Close the exponent gap in the memory bounds

Close the gap between the upper-bound exponent and the error-correcting reservoir's achievable exponent for memory depth as a function of the number of reinitialized input qubits under Markovian depolarizing noise.

Background

The main theorem establishes that the optimal memory depth grows exponentially with the number of fresh qubits per time step, but the exponent in the universal upper bound differs from the exponent achieved by the explicit error-correcting reservoir. The paper therefore determines the scaling class without determining the exact optimal exponential rate.

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

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