Memory-Nonlinearity Trade-off across Quantum Reservoir Computing Frameworks

Abstract

Quantum reservoir computing (QRC) harnesses driven quantum dynamics for time-series processing, yet the mechanisms behind the differing performance levels across its many implementations remain unclear. We show that apparently unrelated approaches-including memory restriction, weak measurements, operation near the edge of quantum chaos, and dissipative dynamics-are in fact governed by the same underlying principle, namely a tunable balance between memory retention and nonlinear response. Using the information processing capacity, a dynamical measure from nonlinear systems theory, we place these behaviors in a unified framework and identify the regimes in which quantum reservoirs surpass the standard protocol. Our results reveal a fundamental connection between memory and nonlinear response. This provides a general design principle for enhanced information processing and enables systematic analysis and optimization inspired by classical dynamical quantifiers.

Figures (6)

• Figure 1: (a) Schematic overview of the quantum reservoir computing protocols: restarting, restricted input, weak measurement, and dissipative variants. (b) Example performance results obtained with these protocols on a representative task, where the restarting protocol is used to compute the edge of chaos. Definitions of memory, nonlinearity, and the total IPC are given in \ref{['subseq:IPC']}. We normalize the values in (a) and (b) to the FRP protocol, in (c) to the ergodic case, which would correspond to a random topology in classical reservoir computing, and in (d) to the maximum of linearity.
• Figure 2: Dependence of the information processing capacities (IPCs) (a-c) and task performance on the reset length $r$ (d) in the memory-restricted QRC.
• Figure 3: Overview of the indirect measurement protocol. First, an ancilla qubit is initialized via an $R_Y (\varphi)$ gate, where the rotation angle $\varphi=\frac{\pi}{2}-\vartheta$ allows for tuning of the measurement strength $\vartheta$. This ancilla then interacts with the system qubit through a CNOT gate. Finally, a projective measurement is performed on the ancilla; the resulting outcome is used to infer the state of the system qubit.
• Figure 4: Dependence of the information processing capacities (IPCs) (a-c) and task performances (d) on the measurement strength $\vartheta$ defined in equation \ref{['eq:m_matrix']}, where the dashed lines are indicating the vanilla QRC limit.
• Figure 5: Dependence of the information processing capacities (IPCs) (a-c) and task performance (d) on the field strength $h$ of the Hamiltonian (\ref{['eq:ising_chaos']}). Averages are computed over 100 sampled Hamiltonians. Blue and red region represent the localized and ergodic regime respectively. The optimal regime appears near the transition point $h \approx 0.5$, corresponding to the onset of quantum chaos.