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.