Qubit ZooFloquet codes are a family of dynamical quantum error-correcting codes where the code space is not defined by a fixed set of stabilizers but instead emerges from a periodic sequence of two-body measurements. The codespace changes at each time step but returns to itself after a complete measurement cycle, defining logical qubits that persist stroboscopically.
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Description
Introduced by Hastings and Haah (2021), the honeycomb Floquet code is the prototypical example. The physical qubits sit on vertices of a honeycomb lattice, and at each time step, two-body Pauli measurements (XX, YY, or ZZ) are performed on pairs of qubits sharing an edge. The three edge colors are measured in a repeating 3-step cycle.
Key advantages:
- Two-body measurements only: No multi-qubit stabilizer measurements needed (vs. weight-4 checks in surface code), simplifying hardware.
- Inherent fault tolerance: The dynamical structure naturally detects errors from measurement failures.
- Competitive thresholds: Comparable to surface code despite simpler measurements.
- Potential for qLDPC integration: Floquet techniques may help implement non-local codes on local hardware.
The main subtlety is that the instantaneous stabilizer group changes at each step — logical information is only well-defined when viewed over complete cycles.
Measurement Cycle
On a honeycomb lattice with edge coloring (r, g, b), the 3-step cycle measures:
The effective code after one complete cycle is equivalent to a topological code with distance set by the lattice size. The check operators from consecutive rounds combine to form the stabilizers of a toric/surface code.
Performance Metrics
| Metric | Value | Notes | Fidelity reference |
|---|---|---|---|
| Measurement weight | 2 | Only two-body measurements (vs. weight-4 for surface code) | hastings-2021-floquet |
| Threshold (circuit-level) | ~0.2–0.5% | Depends on noise model and decoder | hastings-2021-floquet |
| Code distance | = linear lattice dimension | — | |
| Encoding rate | Same scaling as surface code for 2D | — |
Scaling Considerations
- Hardware simplicity: Two-body measurements are natively available on most platforms (especially superconducting and neutral atom).
- Decoding: Requires decoders that handle the time-varying stabilizer structure; matching-based decoders adapted from surface code work well.
- Google interest: Active exploration for next-generation error correction beyond the surface code.