Quantum machine learning encodes classical data into quantum states and processes them through unitary or dissipative dynamics, with the latter governed by Lindblad master equations that generate one-parameter families of CPTP maps [1,2]. Outputs are obtained as expectation values of observables, with learning performed via classical optimization of measurement data [3–6]. The exponentially large Hilbert space of qubit systems supports rich function classes, but this expressivity is practically constrained by barren plateaus in parameter training [7], the existence of efficient classical surrogates for many quantum models [8], and hardware noise. These limitations motivate approaches where the dynamics itself carries the computational load. Quantum reservoir computing realizes this idea: input-driven open quantum evolution with engineered dissipation, as opposed to uncontrolled hardware noise, can induce contractive maps with fading memory, enabling stable temporal processing compatible with near-term quantum devices [9–13]. Experimental demonstrations on NMR platforms confirm the viability of this approach [12].
Central open questions concern how specific dissipation structures, Markovian versus non-Markovian [14], quantitatively shape information processing capacity [15]; which observables maximize extractable information; how computational power scales with system size; and under what conditions quantum reservoirs provably outperform classical counterparts [8]. This thesis aims to investigate these questions, focusing on the interplay between dissipation, measurement, and memory in determining the computational capabilities of open quantum systems used for machine learning.
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