Floquet codes and dynamically generated logical qubits

Short answer: Floquet codes, introduced in a 2021 Quantum paper, are error-correcting codes where logical qubits are generated dynamically by a repeating pattern of two-qubit Pauli measurements, even though the code viewed as a subsystem code has no logical qubits. A later Physical Review paper reports that measuring the stabilizers with dynamic circuits, without ancilla qubits, raises the code's threshold and lowers its logical error rate in simulation. Both are theory and simulation results.

The 2021 idea: dynamically generated logical qubits

The Quantum journal abstract presents a code with dynamically generated logical qubits. Viewed as a subsystem code, it has no logical qubits at all. Yet the authors' measurement patterns generate logical qubits, so the code can act as a fault-tolerant quantum memory. The particular code is described as very similar to the two-dimensional toric code, but with the difference that each measurement is a two-qubit Pauli measurement. That matters because two-qubit measurements are simpler to implement than the larger stabilizer measurements many codes need, though the abstract itself does not claim a hardware advantage.

The follow-up: dynamic circuits

The Physical Review abstract starts from the usual way of running an error-correcting code: each stabilizer is measured by entangling one or more ancilla qubits with the data qubits and then measuring the ancillas. It says a dynamic circuit approach has been introduced in which stabilizers are measured without ancilla qubits. The authors report that dynamic circuits are particularly useful for the Floquet code. According to them, their dynamic circuit increases the timelike distance of the code, automatically removes leakage, and both significantly increases the threshold and lowers the logical error rate compared with the standard ancilla-based circuit. They also report an estimated reduction in the number of qubits needed to reach a target logical error rate at a stated physical error rate. The specific figures did not render on the page when this post was written, so they are not repeated here.

A third source

A 2021 arXiv entry, 2107.02194, was listed as a source, but only its page header was readable, so it is not described.

Limits

The 2021 paper defines the code and shows it can act as a memory in the authors' model. The later result is an estimate for a circuit-level noise model. Neither abstract reports an experiment on a quantum device, and the comparison with ancilla-based circuits depends on the noise assumptions the authors chose.

FAQ

What is a Floquet code?

A code whose logical qubits are generated dynamically by a repeating measurement pattern, per the 2021 Quantum paper.

Why call the logical qubits dynamically generated?

Viewed as a subsystem code the code has no logical qubits, but the measurement sequence creates them.

What do dynamic circuits change?

They measure stabilizers without ancilla qubits. The authors report a higher threshold and a lower logical error rate than the ancilla-based circuit.

Is the code similar to the toric code?

The 2021 abstract describes it as very similar to the two-dimensional toric code, with two-qubit Pauli measurements.

Has it been run on hardware?

Neither abstract reports a hardware experiment.