arXiv subjects

Pablo Sala

Publications and source records attributed to Pablo Sala.

At least 19 recordsLinked to original sources

arXiv2026

Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence

Topological quantum computation relies on braiding non-Abelian anyons, but requires the underlying topological order to survive imperfect state preparation and environmental noise. We show that the instability of topological order to wavefunction deformations and to decoherence, with the latter probed by syndrome distributions, is generically captured by stat-mech models whose $G\times \textrm{Rep}(G)$ symmetry naturally exposes the corrupting anyonic excitations. As an example, we combine this framework with Monte-Carlo simulations to resolve the stability of $D_4$ topological order under deformations and quantum channels that proliferate multiple non-Abelian anyon species that are individually unable to condense. We show that beyond a finite threshold, proliferation of two non-Abelian anyon species parasitically condenses a shared Abelian-anyon fusion outcome---destroying the topological order. Our symmetry-based approach suggests the resulting trivial phase is distinct from that obtained by condensing all Abelian anyons; in other words, the trivial phase "remembers" which anyons condensed. This framework provides a first step into identifying the relevant symmetry for optimal decoders, conditioned on syndrome measurements, of non-Abelian topological order.

quant-ph↗

arXiv2026

Quantum sensing with critical systems: impact of symmetry, imperfections, and decoherence

Entangled many-body states enable high-precision quantum sensing beyond the standard quantum limit. We develop interferometric sensing protocols based on quantum critical wavefunctions and compare their performance with Greenberger-Horne-Zeilinger (GHZ) and spin-squeezed states. Building on the idea of symmetries as a metrological resource, we introduce a symmetry-based algorithm to identify optimal measurement strategies. We illustrate this algorithm both for magnetic systems with internal symmetries and Rydberg-atom arrays with spatial symmetries. We study the robustness of criticality for quantum sensing under non-unitary deformations, symmetry-preserving and symmetry-breaking decoherence, and qubit loss -- identifying regimes where critical systems outperform GHZ states and showing that non-unitary deformation can even enhance sensing precision. Combined with recent results on log-depth preparation of critical wavefunctions, interferometric sensing in this setting appears increasingly promising.

quant-ph↗

arXiv2025

Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order

Topological order (TO) provides a natural platform for storing and manipulating quantum information. However, its stability to noise has only been systematically understood for Abelian TOs. In this work, we exploit the non-deterministic fusion of non-Abelian anyons to inform active error correction and design decoders where the fusion products, instead of flag qubits, herald the noise. This intrinsic heralding enhances thresholds over those of Abelian counterparts when noise is dominated by a single non-Abelian anyon type. Furthermore, we use Bayesian inference to obtain a statistical mechanics model for fixed-point non-Abelian TOs with perfect measurements under any noise model, which yields the optimal threshold conditioned on measuring anyon syndromes. We numerically illustrate these results for $D_4 \cong \mathbb Z_4 \rtimes \mathbb Z_2$ TO. In particular, for non-Abelian charge noise and perfect syndrome measurement, we find a conditioned optimal threshold $p_c=0.218(1)$, whereas an intrinsically heralded minimal-weight perfect-matching (MWPM) decoder already gives $p_c=0.20842(2)$, outperforming standard MWPM with $p_c = 0.15860(1)$. Our work highlights how non-Abelian properties can enhance stability, rather than reduce it, and discusses potential generalizations for achieving fault tolerance.

quant-ph↗

arXiv2025

Practical roadmap to measurement-altered criticality in Rydberg arrays

Weak measurements have been predicted to dramatically alter universal properties of quantum critical wavefunctions, though experimental validation remains an open problem. Here we devise a practical scheme for realizing measurement-altered criticality in a chain of Rydberg atoms tuned to Ising and tricritical Ising phase transitions. In particular, we show that projectively measuring a periodic subset of atoms alters quantum critical correlations in distinct ways that one can control via the choice of measured sites and the measurement outcomes. While our protocol relies on post-selection, the measurement outcomes yielding the most dramatic consequences occur with surprisingly large probabilities: O(10%) with chains featuring O(100) sites. Characterizing the proposed post-measurement states requires only an adjustment in the post-process averaging of outcomes used to characterize unmeasured critical states, resulting in minimal additional experimental overhead for demonstrating measurement-altered criticality.

quant-ph↗

arXiv2025

Entanglement Holography in Quantum Phases via Twisted R\'enyi-N Correlators

We introduce a holographic framework for the entanglement Hamiltonian in symmetry-protected topological (SPT) phases with area-law entanglement, whose reduced density matrix $\rho \propto e^{-H_e}$ can be treated as a lower-dimensional mixed state. By replicating $\rho$, we reconstruct the fixed-point SPT wavefunction, establishing an exact correspondence between the bulk strange correlator of the (d+1)-dimensional SPT state and the twisted R\'enyi-N operator of the d-dimensional reduced density matrix. Notably, the reduced density matrix exhibits long-range or quasi-long-range order along the replica direction, revealing a universal entanglement feature in SPT phases. As a colloary, we generalized the framework of twisted R\'enyi-N correlator to thermal states and open quantum systems, providing an alternative formulation of the Lieb-Schultz-Mattis theorem, applicable to both closed and open systems. Finally, we extend our protocol to mixed-state SPT phases and introduce new quantum information metrics -- twisted R\'enyi-N correlators of the surgery operator -- to characterize the topology of mixed states.

cond-mat.str-el↗

arXiv2025

Entanglement cost hierarchies in quantum fragmented mixed states

Strong symmetries enforce non-trivial quantum entanglement patterns on the stationary states of symmetric open quantum dynamics. Specifically, non-commuting conserved quantities lead to long-range quantum entanglement even for infinite temperature mixed states within fixed symmetry sectors. Leveraging the commutant algebra framework, we show that various bipartite entanglement measures for mixed states -- including exact and asymptotically-exact entanglement costs and squashed entanglement, which are generally intractable for a generic many-body mixed state -- can be computed for this class of states. In particular, we focus on strongly symmetric maximally mixed states arising from the Temperley-Lieb model, which features quantum Hilbert space fragmentation with exponentially large (in system size) non-Abelian commutants. We find that while both the logarithmic negativity and the `exact' entanglement cost for equal-size bipartitions scale with the volume of the system, the entanglement of formation, squashed entanglement, entanglement cost, and distillable entanglement exhibit subextensive scaling. We relate this separation in entanglement measures to a parametric difference between the entanglement cost of exact and asymptotically-exact state preparations, and infer this to be a consequence of a particular pattern of quantum Hilbert space fragmentation.

quant-ph↗

arXiv2025

Dynamics in the presence of local symmetry-breaking impurities

Continuous symmetries lead to universal slow relaxation of correlation functions in quantum many-body systems. In this work, we study how local symmetry-breaking impurities affect the dynamics of these correlation functions using Brownian quantum circuits, which we expect to apply to generic non-integrable systems with the same symmetries. While explicitly breaking the symmetry is generally expected to lead to eventual restoration of full ergodicity, we find that approximately conserved quantities that survive under such circumstances can still induce slow relaxation. This can be understood using a super-Hamiltonian formulation, where low-lying excitations determine the late-time dynamics and exact ground states correspond to conserved quantities. We show that in one dimension, symmetry-breaking impurities modify diffusive and subdiffusive behaviors associated with U$(1)$ and dipole conservation at late-times, e.g., by increasing power-law decay exponents of the decay of autocorrelation functions. This stems from the fact that for these symmetries, impurities are relevant in the renormalization group sense, e.g., bulk impurities effectively disconnect the system, completely modifying both temporal and spatial correlations. On the other hand, for an impurity that disrupts strong Hilbert space fragmentation, the super-Hamiltonian only acquires an exponentially small gap, leading to prethermal plateaus in autocorrelation functions which extend for times that scale exponentially with the distance to the impurity. Overall, our approach systematically characterizes how symmetry breaking impurities affect relaxation dynamics in symmetric systems.

quant-ph↗

arXiv2024

Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wavefunction deformations and quantum channels acting on $D_4$ TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O$(2)$ loop model in the pure state case, and $n$ coupled O$(2)$ loop models for R\'enyi-$n$ quantities in the decoherence case -- corresponding to worldlines of the proliferating anyon with quantum dimension $2$. In particular, we find that the purity ($n=2$) remains deep in the $D_4$ TO for any decoherence strength, while the $n \to \infty$ limit becomes critical upon maximally decohering a particular anyon type, similar to our wavefunction deformation result. The information-theoretic threshold ($n\to 1$) appears to be controlled by a disordered version of these stat-mech models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the $D_4$ TO in addition to critical phases with emergent $U(1)$ symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules.This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders, and which in an ungauged formulation examples of non-Abelian strong-to-weak symmetry breaking.

cond-mat.str-el↗

arXiv2024

Stability and Loop Models from Decohering Non-Abelian Topological Order

Decohering topological order (TO) is central to the many-body physics of open quantum matter and decoding transitions. We identify relevant statistical mechanical models for decohering non-Abelian TO, which have been crucial for understanding the error threshold of Abelian stabilizer codes. The decohered density matrix can be described by loop models, whose topological loop weight $N$ is given by the quantum dimension of the decohering anyon -- reducing to the Ising model if $N=1$. In particular, the R\'enyi-$n$ moments of the decohered state correspond to $n$ coupled O$(N)$ loop models, and we exactly diagonalize the density matrix at maximal error rate. This allows us to relate the fidelity between two logically distinct ground states to properties of random O$(N)$ loop and spin models. Utilizing the literature on loop models, we find a remarkable stability to quantum channels which proliferate non-Abelian anyons with large quantum dimension, with the possibility of critical phases for smaller dimensions. We confirm our framework with exact results for Kitaev quantum double models, and with numerical simulations for the non-Abelian phase of the Kitaev honeycomb model. The latter is an example of a non-fixed-point wavefunction with non-bosonic and non-integral anyon dimensions. Our work opens up the possibility of non-Abelian TO being robust against maximally proliferating certain anyons, which can inform error-correction studies of these topological memories.

quant-ph↗

arXiv2024

Interacting Dirac fields in an expanding universe: dynamical condensates and particle production

The phenomenon of particle production for quantum field theories in curved spacetimes is crucial to understand the large-scale structure of a universe from an inflationary epoch. In contrast to the free and fixed-background case, the production of particles with strong interactions and back reaction is not completely understood, especially in situations that require going beyond perturbation theory. In this work, we present advances in this direction by focusing on a self-interacting field theory of Dirac fermions in an expanding Friedmann-Robertson-Walker universe. By using a Hamiltonian lattice regularization with continuous conformal time and rescaled fields, this model becomes amenable to either a cold-atom analogue-gravity quantum simulation, or a dynamical variational approach. Leveraging a family of variational fermionic Gaussian states, we investigate how dynamical mass generation and the formation of fermion condensates associated to certain broken symmetries modify some well-known results of the free field theory. In particular, we study how the non-perturbative condensates arise and, more importantly, how their real-time evolution has an impact on particle production. Depending on the Hubble expansion rate, we find an interesting interplay of interactions and particle production, including a non-trivial back reaction on the condensates and a parity-breaking spectrum of produced particles.

gr-qc↗

arXiv2024

Highly entangled stationary states from strong symmetries

We find that the presence of strong non-Abelian conserved quantities can lead to highly entangled stationary states even for unital quantum channels. We derive exact expressions for the bipartite logarithmic negativity, R\'enyi negativities, and operator space entanglement for stationary states restricted to one symmetric subspace, with focus on the trivial subspace. We prove that these apply to open quantum evolutions whose commutants, characterizing all strongly conserved quantities, correspond to either the universal enveloping algebra of a Lie algebra or to the Read-Saleur commutants. The latter provides an example of quantum fragmentation, whose dimension is exponentially large in system size. We find a general upper bound for all these quantities given by the logarithm of the dimension of the commutant on the smaller bipartition of the chain. As Abelian examples, we show that strong U($1$) symmetries and classical fragmentation lead to separable stationary states in any symmetric subspace. In contrast, for non-Abelian SU$(N)$ symmetries, both logarithmic and R\'enyi negativities scale logarithmically with system size. Finally, we prove that while R\'enyi negativities with $n>2$ scale logarithmically with system size, the logarithmic negativity (as well as generalized R\'enyi negativities with $n<2$) exhibits a volume law scaling for the Read-Saleur commutants. Our derivations rely on the commutant possessing a Hopf algebra structure in the limit of infinitely large systems, and hence also apply to finite groups and quantum groups.

quant-ph↗

arXiv2024

Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective

We explore the landscape of the decoherence effect in mixed-state ensembles from a purification perspective. We analyze the spontaneous strong-to-weak symmetry breaking (SSSB) in mixed states triggered by local quantum channels by mapping this decoherence process to unitary operations in the purified state within an extended Hilbert space. Our key finding is that mixed-state long-range order and SSSB can be mapped into symmetry-protected topological (SPT) order in the purified state. Notably, the measurement-induced long-range order in the purified SPT state mirrors the long-range order in the mixed state due to SSSB, characterized by the Renyi-2 correlator. We establish a correspondence between fidelity correlators in the mixed state, which serve as a measure of SSSB, and strange correlators in the purification, which signify the SPT order. This purification perspective is further extended to explore intrinsic mixed-state topological order and decoherent symmetry-protected topological phases.

quant-ph↗

arXiv2024

Quantum criticality under imperfect teleportation

Entanglement, measurement, and classical communication together enable teleportation of quantum states between distant parties, in principle with perfect fidelity. To what extent do correlations and entanglement of a many-body wavefunction transfer under imperfect teleportation protocols? We address this question for the case of an imperfectly teleported quantum critical wavefunction, focusing on the ground state of a critical Ising chain. We demonstrate that imperfections, e.g., in the entangling gate adopted for a given protocol, effectively manifest as weak measurements acting on the otherwise pristinely teleported critical state. Armed with this perspective, we leverage and further develop the theory of measurement-altered quantum criticality to quantify the resilience of critical-state teleportation. We identify classes of teleportation protocols for which imperfection $(i)$ preserves both the universal long-range entanglement and correlations of the original quantum critical state, $(ii)$ weakly modifies these quantities away from their universal values, and $(iii)$ obliterates long-range entanglement altogether while preserving power-law correlations, albeit with a new set of exponents. We also show that mixed states describing the average over a series of sequential imperfect teleportation events retain pristine power-law correlations due to a `built-in' decoding algorithm, though their entanglement structure measured by the negativity depends on errors similarly to individual protocol runs. These results may allow one to design teleportation protocols that optimize against errors -- highlighting a potential practical application of measurement-altered criticality.

quant-ph↗

arXiv2023

Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries

We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We do so by introducing a family of one-dimensional local quantum rotor and bosonic models which conserve finite Fourier momenta of the particle number, but not the particle number itself. These correspond to generalizations of the standard Bose-Hubbard model (BHM), and relate to the physics of Bose surfaces. First, we show that while having an infinite-dimensional local Hilbert space, such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice. This is linked to the nature of the conserved quantities having a dense spectrum and provides the first such example. We then characterize the zero-temperature phase diagram for both commensurate and incommensurate momenta. In both cases, analytical and numerical calculations predict a phase transition between a gapped (Mott insulating) and quasi-long range order phase; the latter is characterized by a two-species Luttinger liquid in the infrared, but dressed by oscillatory contributions when computing microscopic expectation values. Following a rigorous Villain formulation of the corresponding rotor model, we derive a dual description, from where we estimate the robustness of this phase using renormalization group arguments, where the driving perturbation has ultra-local correlations in space but power law correlations in time. We support this conclusion using an equivalent representation of the system as a two-dimensional vortex gas with modulated Coulomb interactions within a fixed symmetry sector. We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.

cond-mat.quant-gas↗

arXiv2023

Hilbert Space Fragmentation in Open Quantum Systems

We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems and find that it can stabilize highly entangled steady states. For concreteness, we consider the Temperley-Lieb model, which exhibits quantum HSF in an entangled basis, and investigate the Lindblad dynamics under two different couplings. First, we couple the system to a dephasing bath that reduces quantum fragmentation to a classical one with the resulting stationary state being separable. We observe that despite vanishing quantum correlations, classical correlations develop due to fluctuations of the remaining conserved quantities, which we show can be captured by a classical stochastic circuit evolution. Second, we use a coupling that preserves the quantum fragmentation structure. We derive a general expression for the steady state, which has a strong coherent memory of the initial state due to the extensive number of non-commuting conserved quantities. We show that it is highly entangled as quantified by the logarithmic negativity.

quant-ph↗

arXiv2023

Measurement-altered Ising quantum criticality

Quantum critical systems constitute appealing platforms for the exploration of novel measurement-induced phenomena due to their innate sensitivity to perturbations. We study the impact of measurement on paradigmatic Ising quantum critical chains using an explicit protocol, whereby correlated ancilla are entangled with the critical chain and then projectively measured. Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter long-distance correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations. We derive numerous quantitative predictions for the behavior of correlations in select measurement outcomes, and also identify two strategies for detecting measurement-altered Ising criticality in measurement-averaged quantities. First, averaging the square of the order-parameter expectation value over measurement outcomes retains memory of order parameter condensation germinated in fixed measurement outcomes -- even though on average the order parameter itself vanishes. Second, we show that, in certain cases, observables can be averaged separately over measurement outcomes residing in distinct symmetry sectors, and that these `symmetry-resolved averages' reveal measurement effects even when considering standard linearly averaged observables. We identify complementary regimes in which symmetry-resolved averages and post-selection can be pursued reasonably efficiently in experiment, with the former generically outperforming the latter in the limit of sufficiently weak ancilla-critical chain entanglement. Our framework naturally adapts to more exotic quantum critical points and highlights opportunities for potential experimental realization in NISQ hardware and in Rydberg arrays.

cond-mat.stat-mech↗

arXiv2023

Disorder-Free Localization as a Purely Classical Effect

Disorder-free localization (DFL) is an ergodicity breaking mechanism that has been shown to occur in lattice gauge theories in the quench dynamics of initial states spanning an extensive number of gauge superselection sectors. Whether DFL is intrinsically a quantum interference effect or can arise classically has hitherto remained an open question whose resolution is pertinent to further understanding the far-from-equilibrium dynamics of gauge theories. In this work, we utilize cellular automaton circuits to model the quench dynamics of large-scale quantum link model (QLM) formulations of $(1+1)$D quantum electrodynamics, showing excellent agreement with the exact quantum case for small system sizes. Our results demonstrate that DFL persists in the thermodynamic limit as a purely classical effect arising from the finite-size regularization of the gauge-field operator in the QLM formulation, and that quantum interference, though not a necessary condition, may be employed to enhance DFL.

cond-mat.quant-gas↗

arXiv2022

Fragmentation-induced localization and boundary charges in dimensions two and above

We study higher dimensional models with symmetric correlated hoppings, which generalize a one-dimensional model introduced in the context of dipole-conserving dynamics. We prove rigorously that whenever the local configuration space takes its smallest non-trivial value, these models exhibit localized behavior due to fragmentation, in any dimension. For the same class of models, we then construct a hierarchy of conserved quantities that are power-law localized at the boundary of the system with increasing powers. Combining these with Mazur's bound, we prove that boundary correlations are infinitely long lived, even when the bulk is not localized. We use our results to construct quantum Hamiltonians that exhibit the analogues of strong zero modes in two and higher dimensions.

cond-mat.stat-mech↗