Fig. 3: Control of nonlinearity of reservoir memory via input encoding.

Here the input s_k ∈ [−1, 1] is encoded to the displacement of the ancilla according to ∣α∣ → (1 − λ)(s_k + 1) + λ, \(\arg (\alpha )\to 2\pi \lambda s_k\), where λ ∈ [0, 1] is a parameter controlling how much we encode to the amplitude ∣α∣ or phase \(\arg (\alpha )\) of the displacement. Reservoir memory is measured using information processing capacity, which quantifies the ability of the reservoir to reconstruct functions of the input at different delays. The figure shows how the relative contributions from linear and nonlinear functions to the normalized total capacity can be controlled with λ. Nonlinear contributions are further divided to degrees 2 and 3 (low nonlinear) and higher (high nonlinear). For λ = 0 the encoding is strictly to ∣α∣, leading to linear information processing, while at λ = 1 only \(\arg (\alpha )\) depends on the input, leading to most of the capacity to come from functions of the input with degree at least 4. All results are averages over 100 random reservoirs and error bars show the standard deviation.