arXiv subjects

Lorenzo Piroli

Publications and source records attributed to Lorenzo Piroli.

At least 19 recordsLinked to original sources

arXiv2026

Correlation and entanglement dynamics of free fermions in disguise

We study the nonequilibrium dynamics following a quantum quench in spin chains that can be solved via a mapping to free fermions in disguise. These models feature an exponential degeneracy of all energy eigenvalues, raising the question of the validity of the established framework describing the properties of integrable systems out of equilibrium. We present two main results. First, we develop an analytic method to compute the quasi-momentum distribution function characterizing the generalized Gibbs ensemble, and derive an analytic formula to compute the corresponding expectation values for special observables. Second, we adapt the standard formula for the entanglement growth based on the quasi-particle picture, discussing how our constructions do not explicitly make use of the zero-energy auxiliary free fermions responsible of the exponential degeneracies. We test our theoretical predictions against numerical tensor-network computations for different initial states and Hamiltonian parameters. For the local observables, we find excellent agreement. For the entanglement dynamics, we find small deviations suggesting that the standard quasi-particle picture is only approximately correct for the initial state considered. Our results represent a first step towards the extension of the established framework of integrable systems out of equilibrium to models hosting free fermions in disguise.

cond-mat.stat-mech↗

arXiv2026

Long-range nonstabilizerness of topologically encoded states from mutual information

We study long-range nonstabilizerness (LRN), namely the obstruction to remove nonstabilizerness with shallow-depth local quantum circuits. In one-dimensional settings, the mutual information between disconnected spatial regions has proven to be a powerful tool to diagnose LRN. In this work, we focus on encoded states of two-dimensional topologically-ordered systems, and explore the ability of the mutual information to serve as a diagnostic of LRN. Focusing on the concrete setting of lattice models defined on a torus, we show that information about LRN can be gained from the analysis of the mutual information between non-overlapping regions containing non-contractible loops, and of the change of such mutual information under modular real-space transformations. We exemplify this idea in the toric code and the non-abelian string-net model with doubled Fibonacci topological order. In the former case, we show that the mutual information provides a full classification, certifying LRN for all encoded non-stabilizer states. In the latter case, instead, our approach does not lead to a full classification, as it detects LRN for all states except from a finite subset with special transformation properties under the modular group. Finally, we discuss how our results on LRN constrain the logical gates that can be implemented fault-tolerantly on the torus.

quant-ph↗

arXiv2026

Domain-wall melting in all-to-all QSSEP from random-matrix theory

We study the melting of a domain wall in the quantum simple exclusion process with all-to-all hoppings (a.k.a. the charged SYK$_2$ model). We show that the real-time dynamics of physical quantities of interest can be obtained exploiting spectral results in random matrix theory. We first show that the eigenvalues of the correlation matrix corresponding to the initially charged subsystem evolve according to a Jacobi process, which is defined in terms of a closed system of stochastic differential equations. In turn, this observation allows us to obtain the real-time dynamics of all the eigenvalue moments. We present two physical applications. First, we study the dynamics of the averaged von Neumann entanglement entropy, arriving at a fully explicit expression in the thermodynamic limit. Second, we compute analytically the full-counting statistics of the charge. Our formula allows us to perform a thorough comparison with the full-counting statistics of the classical simple exclusion process. Notably, we show that, in the thermodynamic limit, the quantum and classical full-counting statistics coincide, with no finite-time corrections.

cond-mat.stat-mech↗

arXiv2026

Generalized hydrodynamics of free fermions under extensive-charge monitoring

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

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arXiv2026

An asymmetry lower bound on fermionic non-Gaussianity

Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

quant-ph↗

arXiv2026

Engineering discrete local dynamics in globally driven dual-species atom arrays

We introduce a method for engineering discrete local dynamics in globally-driven dual-species neutral atom experiments, allowing us to study emergent digital models through uniform analog controls. Leveraging the new opportunities offered by dual-species systems, such as species-alternated driving, our construction exploits simple Floquet protocols on static atom arrangements, and benefits of generalized blockade regimes (different inter- and intra-species interactions). We focus on discrete dynamical models that are special examples of Quantum Cellular Automata (QCA), and explicitly consider a number of relevant examples, including the kicked-Ising model, the Floquet Kitaev honeycomb model, and the digitization of generic translation-invariant nearest-neighbor Hamiltonians (e.g., for Trotterized evolution). As an application, we study chaotic features of discretized many-body dynamics that can be detected by leveraging only demonstrated capabilities of globally-driven experiments, and benchmark their ability to discriminate chaotic evolution.

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arXiv2025

Construction and simulability of quantum circuits with free fermions in disguise

We provide a systematic construction for local quantum circuits hosting free fermions in disguise, both with staircase and brickwork architectures. Similar to the original Hamiltonian model introduced by Fendley, these circuits are defined by the fact that the Floquet operator corresponding to a single time step can not be diagonalized by means of any Jordan-Wigner transformation, but still displays a free-fermionic spectrum. Our construction makes use of suitable non-local transfer matrices commuting with the Floquet operator, allowing us to establish the free fermionic spectrum. We also study the dynamics of these circuits after they are initialized in arbitrary product states, proving that the evolution of certain local observables can be simulated efficiently on classical computers. Our work proves recent conjectures in the literature and raises new questions on the classical simulability of free fermions in disguise.

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arXiv2025

Entanglement asymmetry dynamics in random quantum circuits

We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local $U(1)$ charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically non-local RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation time scales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and non-local circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration time scales are again independent of the system size for both local and non-local circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is non-monotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and non-local RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical non-integrable dynamics.

cond-mat.stat-mech↗

arXiv2025

Breaking global symmetries with locality-preserving operations

In the general framework of quantum resource theories, one typically only distinguishes between operations that can or cannot generate the resource of interest. In many-body settings, one can further characterize quantum operations based on underlying geometrical constraints, and a natural question is to understand the power of resource-generating operations that preserve locality. In this work, we address this question within the resource theory of asymmetry, which has recently found applications in the study of many-body symmetry-breaking and symmetry-restoration phenomena. We consider symmetries corresponding to both abelian and non-abelian compact groups with a homogeneous action on the space of $N$ qubits, focusing on the prototypical examples of $U(1)$ and $SU(2)$. We study the so-called $G$-asymmetry $\Delta S^{G}_N$, and present two main results. First, we derive a general bound on the asymmetry that can be generated by locality-preserving operations acting on product states. We prove that, in any spatial dimension, $\Delta S^{G}_N\leq (1/2)\Delta S^{G, \rm max}_N[1+o(1)]$, where $\Delta S^{G, \rm max}_N$ is the maximum value of the $G$-asymmetry in the full many-body Hilbert space. Second, we show that locality-preserving operations can generate maximal asymmetry, $\Delta S^{G}_N\sim\Delta S^{G, \rm max}_N$, when applied to symmetric states featuring long-range entanglement. Our results provide a unified perspective on recent studies of asymmetry in many-body physics, highlighting a non-trivial interplay between asymmetry, locality, and entanglement.

quant-ph↗

arXiv2025

The Hilbert-space structure of free fermions in disguise

Free fermions in disguise (FFD) Hamiltonians describe spin chains which can be mapped to free fermions, but not via a Jordan-Wigner transformation. Although the mapping gives access to the full Hamiltonian spectrum, the computation of spin correlation functions is generally hard. Indeed, the dictionary between states in the spin and free-fermion Hilbert spaces is highly non-trivial, due to the non-linear and non-local nature of the mapping, as well as the exponential degeneracy of the Hamiltonian eigenspaces. In this work, we provide a series of results characterizing the Hilbert space associated to FFD Hamiltonians. We focus on the original model introduced by Paul Fendley and show that the corresponding Hilbert space admits the exact factorization $\mathcal{H}=\mathcal{H}_F\otimes \mathcal{H}_D$, where $\mathcal{H}_F$ hosts the fermionic operators, while $\mathcal{H}_D$ accounts for the exponential degeneracy of the energy eigenspaces. By constructing a family of spin operators generating the operator algebra supported on $\mathcal{H}_D$, we further show that $\mathcal{H}_D=\mathcal{H}_{F'}\otimes \mathcal{H}_{\widetilde{D}}$, where $\mathcal{H}_{F'}$ hosts ancillary free fermions in disguise, while $\mathcal{H}_{\widetilde{D}}$ is generated by the common eigenstates of an extensive set of commuting Pauli strings. Our construction allows us to fully resolve the exponential degeneracy of all Hamiltonian eigenspaces and is expected to have implications for the computation of spin correlation functions, both in and out of equilibrium.

cond-mat.stat-mech↗

arXiv2025

Learning mixed quantum states in large-scale experiments

We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to $N = 96$ qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.

quant-ph↗

arXiv2025

Entanglement dynamics and Page curves in random permutation circuits

The characterization of ensembles of many-qubit random states and their realization via quantum circuits are crucial tasks in quantum-information theory. In this work, we study the ensembles generated by quantum circuits that randomly permute the computational basis, thus acting classically on the corresponding states. We focus on the averaged entanglement and present two main results. First, we derive generically tight upper bounds on the entanglement that can be generated by applying permutation circuits to arbitrary initial states. We show that the late-time ``entanglement Page curves'' are bounded in terms of the initial state participation entropies and its overlap with the ``maximally antilocalized'' state. Second, comparing the averaged R\'enyi-$2$ entropies generated by $(i)$ an infinitely deep random circuit of two-qubit gates and $(ii)$ global random permutations, we show that the two quantities are different for finite $N$ but the corresponding Page curves coincide in the thermodynamic limit. We also discuss how these conclusions are modified by additional random phases or considering circuits of $k$-local gates with $k\geq 3$. Our results are exact and highlight the implications of classical features on entanglement generation in many-body systems.

cond-mat.stat-mech↗

arXiv2025

Approximate inverse measurement channel for shallow shadows

Classical shadows are a versatile tool to probe many-body quantum systems, consisting of a combination of randomised measurements and classical post-processing computations. In a recently introduced version of the protocol, the randomization step is performed via unitary circuits of variable depth $t$, defining the so-called shallow shadows. For sufficiently large $t$, this approach allows one to get around the use of non-local unitaries to probe global properties such as the fidelity with respect to a target state or the purity. Still, shallow shadows involve the inversion of a many-body map, the measurement channel, which requires non-trivial computations in the post-processing step, thus limiting its applicability when the number of qubits $N$ is large. In this work, we put forward a simple approximate post-processing scheme where the infinite-depth inverse channel is applied to the finite-depth classical shadows and study its performance for fidelity and purity estimation. The scheme allows for different circuit connectivity, as we illustrate for geometrically local circuits in one and two spatial dimensions and geometrically non-local circuits made of two-qubit gates. For the fidelity, we find that the resulting estimator coincides with a known linear cross-entropy, achieving an arbitrary small approximation error $δ$ at depth $t=O(\log (N/δ))$ (independent of the circuit connectivity). For the purity, we show that the estimator becomes accurate at a depth $O(N)$. In addition, at those depths, the variances of both the fidelity and purity estimators display the same scaling with $N$ as in the case of global random unitaries. We establish these bounds by analytic arguments and extensive numerical computations in several cases of interest. Our work extends the applicability of shallow shadows to large system sizes and general circuit connectivity.

quant-ph↗

arXiv2025

Adiabatic quantum state preparation in integrable models

We propose applying the adiabatic algorithm to prepare high-energy eigenstates of integrable models on a quantum computer. We first review the standard adiabatic algorithm to prepare ground states in each magnetization sector of the prototypical XXZ Heisenberg chain. Based on the thermodynamic Bethe ansatz, we show that the algorithm circuit depth is polynomial in the number of qubits $N$, outperforming previous methods explicitly relying on integrability. Next, we propose a protocol to prepare arbitrary eigenstates of integrable models that satisfy certain conditions. For a given target eigenstate, we construct a suitable parent Hamiltonian written in terms of a complete set of local conserved quantities. We propose using such Hamiltonian as an input for an adiabatic algorithm. After benchmarking this construction in the case of the non-interacting XY spin chain, where we can rigorously prove its efficiency, we apply it to prepare arbitrary eigenstates of the Richardson-Gaudin models. In this case, we provide numerical evidence that the circuit depth of our algorithm is polynomial in $N$ for all eigenstates, despite the models being interacting.

quant-ph↗

arXiv2025

Generalized hydrodynamics of integrable quantum circuits

Quantum circuits make it possible to simulate the continuous-time dynamics of a many-body Hamiltonian by implementing discrete Trotter steps of duration $τ$. However, when $τ$ is sufficiently large, the discrete dynamics exhibit qualitative differences compared to the original evolution, potentially displaying novel features and many-body effects. We study an interesting example of this phenomenon, by considering the integrable Trotterization of a prototypical integrable model, the XXZ Heisenberg spin chain. We focus on the well-known bipartition protocol, where two halves of a large system are prepared in different macrostates and suddenly joined together, yielding non-trivial nonequilibrium dynamics. Building upon recent results and adapting the generalized hydrodynamics (GHD) of integrable models, we develop an exact large-scale description of an explicit one-dimensional quantum-circuit setting, where the input left and right qubits are initialized in two distinct product states. We explore the phenomenology predicted by the GHD equations, which depend on the Trotter step and the gate parameters. In some phases of the parameter space, we show that the quantum-circuit large-scale dynamics is qualitatively different compared to the continuous-time evolution. In particular, we find that a single microscopic defect at the junction, such as the addition of a single qubit, may change the nonequilibrium macrostate appearing at late time.

cond-mat.stat-mech↗

arXiv2025

Long-range nonstabilizerness and phases of matter

Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits. In this work, we study long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error correcting codes. After presenting a simple argument showing that long-range nonstabilizerness is a generic property of many-body states, we restrict to the class of ground states of gapped local Hamiltonians. We focus on one-dimensional systems and present rigorous results in the context of translation-invariant matrix product states (MPSs). By analyzing the fixed points of the MPS renormalization-group flow, we provide a sufficient condition for long-range nonstabilizerness, which depends entirely on the local MPS tensors. Physically, our condition captures the fact that the mutual information between distant regions of stabilizer fixed points is quantized, and this fact is not changed after applying shallow quantum circuits. We also discuss possible ramifications in the classification of phases of matter and quantum error correction.

quant-ph↗

arXiv2024

Monitored fermions with conserved $\mathrm{U}(1)$ charge

We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$σ$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$σ$M and also discuss higher dimensional generalizations.

cond-mat.stat-mech↗

arXiv2024

Approximating many-body quantum states with quantum circuits and measurements

We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called $W$ and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a byproduct of our work, we introduce an efficient scheme to implement certain non-local, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.

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