Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits

TL;DR

This paper demonstrates lattice surgery between two distance-three repetition-code qubits using superconducting circuits, showing improved logical two-qubit operations and paving the way for scalable fault-tolerant quantum computing.

Contribution

It presents the first implementation of lattice surgery between two distance-three repetition codes on superconducting qubits, including logical two-qubit gate characterization.

Findings

Improved logical $ZZ$ observable measurement compared to non-encoded circuits.

Successful logical two-qubit tomography of lattice surgery operation.

Demonstration of fundamental lattice surgery components for larger codes.

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.