Persistence of the explicit-memory versus recurrent-memory trade-off at larger system sizes

Establish whether the trade-offs between explicit input encoding and recurrent quantum memory reported for the ten-qubit nearest-neighbor mixed-field Ising reservoir persist at larger system sizes, where the recurrent state grows exponentially while the encoding register and measured observable set grow only polynomially.

Background

All numerical results in the paper use a ten-qubit one-dimensional Mixed-Field Ising reservoir. The authors identify a trade-off controlled by the encoding-window length: recurrent quantum memory is important for tasks requiring access to distant history, while an explicit register can suffice for tasks with short relevant correlations.

Scaling this conclusion is nontrivial because the quantum state space grows exponentially with system size, whereas the number of encoding qubits and the measured one- and two-body observables grows only polynomially. The authors therefore leave unresolved whether the observed memory trade-offs survive beyond the studied system size.

References

This study is finally limited to $N = 10$ qubits, and whether the reported trade-offs persist at larger sizes, where the recurrent state grows exponentially while both the register and the measured observable set grow only polynomially, remains to be established, a question made timely by recent analog realizations of quantum reservoirs.

— From quantum reservoirs to quantum extreme learning machines through a nearest-neighbor spin chain with tunable quantum memory  (2608.28440 - Ramon-Escandell et al., 28 Aug 2026) in Section 4, Conclusions

The Bose--Hubbard result would be much less informative if the same type of state were always preferred. We therefore apply the selection procedure to a microscopically different working medium and ask whether it can identify a different representation when the dynamics demands one.

— Finite Quantum Engineering Thermodynamics  (2610.13511 - Ahmadi, 9 Oct 2026) in Section 4, immediately before Section 4.1 (Selecting the thermodynamic representation)