Determine whether quantum codes can surpass the classical memory rate

Determine whether a quantum error-correcting code can achieve a memory-scaling rate exceeding the classical rate $\alpha_q=\tfrac12\ln\frac1{1-q^2}$ under the paper's depolarizing-noise and fresh-qubit model.

Background

The explicit construction attaining the lower bound is a classical reversible repetition-code reservoir implemented on qubits. Its exponential rate is denoted by αq\alpha_q. The paper leaves unresolved whether genuinely quantum coding strategies can improve on this classical rate while retaining the same noise model and fresh-qubit resource constraints.

References

Open problems include closing the exponent gap, whether a quantum code can beat the classical rate $\alpha_q$, what limits memory with feedback or non-Markovian noise, and testing the scaling by varying $k$ at fixed $n$ with mid-circuit resets.

— The Fundamental Memory Ceiling of Noisy Quantum Reservoirs  (2610.26228 - Baumann et al., 19 Oct 2026) in Conclusion