arXiv subjects

Thomas Quella

Publications and source records attributed to Thomas Quella.

At least 19 recordsLinked to original sources

arXiv2025

Unitary and Nonunitary A-D-E minimal models: Coset graph fusion algebras, defects, entropies, SREEs and dilogarithm identities

We consider both unitary and nonunitary A-D-E minimal models on the cylinder with topological defects along the non-contractible cycle of the cylinder. We define the coset graph $A \otimes G/\mathbb{Z}_2$ and argue that it encodes not only the (i) coset graph fusion algebra, but also (ii) the Affleck-Ludwig boundary g-factors; (iii) the defect g-factors (quantum dimensions) and (iv) the relative symmetry resolved entanglement entropy. By studying A-D-E restricted solid-on-solid models, we find that these boundary conformal field theory structures are also present on the lattice: defects (seams) are implemented by face weights with special values of the spectral parameter. Integrability allows the study of lattice transfer matrix T- and Y-system functional equations to reproduce the fusion algebra of defect lines. The effective central charges and conformal weights are expressed in terms of dilogarithms of the braid and bulk asymptotics of the Y-system expressed in terms of the quantum dimensions.

hep-th↗

arXiv2025

Symmetry-protected topological scar subspaces

We propose a framework that extends the notion of symmetry-protected topological properties beyond the ground-state paradigm to dynamically isolated subspaces formed by exceptional non-thermal energy eigenstates of non-integrable systems, known as quantum many-body scars (QMBS). We introduce the concept of a symmetry-protected topological (SPT) scar subspace -- a Hilbert subspace stabilized by a restricted spectrum-generating algebra (rSGA) while being protected by on-site, inversion, and time-reversal symmetries. QMBS often admit a non-interacting quasiparticle description, which enables matrix-product representations with small bond dimension. Although individual QMBS do not necessarily retain the protecting symmetries of the Hamiltonian, we show that the subspace formed by the symmetry-connected QMBS does retain them, giving rise to consistently emerging topological properties across the entire scar subspace. Using the spin-$1$ Affleck--Kennedy--Lieb--Tasaki (AKLT) model, we demonstrate that its bimagnon scar subspace reflects the topological properties of the SPT ground state, as evidenced by the appropriate bond-space symmetry representations, the expected topological response, and the numerically verified long-range string order. Our findings indicate that scar subspaces can inherit -- and in inhomogeneous cases systematically modify -- the topological character of the SPT ground state, offering a new and experimentally accessible platform for probing symmetry-protected topology beyond the ground-state regime.

cond-mat.str-el↗

arXiv2025

GCAMPS: A Scalable Classical Simulator for Qudit Systems

Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently introduced Clifford Augmented Matrix Product State (CAMPS) method offer scalability and efficiency by combining both tensor network and stabilizer simulation techniques and leveraging their complementary advantages. This hybrid simulation method has indeed demonstrated significant improvements in simulation performance for qubit circuits. Our work generalises the CAMPS method to higher quantum degrees of freedom -- qudit simulation, resulting in a generalised CAMPS (GCAMPS). Benchmarking this extended simulator on quantum systems with three degrees of freedom, i.e. qutrits, we show that similar to the case of qubits, qutrit systems also benefit from a comparable speedup using these techniques. Indeed, we see a greater improvement with qutrit simulation compared to qubit simulation on the same $T$-doped random Clifford benchmarking circuit as a result of the increased difficulty of conventional qutrit simulation using tensor networks. This extension allows for the classical simulation of problems that were previously intractable without access to a quantum device and will open new avenues to study complex many-body physics and to develop efficient methods for quantum information processing.

quant-ph↗

arXiv2025

A graph-theoretic approach to chaos and complexity in quantum systems

There has recently been considerable interest in studying quantum systems via dynamical Lie algebras (DLAs) -- Lie algebras generated by the terms which appear in the Hamiltonian of the system. However, there are some important properties that are revealed only at a finer level of granularity than the DLA. In this work we explore, via the commutator graph, average notions of scrambling, chaos and complexity over ensembles of systems with DLAs that possess a basis consisting of Pauli strings. Unlike DLAs, commutator graphs are sensitive to short-time dynamics, and therefore constitute a finer probe to various characteristics of the corresponding ensemble. We link graph-theoretic properties of the commutator graph to the out-of-time-order correlator (OTOC), the frame potential, the frustration graph of the Hamiltonian of the system, and the Krylov complexity of operators evolving under the dynamics. For example, we reduce the calculation of average OTOCs to a counting problem on the graph; separately, we connect the Krylov complexity of an operator to the module structure of the adjoint action of the DLA on the space of operators in which it resides, and prove that its average over the ensemble is lower bounded by the average shortest path length between the initial operator and the other operators in the commutator graph.

quant-ph↗

arXiv2024

Stabilizer Tensor Networks with Magic State Injection

This work augments the recently introduced Stabilizer Tensor Network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford operations. Specifically, for random $T$-doped $N$-qubit Clifford circuits the computational cost of circuits prepared with magic state injection scales as $\mathcal{O}(\text{poly}(N))$ when the circuit has $t \lesssim N$ $T$-gates compared to an exponential scaling for the STN approach, which is demonstrated in systems of up to $200$ qubits. In the case of the Hidden Bit Shift circuit, a paradigmatic benchmarking system for extended stabilizer methods with a tunable amount of magic, we report that our magic state injected STN framework can efficiently simulate $4000$ qubits and $320$ $T$-gates. These findings provide a promising outlook for the use of this protocol in the classical modelling of quantum circuits that are conventionally difficult to simulate efficiently.

quant-ph↗

arXiv2024

Representation theory of Gaussian unitary transformations for bosonic and fermionic systems

Gaussian unitary transformations are generated by quadratic Hamiltonians, i.e., Hamiltonians containing quadratic terms in creations and annihilation operators, and are heavily used in many areas of quantum physics, ranging from quantum optics and condensed matter theory to quantum information and quantum field theory in curved spacetime. They are known to form a representation of the metaplectic and spin group for bosons and fermions, respectively. These groups are the double covers of the symplectic and special orthogonal group, respectively, and our goal is to analyze the behavior of the sign ambiguity that one needs to deal with when moving between these groups and their double cover. We relate this sign ambiguity to expectation values of the form $\langle 0|\exp{(-i\hat{H})}|0\rangle$, where $|0\rangle$ is a Gaussian state and $\hat{H}$ an arbitrary quadratic Hamiltonian. We provide closed formulas for $\langle 0|\exp{(-i\hat{H})}|0\rangle$ and show how we can efficiently describe group multiplications in the double cover without the need of going to a faithful representation on an exponentially large or even infinite-dimensional space. Our construction relies on an explicit parametrization of these two groups (metaplectic, spin) in terms of symplectic and orthogonal group elements together with a twisted U(1) group.

quant-ph↗

arXiv2024

Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1{+}1$d conformal field theories

Recently, a framework for computing the symmetry-resolved entanglement entropy for non-invertible symmetries in $1{+}1$d conformal field theories has been proposed by Saura-Bastida, Das, Sierra and Molina-Vilaplana [Phys. Rev. D109, 105026]. We revisit their theoretical setup, paying particular attention to possible contributions from the conformal boundary conditions imposed at the entangling surface -- a potential subtlety that was not addressed in the original proposal. We find that the presence of boundaries modifies the construction of projectors onto irreducible sectors, compared to what can be expected from a pure bulk approach. This is a direct consequence of the fusion algebra of non-invertible symmetries being different in the presence or absence of boundaries on which defects can end. We apply our formalism to the case of the Fibonacci category symmetry in the three-state Potts and tricritical Ising model and the Rep($S_3$) fusion category symmetry in the $SU(2)_4$ Wess-Zumino-Witten conformal field theory. We numerically corroborate our findings by simulating critical anyonic chains with these symmetries as a finite lattice substitute for the expected entanglement Hamiltonian. Our predictions for the symmetry-resolved entanglement for non-invertible symmetries seem to disagree with the recent work by Saura-Bastida et al.

hep-th↗

arXiv2024

Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model

We revisit the question of string order and hidden symmetry breaking in the q-deformed AKLT model, an example of a spin chain that possesses generalized symmetry. We first argue that the non-local Kennedy-Tasaki duality transformation that was previously proposed to relate the string order to a local order parameter leads to a non-local Hamiltonian and thus does not provide a physically adequate description of the symmetry breaking. We then present a modified non-local transformation which is based on a recently developed generalization of Witten's Conjugation to frustration-free lattice models and capable of resolving this issue.

cond-mat.str-el↗

arXiv2023

Calibrating the role of entanglement in variational quantum circuits

Entanglement is a key property of quantum computing that separates it from its classical counterpart, however, its exact role in the performance of quantum algorithms, especially variational quantum algorithms, is not well understood. In this work, we utilise tensor network methods to systematically probe the role of entanglement in the working of two variational quantum algorithms, the Quantum Approximate Optimisation Algorithm (QAOA) and Quantum Neural Networks (QNNs), on prototypical problems under controlled entanglement environments. We find that for the MAX-CUT problem solved using QAOA, the fidelity as a function of entanglement is highly dependent on the number of layers, layout of edges in the graph, and edge density, generally exhibiting that a high number of layers indicates a higher resilience to truncation of entanglement. This is in contrast to previous studies based on no more than four QAOA layers which show that the fidelity of QAOA follows a scaling law with respect to the entanglement per qubit of the system. Contrarily, in the case of QNNs, trained circuits with high test accuracies are underpinned by higher entanglement, with any enforced limitation in entanglement resulting in a sharp decline in test accuracy. This is corroborated by the entanglement entropy of these circuits which is consistently high suggesting that, unlike QAOA, QNNs may require quantum devices capable of generating highly entangled states. Overall our work provides a deeper understanding of the role of entanglement in the working of variational quantum algorithms which may help to implement these algorithms on NISQ-era quantum hardware in a way that maximises their accuracies.

quant-ph↗

arXiv2022

Inducing Heat Reversal in a Three-Qubit Spin Chain

By the standard second law of thermodynamics, heat spontaneously flows from a hotter body to a colder body. However, quantum systems in which quantum correlations play a prominent role can exhibit a non-classical reversal of such heat flow. We propose a quantum system consisting of a chain of qubits, each in local Gibbs states, where only adjacent qubits are allowed to thermally interact. By controlling initial quantum correlations along the chain, we then demonstrate non-classical heat reversal for the special case of a three-qubit chain on a quantum computer. We explore multiple initial conditions for the spin chain to showcase exotic behaviour such as the preferential pumping of heat afforded by unequal initial correlations between adjacent pairs of qubits, reinforcing the role that initial correlations play in influencing the dynamics of heat flow.

quant-ph↗

arXiv2020

Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain

We study the phase diagram of the $SO_q(3)$ quantum group invariant spin-1 bilinear-biquadratic spin chain for real values of $q>1$. Numerical computations suggest that the chain has at least three clearly distinguished phases: A chiral analogue of the Haldane phase, a dimerized phase and a ferromagnetic phase. In contrast, the counterpart of the extended critical region that is known to exist for $q=1$ remains elusive. Our results show that the Haldane phase fails to exhibit a two-fold degeneracy in the entanglement spectrum but that the degeneracy is restored upon a suitable $q$-deformation of the entanglement Hamiltonian which can be interpreted as a Zeeman field. The structure of the phase diagram is confirmed through analytical calculations in the extreme anisotropic limit $q\to\infty$. Our results suggest that symmetries of the form $U_q[su(2)]$ for distinct choices of $q$ should be interpreted as one single family instead of separate symmetries when defining SPT phases, leading naturally to the notion of a qSPT phase.

cond-mat.str-el↗

arXiv2020

Deep Learning is Singular, and That's Good

In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus "dividing" by the determinant of the Hessian or employing the Laplace approximation are not appropriate. Despite its potential for addressing fundamental issues in deep learning, singular learning theory appears to have made little inroads into the developing canon of deep learning theory. Via a mix of theory and experiment, we present an invitation to singular learning theory as a vehicle for understanding deep learning and suggest important future work to make singular learning theory directly applicable to how deep learning is performed in practice.

cs.LG↗

arXiv2020

Symmetry protected topological phases beyond groups: The q-deformed Affleck-Kennedy-Lieb-Tasaki model

We argue that the $q$-deformed spin-1 AKLT Hamiltonian should be regarded as a representative of a symmetry protected topological phase. Even though it fails to exhibit any of the standard symmetries known to protect the Haldane phase it still displays all characteristics of this phase: Fractionalized spin-$\frac{1}{2}$ boundary spins, non-trivial string order and - when using an appropriate definition - a two-fold degeneracy in the entanglement spectrum. We trace these properties back to the existence of an $SO_q(3)$ quantum group symmetry and speculate about potential links to discrete duality symmetries. We expect our findings and methods to be relevant for the identification, characterization and classification of other symmetry-protected topological phases with non-standard symmetries.

cond-mat.str-el↗

arXiv2020

On conformal field theories based on Takiff superalgebras

We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with Z-grading which arise from taking p copies of a Lie superalgebra g and placing them in the degrees s=0,...,p-1. Using suitably defined non-degenerate invariant forms we show that Takiff superalgebras give rise to families of conformal field theories with central charge c=p sdim(g). The resulting conformal field theories are defined in the standard way, i.e. they lend themselves to a Lagrangian description in terms of a WZW model and their chiral energy momentum tensor is the one obtained naturally from the usual Sugawara construction. In view of their intricate representation theory they provide interesting examples of conformal field theories.

hep-th↗

arXiv2019

Conformal field theory and the non-abelian $SU(2)_k$ chiral spin liquid

We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions in $SU(2)_k$ WZW models. Our results provide a conformal field theory foundation for recent proposals by Greiter and coauthors regarding the realization of non-abelian chiral spin liquids. We explain, in particular, how the symmetrization procedure for the amplitudes of the ground state wave function suggested in Ref. arXiv:0903.4547 originates from the conformal field theory description.

cond-mat.str-el↗

arXiv2015

Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation

Gapped quantum spin chains with symmetry PSU(N)=SU(N)/Z(N) are known to possess N distinct symmetry protected topological phases. Besides the trivial phase, there are N-1 Haldane phases which are distinguished by the occurrence of massless boundary spins. Motivated by the potential realization in alkaline-earth atomic Fermi gases, we explicitly construct previously unknown Hamiltonians for two classes of chiral AKLT states and we discuss their physical properties. We also point out a deep connection between symmetry protection in gapped and gapless 1D quantum spin systems and its implications for a potential multicritical nature of topological phase transitions.

cond-mat.str-el↗

arXiv2014

Superspace conformal field theory

Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and developments, including the general construction of WZW models on type I supergroups, the classification of conformal sigma models and their embedding into string theory.

hep-th↗

arXiv2014

Infinite Matrix Product States for long range SU(N) spin models

We construct 1D and 2D long-range SU(N) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N) level 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N) level 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models.

cond-mat.str-el↗