arXiv subjects

Ruben Verresen

Publications and source records attributed to Ruben Verresen.

At least 19 recordsLinked to original sources

arXiv2026

Quasi-Phases of Quantum Matter

Within quantum many-body phase diagrams, continuous transition lines can appear and then terminate. However, it has remained unclear whether the neighboring regimes can be meaningfully described as distinct phases, akin to water and vapour, since any sharp characterization would have to go beyond the usual notion of phases of matter. We answer this in the affirmative by introducing quasi-phases: gapped regimes near a critical point that are connected in the broader phase diagram, but not by any gapped path accessible from small perturbations of the critical theory. The physical consequences include interface modes between regimes in the same phase of matter. More striking still, describing both the extended critical line and the gapped path connecting the regimes requires a bigger multicritical parent theory. In spin-chain examples with continuous terminating lines with central charge $c=1$, we find multicritical $c=3/2$ and $c=9/5$ orbifolds describing so-called 'quotient symmetry protected' and 'representation symmetry protected' topological phenomena. While one-dimensional symmetry-protected topological phases are labeled by projective representation classes, these quasi-phases can have interface modes carrying higher-dimensional linear representations. We turn this into a constructive principle through a weakening of the Lieb-Schultz-Mattis anomaly. Supporting distinct quasi-phases makes an unnecessary critical point infrared-necessary, even if it is unnecessary at the ultraviolet scale. This condition is more restrictive than simply having a codimension-one critical line, revealing richer structure within phases of matter than their conventional classification suggests.

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arXiv2026

Gapless and Non-Equilibrium Topology in Blockaded Ladders

We propose a multi-leg PXYP model as a minimal setting to explore constraint-induced intertwinement between itinerant and internal degrees of freedom. We argue that the Rydberg-like blockade induces correlations in squeezed space, providing a unified mechanism for nontrivial string order both in and out of equilibrium. In a two-leg geometry, this leads to an intrinsically gapless topological ground state, which can terminate at a supersymmetric multicritical point. This mechanism also leads to the preservation of string order for parametrically long times after a quench, which we verify using tensor network simulations and a classical stochastic approximation to the dynamics. In a three-leg geometry, the blockade leads to an additional emergent $U(1)$ symmetry, resulting in a multicomponent Luttinger liquid where both itinerant and internal degrees of freedom are critical. This family of models arises naturally in a range of quantum simulator platforms such as Rydberg tweezer arrays and dipolar atoms in optical lattices.

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arXiv2026

Symmetry-twisted multi-entropies: Order parameters for 2D SPT phases

Although symmetry-protected topological phases (SPTs) can be distinguished by their entanglement properties, it has been unclear how to extract this information directly from expectation values beyond the 1D case. Here, we close this gap and propose a pair of nonlocal order parameters that can detect and distinguish all bosonic SPTs in 2D protected by internal discrete, Abelian unitary symmetries. The desired topological invariants are extracted by these quantities by effectively simulating the SPT path integral on topologically non-trivial spacetime manifolds. Our order parameters are defined in terms of expectation values of partial symmetry and permutation operations acting on fixed numbers of replicas of the system in finite spatial regions. These expectation values correspond to symmetry-twisted versions of multipartite entanglement quantities known as multi-entropies. We show explicitly that our two order parameters detect symmetry-protected four-party and six-party entanglement, respectively, and we constrain possible "spurious" contributions. We analytically test our proposal in fixed-point lattice models. Our results suggest multipartite entanglement to be a defining feature of SPTs; indeed, we expect our methods to generalize to fermionic and higher-dimensional systems.

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arXiv2026

Rewire and reset are all you need: Minimal resources for manipulating non-Abelions

Braiding and fusing anyons are fundamental to topological quantum computation, yet existing circuit protocols often employ ancillas and measurements. We determine the minimal circuit resources for performing such anyon operations in quantum double models of generic finite groups. Our approach braids anyons through a sequential unitary circuit without ancillas. Intuitively, this is obtained by deforming the underlying graph on which the anyons live. More generally, we introduce graph rewiring, a diagrammatic calculus that assigns a geometric interpretation to individual two-qudit gates and tracks their action on stabilizers. For fusion, we prove a general no-go theorem excluding purely unitary protocols for fusing unknown anyon types without introducing ancillas. Remarkably, we show such "input-agnostic" fusion is enabled by simply using a qudit reset. Hence, contrary to folklore, ancilla resources are not needed to braid or fuse non-Abelian anyons (non-Abelions). This work has implications in experimental efforts in error correction: our fusion protocol highlights reset as an underutilized primitive for error correction without the spacetime-overhead of ancillas and measurements.

quant-ph↗

arXiv2026

Disentangling the Toric Code

Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.

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arXiv2026

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↗

arXiv2026

Integer Linear Programming Decoder for Abelian and Non-Abelian Topological Codes

Topological orders (TOs) are widely used as quantum error-correcting codes, with anyon excitations serving as error syndromes. For certain Abelian TOs, decoding can be performed by independently matching particle-antiparticle pairs of each species. However, matching-based decoders cannot handle more general fusion rules in either Abelian or non-Abelian TOs, nor account for noise that correlates different anyon species. While clustering decoders are more broadly applicable, they typically neglect anyon data and fusion properties, leading to poor performance in practice. In this work, we introduce a fundamentally different decoder for arbitrary TOs based on integer linear programming (ILP). The ILP formulation linearizes the error-correction problem through the introduction of auxiliary variables and encodes fusion rules as linear constraints. Classical optimization then identifies the minimum-weight error configuration. As concrete examples, we determine error-correction thresholds for three TOs: the Abelian $\mathbb{Z}_2$ TO under depolarizing noise, where charge and flux errors are correlated; the Abelian $\mathbb{Z}_3$ TO, which does not admit a pairwise matching decoder; and the non-Abelian $D_4$ TO under noise channels that generate all anyon species. We demonstrate the versatility of the ILP decoder by showing a clear performance advantage over most existing decoders in all three cases. We further extend the method to incorporate noisy syndrome measurements and propose a just-in-time variant for continuous error correction. Our results establish ILP as a natural framework for handling correlated errors and general anyon fusion rules, and as a powerful and flexible general-purpose decoder for incoherent anyon noise in arbitrary TOs, with applications to fault-tolerant quantum computation.

quant-ph↗

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

Correlation versus Causation in Quantum Criticality

Correlation functions $\langle O_1(x) O_2(0) \rangle$ reveal scaling dimensions through spatial decay. We instead consider static susceptibility, the change in $\langle O_1(x) \rangle$ from perturbing the Hamiltonian by $O_2(0)$, which we term causation for short. In a conformal field theory (CFT), dimensional analysis predicts decay of $|x|^{-2Δ}$ for correlation and $|x|^{-2Δ+1}$ for causation. Yet we find causation can decay up to fifteen additional orders in $x$ through a general mechanism, which we trace to time-derivative fields being unable to contribute to static response. In higher-dimensional CFTs, this mechanism ensures leading causation arises from primaries, even when descendants dominate correlation, which we leverage with DMRG to identify a previously unresolved corner primary of $Δ\approx 8.8$ and a heavy magnetic line defect primary of $Δ\approx 4.6$ in the $(2+1)$D critical Ising model. Moreover, the same mechanism governs edge-mode localization in $(1+1)$D gapless symmetry-protected topological phases, explaining previously observed anomalously small edge-mode splittings and guiding our construction of spin chains with splittings as small as $1/L^{18}$ and $1/L^{25}$.

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arXiv2026

Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice

We argue that the presence of any exact $U(1)$ higher-form symmetry, under mild assumptions, presents a fundamental obstruction to ergodicity under unitary dynamics in lattice systems with local interactions and finite on-site Hilbert space dimension. Focusing on the two-dimensional case, we show that such systems necessarily exhibit Hilbert space fragmentation and explicitly construct Krylov sectors whose number scales exponentially with system size. While these sectors cannot be distinguished by symmetry quantum numbers, we identify the emergent integrals of motion which characterize them. Our symmetry-based approach is insensitive to details of the Hamiltonian and the lattice, providing a systematic explanation for ergodicity-breaking in a range of systems, including quantum link models.

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arXiv2026

Universal Gates from Braiding and Fusing Anyons on Quantum Hardware

Topological quantum computation encodes quantum information in the internal fusion space of non-Abelian anyonic quasiparticles, whose braiding implements logical gates. This goes beyond Abelian topological order (TO) such as the toric code, as its anyons lack internal structure. However, the simplest non-Abelian generalizations of the toric code do not support universality via braiding alone. Here we demonstrate that such minimally non-Abelian TOs can be made universal by treating anyon fusion as a computational primitive. We prepare a 54-qubit TO wavefunction associated with the smallest non-Abelian group, $S_3$, on Quantinuum's H2 quantum processor. This phase of matter exhibits cyclic anyon fusion rules, known to underpin universality, which we evidence by trapping a single non-Abelian anyon on the torus. We encode logical qutrits in the nonlocal fusion space of non-Abelian fluxes and, by combining an entangling braiding operation with anyon charge measurements, realize a universal topological gate set and read-out, which we further demonstrate by topologically preparing a magic state. This work establishes $S_3$ TO as simple enough to be prepared efficiently, yet rich enough to enable universal topological quantum computation.

quant-ph↗

arXiv2026

Exact quantum scars from kinetic frustration for cross-platform realizations

Quantum many-body scars are nonthermal states exhibiting persistent revivals in an otherwise ergodic, nonintegrable quantum system. Here we leverage the phenomenon of kinetic frustration -- the destructive interference of multiple quantum paths -- to create exact scars. The simplicity makes these models directly suitable for implementation on multiple existing quantum simulation platforms. In particular, we show how frustrated hardcore bosons in cold atom Bose-Hubbard simulators and polar molecule or Rydberg atom tweezer arrays have persistent oscillations whose lifetimes can be tuned with experimentally accessible parameters, like the Hubbard interaction or a Floquet drive. Second, we propose an experimentally realizable scar within a non-integrable Fermi-Hubbard model where the frustration arises from the fermionic exchange statistics, which admits a one-to-one mapping with the bosonic model in the scar subspace. Finally, we introduce a practical heuristic based on the energy distribution of eigenstates for systematically predicting and optimizing quantum many-body scar lifetimes. Their cross-platform realizability and long lifetimes make them well-suited for benchmarking coherence and exploring nonergodic dynamics in current and near-term quantum devices.

quant-ph↗

arXiv2026

Engineering quantum criticality and dynamics on an analog-digital simulator

Understanding emergent phenomena in out-of-equilibrium interacting many-body systems is an exciting frontier in physical science. While quantum simulators represent a promising approach to this long-standing problem, in practice it can be challenging to directly realize the required interactions, measure arbitrary observables, and mitigate errors. Here we use coherent mapping between the Rydberg and hyperfine qubits in a neutral atom array simulator to engineer and probe complex quantum dynamics. We combine efficient analog dynamics with fully programmable state preparation and measurement, leverage non-destructive readout for loss information and atomic qubit reuse, and use an atom reservoir for replacing lost atoms. With this analog-digital approach, we first demonstrate dynamical engineering of ring-exchange and particle hopping dynamics via Floquet driving and measure the spectral function of single excitations by evolving initial superposition states. Extending these techniques to a 271-site kagome lattice, we employ closed-loop optimization to target an out-of-equilibrium critical quantum spin liquid of the Rokhsar-Kivelson type. We observe the key features of such a state, including the absence of local order, many-body coherences between nearly equal-amplitude dimer configurations over up to 18 sites, and universal correlations consistent with predictions from field theory. Together, these results pave the way for using dynamical control in analog-digital quantum simulators to study complex quantum many-body systems.

quant-ph↗

arXiv2025

Non-Invertible Interfaces Between Symmetry-Enriched Critical Phases

Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the question of how the bulk-boundary correspondence is generalized to gapless cases. We propose that the spatial interface between gapless phases -- rather than their boundaries -- provides a more robust fingerprint. We show that whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect. We illustrate this general result for different versions of the Ising CFT with $\mathbb{Z}_2 \times \mathbb{Z}_2^T$ symmetry, obtaining a complete classification of allowed conformal interfaces. When the Ising CFTs differ by nonlocal operator charges, the interface hosts 0+1d symmetry-breaking phases with finite-size splittings scaling as $1/L^3$, as well as continuous phase transitions between them. For general gapless phases differing by an SPT entangler, the interfaces between them can be mapped to conformal defects with a certain defect 't Hooft anomaly. This classification also gives implications for higher-dimensional examples, including symmetry-enriched variants of the 2+1d Ising CFT. Our results establish a physical indicator for symmetry-enriched criticality through symmetry-protected interfaces, giving a new handle on the interplay between topology and gapless phases.

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arXiv2025

Protocols for Creating Anyons and Defects via Gauging

Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this work, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the $\mathbb{Z}_3$ toric code and $S_3$ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles.

quant-ph↗

arXiv2025

Charge pumps, pivot Hamiltonians and symmetry-protected topological phases

Generalised charge pumps are topological obstructions to trivialising loops in the space of symmetric gapped Hamiltonians. We show that given mild conditions on such pumps, the associated loop has high-symmetry points which must be in distinct symmetry-protected topological (SPT) phases. To further elucidate the connection between pumps and SPTs, we focus on closed paths, `pivot loops', defined by two Hamiltonians, where the first is unitarily evolved by the second `pivot' Hamiltonian. While such pivot loops have been studied as entanglers for SPTs, here we explore their connection to pumps. We construct families of pivot loops which pump charge for various symmetry groups, often leading to SPT phases -- including dipole SPTs. Intriguingly, we find examples where non-trivial pumps do not lead to genuine SPTs but still entangle representation-SPTs (RSPTs). We use the anomaly associated to the non-trivial pump to explain the a priori `unnecessary' criticality between these RSPTs. We also find that particularly nice pivot families form circles in Hamiltonian space, which we show is equivalent to the Hamiltonians satisfying the Dolan-Grady relation -- known from the study of integrable models. This additional structure allows us to derive more powerful constraints on the phase diagram. Natural examples of such circular loops arise from pivoting with the Onsager-integrable chiral clock models, containing the aforementioned RSPT example. In fact, we show that these Onsager pivots underlie general group cohomology-based pumps in one spatial dimension. Finally, we recast the above in the language of equivariant families of Hamiltonians and relate the invariants of the pump to the candidate SPTs. We also highlight how certain SPTs arise in cases where the equivariant family is labelled by spaces that are not manifolds.

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arXiv2025

Multicriticality between Purely Gapless SPT Phases with Unitary Symmetry

Symmetry-protected topological (SPT) phases are commonly required to have an energy gap, but recent work has extended the concept to gapless settings. This raises a natural question: what happens at transitions between inequivalent gapless SPTs? We address this for the simplest known case among gapless SPTs protected by a unitary symmetry group acting faithfully on the low-energy theory. To this end, we consider a qutrit version of the nearest-neighbor XX chain. Trimerizing the chain explicitly breaks an anomalous symmetry and produces three distinct gapped SPT phases protected by a unitary $\mathbb{Z}_3 \times \mathbb{Z}_3$ symmetry. Their phase boundaries are given by three inequivalent gapless SPTs without any gapped symmetry sectors, each described by a symmetry-enriched version of an orbifolded Potts$^2$ conformal field theory with central charge $c=\frac{8}{5}$. We provide an analytic derivation of this critical theory in a particular regime and confirm its stability using tensor network simulations. Remarkably, the three gapless SPTs meet at a $c = 2$ multicritical point, where the protecting $\mathbb{Z}_3 \times \mathbb{Z}_3$ symmetry exhibits a mixed anomaly with the $\mathbb Z_3$ entangler symmetry that permutes the SPT classes. We further explore how discrete gauging gives dipole-symmetric models, offering insights into dipole symmetry-breaking and SPTs, as well as symmetry-enriched multiversality. Altogether, this work uncovers a rich phase diagram of a minimal qutrit chain, whose purely nearest-neighbor interactions make it a promising candidate for experimental realization, including the prospect of critical phases with stable edge modes.

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arXiv2025

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 Rényi-$n$ 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.

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