Enhanced performance of quantum reservoir computing has been associated with dynamical phase transitions, but whether this connection extends to dissipative systems and which relaxation mechanisms underlie it remain insufficiently understood. We systematically compare driven-dissipative Kerr reservoirs across first-order and continuous dissipative phase transitions and find enhanced memory and nonlinear processing near both phase boundaries. Although the closure of the Liouvillian gap marks the transitions in the thermodynamic limit, computational performance does not generally follow gap suppression. An exact post-training Liouvillian-mode decomposition quantitatively attributes the trained memory to intrinsic relaxation channels. It shows that the gap mode contributes only weakly, while finite-rate modes and their cross-contributions dominate the enhanced capacity. These results go beyond phenomenological correlations by directly linking memory capacity to the intrinsic Liouvillian relaxation spectrum. Moreover, these findings provide a physical basis for designing dissipative quantum reservoirs and testing memory-enhancement mechanisms in experimentally accessible Kerr platforms.
Enhanced performance of quantum reservoir computing has been associated with dynamical phase transitions, but whether this connection extends to dissipative systems and which relaxation mechanisms underlie it remain insufficiently understood. We systematically compare driven-dissipative Kerr reservoirs across first-order and continuous dissipative phase transitions and find enhanced memory and nonlinear processing near both phase boundaries. Although the closure of the Liouvillian gap marks the transitions in the thermodynamic limit, computational performance does not generally follow gap suppression. An exact post-training Liouvillian-mode decomposition quantitatively attributes the trained memory to intrinsic relaxation channels. It shows that the gap mode contributes only weakly, while finite-rate modes and their cross-contributions dominate the enhanced capacity. These results go beyond phenomenological correlations by directly linking memory capacity to the intrinsic Liouvillian relaxation spectrum. Moreover, these findings provide a physical basis for designing dissipative quantum reservoirs and testing memory-enhancement mechanisms in experimentally accessible Kerr platforms.
Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a spectral resonance: the closing of the intrinsic energy gap forces the reservoir's internal transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data retained by the reservoir. This allows us to derive a generalized Landauer bound for continuous temporal processing, which reveals a fundamental thermodynamic trade-off: the critical resonance that maximizes predictive capacity simultaneously maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that quantum coherences amplify predictive capacity without demanding additional mechanical work. These findings establish the fundamental energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.
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.
Quantum reservoir computing (QRC) has emerged as a promising paradigm for harnessing near-term quantum devices to tackle temporal machine learning tasks. Yet, identifying the mechanisms that underlie enhanced performance remains challenging, particularly in many-body open systems where nonlinear interactions and dissipation intertwine in complex ways. Here, we investigate a minimal model of a driven-dissipative quantum reservoir described by two coupled Kerr-nonlinear oscillators, an experimentally realizable platform that features controllable coupling, intrinsic nonlinearity, and tunable photon loss. Using Partial Information Decomposition (PID), we examine how different dynamical regimes encode input drive signals in terms of redundancy (information shared by each oscillator) and synergy (information accessible only through their joint observation). Our key results show that, near a critical point marking a dynamical bifurcation, the system transitions from predominantly redundant to synergistic encoding. We further demonstrate that synergy amplifies short-term responsiveness, thereby enhancing immediate memory retention, whereas strong dissipation leads to more redundant encoding that supports long-term memory retention. These findings elucidate how the interplay of instability and dissipation shapes information processing in small quantum systems, providing a fine-grained, information-theoretic perspective for analyzing and designing QRC platforms.
Open quantum systems offer a physical substrate for temporal information processing in quantum reservoir computing, yet the microscopic mechanisms linking their dynamics to computational performance remain unclear. Here we establish a microscopic response-to-performance framework that connects Liouvillian dynamics directly to task performance. We decompose observable Volterra weights as W(q)=BH(q), separating internal input-history pathways from their readout visibility, and show that a dynamical response contributes to a task only if it is input-generated, readout-visible, target-correlated, and resolvable above the regularization scale. This framework reveals how Liouvillian modes govern the retention and propagation of task-relevant information, while symmetries determine which components remain visible to the readout. It further establishes how distinct covariance modes encode different temporal information structures and how system parameters and processing protocols can reshape their contributions to improve QRC performance. Thermalization drives the reservoir from processing that retains input history to a response dominated by the most recent input before regularization suppresses the residual information. We finally show that weak measurement can activate task-relevant covariance modes by lifting symmetry-imposed channel equivalence, whereas delayed feedback creates controlled return pathways for historical information. These results establish a microscopic connection between open-system dynamics and computational performance, providing principles for engineering task-relevant information flow in quantum reservoirs.
We investigate quantum thermometry in a driven--dissipative Kerr cavity coupled to a thermal reservoir. The system exhibits a finite-size precursor of a dissipative phase transition, characterized by a pronounced minimum of the Liouvillian gap and a sharp jump in the steady-state physical observables such as average photon number at the critical driving strength. We show that this regime leads to strong enhancement of the quantum Fisher information (QFI) for temperature estimation. Using an effective two-branch description, we show that the enhancement originates from temperature-induced redistribution of the weight factors in photon number distribution between low- and high-photon-number branches, which is described by an effective binary Fisher information. By optimizing the coherent drive, the enhanced response persists over an extended low-temperature, low-thermal-occupation regime and yields a favorable relative temperature-uncertainty bound. These results identify finite-size precursors of dissipative phase transitions in Kerr-cavity platforms as useful resources for tunable nonequilibrium quantum thermometry. We further show that the predicted thermometric enhancement is accessible in a parameter regime compatible with circuit quantum electrodynamics (circuit-QED) platforms.
In the thermodynamic limit, the steady states of open quantum many-body systems can undergo nonequilibrium phase transitions due to a competition between coherent and driven-dissipative dynamics. Here, we consider Markovian systems and elucidate structures of the Liouville superoperator that generates the time evolution. In many cases of interest, an operator-basis transformation can bring the Liouvillian into a block-triangular form, making it possible to assess its spectrum. The spectral gap sets the asymptotic decay rate. The superoperator structure can be used to bound gaps from below, showing that, in a large class of systems, dissipative phase transitions are actually impossible and that the convergence to steady states follows an exponential temporal decay. Furthermore, when the blocks on the diagonal are Hermitian, the Liouvillian spectra obey Weyl ordering relations. The results apply, for example, to Davies generators and quadratic systems and are also demonstrated for various spin models.