We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of every density-matrix element for an arbitrary time-independent Hamiltonian and show that the Hamiltonian enters the dynamics only through the corresponding Bohr frequencies. This leads to a natural distinction between two classes of quantum systems: gapped and gapless. In \emph{gapped systems} (systems with a discrete energy spectrum), while the diagonal elements remain unchanged, the off-diagonal elements of the density matrix in the energy eigenbasis decay algebraically with a continuously varying exponent and with an amplitude that oscillates periodically in $\log t$. The system therefore approaches a stationary state that is independent of the resetting rate and retains a strong memory of the initial state. In \emph{gapless systems} (systems with a continuous energy spectrum), arbitrarily small Bohr frequencies prevent stationarity. Instead, the position distribution spreads on the universal (ultra-slow) scale $\log(rt)/r$, independently of the initial state and of the details of the Hamiltonian. We illustrate these results with a two-level system, a harmonic oscillator, and a free quantum particle, and contrast them with their classical counterparts.
Restart of a quantum process is typically modeled as a global reinitialization that erases the system's entire history. Here we introduce subspace restart, a protocol that periodically resets only the internal degrees of freedom while preserving the spatial distribution, as a tunable knob for the quantum-to-classical crossover. Using the discrete-time quantum walk as an example, we show that this selective reset drives the walker into an engineered drifted-diffusion regime. This phenomenon can be understood by a Huygens-Fresnel mechanism, where each restart fragments the wave function into a set of independent secondary sources to screen long-range correlations and isolate a robust classical backbone, whose drift and diffusivity are set by the geometric orientation of the initial coin and the restart period. Residual quantum interference, confined to effective light cones, survives only as a short-range correction that renormalizes these coefficients and imprints periodic modulations on the cumulants. Our results establish subspace restart as a route to controlling the quantum-to-classical crossover in synthetic lattices.
Non-Markovianity can be characterized by performing a series of successive measurements and analyzing departures of the corresponding outcome statistics from a Markovian probabilistic structure. Considering a system coupled with its environment via a dephasing interaction, we show that joint outcome probabilities can be written in terms of a set of two-time environment correlations. Their definition involves forward and backward propagators with different Hamiltonians, associated with a recently introduced generalization of standard Loschmidt echoes [Cormick and Budini, Phys. Lett. A 593, 132011 (2026)]. This result establishes a solid connection between quantum non-Markovianity defined in an operational (measurement-based) way and complex quantum dynamics studied through their sensitivity to dynamical perturbations. We find conditions that guarantee a Markovian (system) behavior and also determine how the generalized echoes can identify information exchanges between the system and its environment. We illustrate our ideas considering examples of spin environments that realize these different dynamical regimes.
The physics of information scrambling in quantum many-body systems is intimately related to thermalisation and emergence of chaos. However, its standard characterisation through bipartite entanglement or operator growth remains inherently coarse-grained, obscuring the spatiotemporal anatomy of how quantum information flows between different regions of the system and across various length scales. In this work, we develop a theory for the dynamics of local information in local random unitary circuits which resolves the fine-grained microscopic structures of local information flow in such systems. Using the framework of information lattice which systematises the information content at each length scale within each subsystem, we identify a distribution of length scales at which information resides and obtain the dynamics of the distribution. For Haar-random circuits with infinite local Hilbert-space dimensions, we map this dynamics onto an exact classical stochastic process which reveals that this distribution is described by a Tracy-Widom form which moves ballistically in time ($ \propto t$) toward larger scales, accompanied by a $\sim t^{1/3}$ broadening. We also find the same qualitative behaviour for random Clifford circuits acting on qubits. The similar scaling behaviour in two rather different settings hints strongly towards the universality of our results. In the case of Clifford circuits, we develop a phenomenological Markov process for the dynamics of the stabiliser generators in a specific gauge which confirms the Tracy-Widom distribution and the $t^{1/3}$ scaling of the fluctuations. Ultimately, our results establish the universal properties of the dynamics of local quantum information in a length scale-resolved fashion and provide a possible route towards bridging exact microscopic theories for information dynamics with emergent hydrodynamic descriptions of information flow.
Existing quantum algorithms for simulating dynamical systems -- from Hamiltonian simulation to linear and nonlinear differential equations solvers -- simulate Markovian dynamics, in which the system's future evolution depends solely on its current state. We turn our attention to developing quantum algorithms for non-Markovian dynamical systems where the system's future evolution depends on its past history and thus has memory. Specifically, we develop efficient algorithms for linear Volterra integro-differential equations (VIDEs) with a convolution memory kernel that output a quantum state encoding the state description over a time interval or at a particular time. Given efficient circuits for the problem inputs, our algorithms achieve an exponential speedup in system size over existing classical algorithms. We develop an algorithm for general kernels assuming that $\textsf{M}<1$, where $\textsf{M}$ characterizes the strength of the memory term relative to the dissipation of the Markovian part of the dynamics. We complement this with lower bounds for general-kernel VIDEs when $\textsf{M} \geq 1$, showing that the problem becomes intractable for a family of systems. However, by specializing to structured kernels which admit concise decompositions over exponentials, we develop efficient quantum algorithms even when $\textsf M \geq 1$ by converting the VIDE into a larger set of ODEs, a procedure which we call Markovianization. As an application of the overall framework, we discuss the Mori-Zwanzig formalism used in open quantum systems and fluid dynamics. Overall, our results expand the range of dynamical systems that quantum computers can simulate efficiently.
The quantum Rabi model is a standard effective Hamiltonian in studies of light-matter interaction, capturing the simplest nontrivial setting in which a qubit couples to a single harmonic oscillator. Within the broader Rabi family, we focus on two special cases: the Jaynes-Cummings (JC) model, which carries an explicit $U(1)$ symmetry, and the asymmetric quantum Rabi model (AQRM), which possesses a parameter-dependent"hidden''symmetry that appears only at integer bias, $\varepsilon/\omega\in\mathbb{Z}$, and is not manifest in the Hamiltonian. We use the time-averaged entangling power as an operator-level diagnostic of these symmetry structures. Since the oscillator Hilbert space is infinite-dimensional, we compare two finite input ensembles: a Haar average after Fock-space truncation and a coherent-state average at fixed mean occupation $\bar{n}$. Both diagnostics show peaks at the integer-bias points of the AQRM, where the hidden symmetry resides. In contrast, the manifest $U(1)$ symmetry at the JC point instead gives a weak dip. Thus, the time-averaged entangling power responds to both the hidden symmetry and the $U(1)$ symmetry in the Rabi family, with the sign of the response indicating how the symmetry reorganizes the spectral expansion. These results demonstrate that the entangling power can serve as an operator diagnostic to reveal the presence and properties of hidden and manifest symmetries in light-matter systems.
We challenge the common belief that if there is no absolute time parameter in physics, a quantum system described without reference to an external clock can be assumed to be in a stationary state of its Hamiltonian. We present a time-reparameterisation invariant quantum evolution law, which for a given initial condition predicts the same trajectory in state space as the Schr\"odinger equation, except that for nontrivial trajectories it does not predict the speed at which the trajectory is traversed. The solutions of this evolution law are all time-reparameterised solutions of the Schr\"odinger equation. We show how the predictions of the Schr\"odinger equation are recovered relative to an internal clock in this framework. In contrast to the Page-Wootters formalism or Dirac's quantisation of the Hamiltonian constraint, here the global sate is not stationary. We discuss the assumptions leading to the common conclusion that the state can be taken stationary and suggest that they need to be revisited.