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Free fermionic Gaussian, also known as matchgate, random circuits exhibit atypical behavior compared to generic interacting systems. They produce anomalously slow entanglement growth, characterized by diffusive scaling S(t)∼√t, and evolve into volume-law entangled states at late times, S∼N, which are highly unstable under measurements. Here, we investigate how doping such circuits with non-Gaussian resources (gates) restores entanglement structures of typical dynamics. We demonstrate that ballistic entanglement growth S(t)∼t is recovered after injecting an extensive total amount of non-Gaussian gates, which also restores Kardar-Parisi-Zhang fluctuations. When the evolution is perturbed with measurements, we uncover a measurement-induced phase transition between an area-law and a power-law entangled phase, S∼N^α, with α controlled by the doping. A genuine volume-law entangled phase is recovered only when non-Gaussian gates are injected at an extensive rate. Our findings bridge the dynamics of free and interacting fermionic systems, identifying non-Gaussianity as a key resource driving the emergence of nonintegrable behavior.

We introduce an efficient method to quantify nonstabilizerness in fermionic Gaussian states, overcoming the long-standing challenge posed by their extensive entanglement. Using a perfect sampling scheme based on an underlying determinantal point process, we compute the Stabilizer Rényi Entropies (SREs) for systems with hundreds of qubits. Benchmarking on random Gaussian states with and without particle conservation, we reveal an extensive leading behavior equal to that of Haar random states, with logarithmic subleading corrections. We support these findings with analytical calculations for a set of related quantities, the participation entropies in the computational (or Fock) basis, for which we derive an exact formula. We also investigate the time evolution of non-stabilizerness in a random unitary circuit with Gaussian gates, observing that it converges in a time that scales logarithmically with the system size. Applying the sampling algorithm to a two-dimensional free-fermionic topological model, we uncover a sharp transition in non-stabilizerness at the phase boundaries, highlighting the power of our approach in exploring different phases of quantum many-body systems, even in higher dimensions.

We investigate the dynamics of nonstabilizerness-also known as "magic"-in monitored quantum circuits composed of random Clifford unitaries and local measurements. For measurements in the computational basis, we derive an analytical model for dynamics of the stabilizer nullity, showing that it decays in quantized steps and requires exponentially many measurements to vanish, which reveals the strong protection through Clifford scrambling. On the other hand, for measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness. Here, the dynamics leads to a steady state with nontrivial nonstabilizerness, independent of the initial state. We find that Haar-random states equilibrate in constant time, whereas stabilizer states exhibit linear-in-size relaxation time. While the stabilizer nullity is insensitive to the rotation angle, stabilizer Rényi entropies expose a richer structure in their dynamics. Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics and demonstrate how measurements can both suppress and sustain quantum computational resources.

We study the behavior of magic as a bipartite correlation in the quantum Ising chain across its quantum phase transition and at finite temperature. To quantify the magic of partitions rigorously, we formulate a hybrid scheme that combines stochastic sampling of reduced density matrices via quantum Monte Carlo, with state-of-the-art estimators for the robustness of magic - a bona fide measure of magic for mixed states. This allows us to compute the mutual robustness of magic for partitions up to eight sites, embedded into a much larger system. We show how mutual robustness is directly related to critical behaviors: at the critical point, it displays a power-law decay as a function of the distance between partitions, whose exponent is related to the partition size. Once finite temperature is included, mutual magic retains its low temperature value up to an effective critical temperature, whose dependence on size is also algebraic. This suggests that magic, differently from entanglement, does not necessarily undergo a sudden death.

We introduce a methodology to estimate nonstabilizerness or “magic,” a key resource for quantum complexity, with neural quantum states (NQS). Our framework relies on two schemes based on Monte Carlo sampling to quantify nonstabilizerness via stabilizer Rényi entropy (SRE) in arbitrary variational wave functions. When combined with NQS, this approach is effective for systems with strong correlations and in dimensions larger than one, unlike tensor network methods. First, we study the magic content in an ensemble of random NQS, demonstrating that neural network parametrizations of the wave function capture finite nonstabilizerness besides large entanglement. Second, we investigate the nonstabilizerness in the ground state of the J1-J2 Heisenberg model. In one dimension, we find that the SRE vanishes at the Majumdar-Ghosh point J2 = J1/2, consistent with a stabilizer ground state. In two dimensions, a dip in the SRE is observed near maximum frustration around J2/J1 ≈ 0.6, suggesting a valence bond solid between the two antiferromagnetic phases.

Unitary integrable models typically relax to a stationary generalized Gibbs ensemble (GGE), but in experimental realizations dissipation often breaks integrability. In this work, we use the recently introduced time-dependent GGE (t-GGE) approach to describe the open dynamics of a gas of bosons subject to atom losses and gains. We employ tensor network methods to provide numerical evidence of the exactness of the t-GGE in the limit of adiabatic dissipation, and of its accuracy in the regime of weak but finite dissipation. That accuracy is tested for two-point functions via the rapidity distribution, and for more complicated correlations through a non-Gaussianity measure. We combine this description with generalized hydrodynamics and we show that it correctly captures transport at large scales. Our results demonstrate that the t-GGE approach is robust in both homogeneous and inhomogeneous settings.

We extend the recently introduced Clifford-dressed time-dependent variational principle (TDVP) to efficiently compute many-body wave-function amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wave function. By incorporating Clifford-disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a matrix product state (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a nonintegrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.

Understanding how entanglement can be reduced through simple operations is crucial for both classical and quantum algorithms. We investigate the entanglement properties of lattice models hosting conformal field theories cooled via local Clifford operations, a procedure we refer to as stabilizer disentangling. We uncover two distinct regimes: a constant gain regime, where disentangling is volume-independent, and a log-gain regime, where disentanglement increases with volume, characterized by a reduced effective central charge. In both cases, disentangling efficiency correlates with the target state magic, with larger magic leading to more effective cooling. The dichotomy between the two cases stems from mutual stabilizer Rényi entropy, which influences the entanglement cooling process. We provide an analytical understanding of such effect in the context of cluster Ising models, that feature disentangling global Clifford operations. Our findings indicate that matrix product states possess subclasses based on the relationship between entanglement and magic, and clarifying the potential of new classes of variational states embedding Clifford dynamics within matrix product states.

We propose an enhanced time-dependent variational principle (TDVP) algorithm for matrix product states that integrates Clifford disentangling techniques to efficiently manage entanglement growth. By leveraging the Clifford group, which maps Pauli strings to other Pauli strings while maintaining low computational complexity, we introduce a Clifford dressed single-site 1-TDVP scheme. During the TDVP integration, we apply a global Clifford transformation as needed to reduce entanglement by iteratively sweeping over two-qubit Clifford unitaries that connect neighboring sites in a checkerboard pattern. We validate the new algorithm numerically using various quantum many-body models, including both integrable and nonintegrable systems. Our results demonstrate that the Clifford dressed TDVP significantly improves entanglement management and computational efficiency, achieving higher accuracy, extended simulation times, and enhanced precision in computed observables compared to standard TDVP approaches. Additionally, we propose incorporating Clifford gates directly within the two-site 2-TDVP scheme.

We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement variational manifolds and target Hamiltonians with classical ground states. Despite highly entangled intermediate states along the exact adiabatic path, the variational evolution converges to the target ground state. We demonstrate this approach with several examples that align with our theoretical analysis.

Monitored quantum system have sparked great interest in recent years due to the possibility of observing measurement-induced phase transitions (MIPTs) in the full-counting statistics of quantum trajectories. Here, we investigate the dynamics of the Lipkin-Meshkov-Glick model, composed of N all-to-all interacting spins 1/2, under a weak external monitoring. In the thermodynamic limit, we derive a set of semiclassical stochastic equations describing the evolution of the expectation values of global spin observables. Our results show that the limit N→∞ does not commute with the long-time limit: while for any finite N the average over trajectories is expected to converge towards a trivial steady state, in the thermodynamic limit a MIPT appears. The transition is not affected by postselection issues, as it is already visible at the level of ensemble averages. We derive a quantitative theoretical picture explaining the nature of the transition within our semiclassical approach.

Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a different approach leveraging convolutional neural networks (CNNs) to classify quantum states based on their nonstabilizerness content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between stabilizer Rényi entropies and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources.

We investigate the dynamical deconfinement transition driven by excitations in a long-range Ising model. At low temperatures, spatially separated pairs of domain wall kinks are bound by the confining potential and exhibit uncorrelated Bloch oscillations in time. This picture is analogous to bound mesons in quark confinement. As the temperature increases, the meson picture breaks down as the domain wall kinks in proximity interact and disperse, leading to an extended deconfined regime. In this paper, we characterize the deconfinement transition with signatures observed in the average density of domain wall kinks and nonequilibrium changes in its fluctuation. Our findings provide insights into the mechanisms of confinement and deconfinement in long-range spin models, thus opening avenues for further exploration and experimental verification.

We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. By integrating these techniques, we enhance our ability to accurately model unitary dynamics while mitigating the exponential growth of entanglement encountered in classical simulations. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and random Clifford Floquet dynamics. This approach offers promising prospects for advancing our understanding of complex quantum phenomena and accelerating progress in quantum simulation.

We investigate the robustness of the many-body localized (MBL) phase to the quantum-avalanche instability by studying the dynamics of a localized spin chain coupled to a T=∞ thermal bath through its leftmost site. By analyzing local magnetizations we estimate the size of the thermalized sector of the chain and find that it increases logarithmically slowly in time. This logarithmically slow propagation of the thermalization front allows us to lower-bound the slowest thermalization time, and find a broad parameter range where it scales fast enough with the system size that MBL is robust against thermalization induced by avalanches. The further finding that the imbalance - a global quantity measuring localization - thermalizes over a timescale that is exponential both in disorder strength and system size is in agreement with these results.

In this paper, we investigate the relationship between entanglement and nonstabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the nonstabilizer analog of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for nonstabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with 1/χ2, with χ being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-χ correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a byproduct of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower - if at all - with the partition size, while for disconnected partitions, both are constant in size.

We present a novel classical algorithm designed to learn the stabilizer group - namely, the group of Pauli strings for which a state is a ±1 eigenvector - of a given matrix product state (MPS). The algorithm is based on a clever and theoretically grounded biased sampling in the Pauli (or Bell) basis. Its output is a set of independent stabilizer generators whose total number is directly associated with the stabilizer nullity, notably a well-established nonstabilizer monotone. We benchmark our method on T-doped states randomly scrambled via Clifford unitary dynamics, demonstrating very accurate estimates up to highly entangled MPS with bond dimension χ∼103. Our method, thanks to a very favorable scaling O(χ3), represents the first effective approach to obtain a genuine magic monotone for MPS, enabling systematic investigations of quantum many-body physics out of equilibrium.

Conserved-charge densities are very special observables in quantum many-body systems as, by construction, they encode information about the dynamics. Therefore, their evolution is expected to be of much simpler interpretation than that of generic observables and to return universal information on the state of the system at any given time. Here, we study the dynamics of the fluctuations of conserved U(1) charges in systems that are prepared in charge-asymmetric initial states. We characterize the charge fluctuations in a given subsystem using the full-counting statistics of the truncated charge and the quantum entanglement between the subsystem and the rest resolved to the symmetry sectors of the charge. We show that, even though the initial states considered are homogeneous in space, the charge fluctuations generate an effective inhomogeneity due to the charge-asymmetric nature of the initial states. We use this observation to map the problem into that of charge fluctuations on inhomogeneous, charge-symmetric states and treat it using a recently developed space-time duality approach. Specializing the treatment to interacting integrable systems we combine the space-time duality approach with generalized hydrodynamics to find explicit predictions.

We study the thermalization of the transverse field Ising chain with a power law decaying interaction ∼ 1/r^α following a global quantum quench of the transverse field in two different dynamical regimes. The thermalization behavior is quantified by comparing the full probability distribution function (PDF) of the evolving states with the corresponding thermal state given by the canonical Gibbs ensemble (CGE). To this end, we used the matrix product state (MPS)-based Time Dependent Variational Principle (TDVP) algorithm to simulate both real time evolution following a global quantum quench and the finite temperature density operator. We observe that thermalization is strongly suppressed in the region with strong confinement for all interaction strengths α, whereas thermalization occurs in the region with weak confinement.

Repeated measurements can induce entanglement phase transitions in the dynamics of quantum systems. Interacting models, both chaotic and integrable, generically show a stable volume-law entangled phase at low measurement rates that disappears for free, Gaussian fermions. Interactions break the Gaussianity of a dynamical map in its unitary part, but non-Gaussianity can be introduced through measurements as well. By comparing the entanglement and non-Gaussianity structure of different protocols, we propose a single particle indicator of the measurement-induced phase transition, and we use it to argue in favor of the stability of the transition when non-Gaussianity is purely provided by measurements.