Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits, Part 1: Logical Bell State Preparation

Quantum error correction provides a pathway toward quantum computers capable of fault-tolerantly executing algorithms involving millions of qubits. A recent experiment with superconducting qubits has demonstrated sub-threshold distance-scaling of error rates for a single logical qubit [1]. However, the realization of universal quantum computation requires logical entangling gates, for which lattice surgery offers a practical approach. In this work, we encode a logical qubit in a distance-three surface code of superconducting qubits and employ a lattice surgery split operation to prepare an entangled state of two distance-three repetition codes. By stabilizing the surface code qubit and performing mid-cycle data qubit readout followed by Pauli frame updates, we herald one of the four logical Bell states. 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, demonstrating the effectiveness of our error-correction scheme, focusing on bit-flip errors.

[1] Google Quantum AI, arXiv:2408.13687 (2024)