Ilya Besedin, Michael Kerschbaum, Jonathan Knoll, Ian Hesner, Lukas Bödeker, Luis Colmenarez, Luca Hofele, Nathan Lacroix, Christoph Hellings, François Swiadek, Alexander Flasby, Mohsen Bahrami Panah, Dante Colao Zanuz, Markus Müller, Andreas Wallraff (Jan 09 2025).
Abstract: Quantum error correction is needed for quantum computers to be capable of fault-tolerantly executing algorithms using hundreds of logical qubits. Recent experiments have demonstrated subthreshold error rates for state preservation of a single logical qubit. In addition, the realization of universal quantum computation requires the implementation of logical entangling gates. Lattice surgery offers a practical approach for implementing such gates, particularly in planar quantum processor layouts. In this work, we demonstrate lattice surgery between two distance-three repetition-code qubits by splitting a single distance-three surface-code qubit. Using a quantum circuit fault-tolerant to bit-flip errors, we achieve an improvement in the value of the decoded
ZZ logical two-qubit observable compared to a similar non-encoded circuit. By preparing the surface-code qubit in initial states parametrized by a varying polar angle, we evaluate the performance of the lattice surgery operation for non-cardinal states on the logical Bloch sphere and employ logical two-qubit tomography to reconstruct the Pauli transfer matrix of the operation. In this way, we demonstrate the functional building blocks needed for lattice surgery operations on larger-distance codes based on superconducting circuits.
