilation as a “mapping” and “routing” problem on a coarse-grained routing graph. We exemplify this framework with detailed constructions for the color code and folded surface code. To challenge the second paradigm, we exploit movable logical qubits through teleportation during logical CNOT execution. Building on the color code substrate, we adapt the measurement-based CNOT scheme to incorporate logical qubit teleportations without additional time overhead. This enables data qubits to dynamically change positions during compilation – “mapping” and “routing” are thus not viewed as independent and subsequent steps, as previous methods have in an overly simplified manner. This flexibility has the potential to substantially reduce routed circuit depth. Thus, movable logical qubits can be exploited even when physical qubits remain static, making movement-based compilation applicable not only to trapped ion and neutral atom platforms - where physical qubits are dynamic by design - but also to superconducting architectures. In addition to the conceptual work, we provide a set of open-source tools for the compilation of logical circuits for the color code on GitHub https://github.com/munich-quantum-toolkit/qecc.

Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no sin- gle error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all gates required for universal quantum computation. Code switching addresses this limitation by moving quantum information between different codes that, to- gether, support a universal gate set. Unfortunately, each switch is costly—adding time and space overhead and increasing the logical error rate. Minimizing the number of switching operations is, there- fore, essential for quantum computations using code switching. In this work, we study the problem of minimizing the number of code switches required to run a given quantum circuit. We show that this problem can be solved efficiently in polynomial time by reducing it to a minimum-cut instance on a graph derived from the circuit. Our formulation is flexible and can incorporate additional consid- erations, such as reducing depth overhead by preferring switches during idle periods or biasing the compilation to favor one code over another. To the best of our knowledge, this is the first automated approach for compiling and optimizing code-switching-based quan- tum computations at the logical level.