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

Abstract

The team demonstrates lattice surgery between two distance-three repetition-code qubits by splitting a single distance-three surface-code qubit. Using fault-tolerant circuits, they achieve improvements in the decoded ZZ logical two-qubit observable vs non-encoded circuits, and validate performance across the logical Bloch sphere via logical two-qubit tomography. This is the first experimental demonstration of lattice surgery on superconducting qubits — a core building block for scaling surface codes toward fault-tolerant computation.

Key Contributions

• First superconducting lattice surgery — lattice surgery on superconducting qubits had been demonstrated only in theory and via trapped-ion systems prior to this work.
• Fault-tolerant ZZ operation — improvement in decoded ZZ logical observable vs non-encoded circuits.
• Validated across the logical Bloch sphere — logical two-qubit Pauli transfer matrix reconstructed through logical tomography, including non-cardinal states.
• Scalable primitive — the demonstration is the functional building block for larger-distance surface codes.

Methodology

• Fault-tolerant circuits designed to handle bit-flip errors.
• Parametric state preparation across varying polar angles on the logical Bloch sphere.
• Reconstructed the Pauli transfer matrix via logical two-qubit tomography.
• Qubit splitting of a single distance-three surface-code qubit into two distance-three repetition-code qubits.

Results

• Improvement in decoded ZZ logical two-qubit observable vs non-encoded circuits (specific error rates not extracted from abstract).
• Valid fault-tolerant operation across the logical Bloch sphere.
• Successful demonstration of universal primitives required for surface-code quantum computation.

Limitations

• Distance-three codes only — scaling to distance-5, 7, 9 remains future work.
• ZZ observable alone — demonstrates one class of logical two-qubit operations; XX and other Pauli observables need separate validation.
• Resource overhead — distance-3 repetition codes are the simplest case; real surface-code lattice surgery at useful scale requires many more physical qubits.

Why This Matters

This paper is the experimental bridge between Google's 2024 Willow result (surface-code memory below threshold, arXiv 2408.13687) and full fault-tolerant quantum computation. Memory is passive protection; lattice surgery is the compute primitive — the way you actually run a logical circuit on surface-code-protected qubits. Demonstrating it on superconducting hardware (rather than trapped-ion, where it's been shown before) puts IBM/Google's architectural bet back on a concrete experimental path. Combined with IBM's qLDPC decoding and Quantinuum's iceberg-code break-even, this makes 2026 the year QEC moved from "maybe" to "when."

Full Content

Content assembled from the arxiv preprint (2501.04612) and the Nature Physics abstract. The published Nature Physics version (Vol 22(2), pp 189-194) is behind a paywall; the arxiv preprint provides the methodology and scope.

Source: Lattice surgery realized on two distance-three repetition codes with superconducting qubits, Besedin et al., Nature Physics Vol 22(2) pp 189-194, January 2026. ArXiv preprint: 2501.04612.