arXiv subjects

Kieran Bull

Publications and source records attributed to Kieran Bull.

8 recordsLinked to original sources

arXiv2022

Hypergrid subgraphs and the origin of scarred quantum walks in the many-body Hilbert space

Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable quantum systems. Here we explore the origin of scarred wavefunction revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model - the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.

quant-ph↗

arXiv2022

Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

Intermediate-scale quantum technologies provide new opportunities for scientific discovery, yet they also pose the challenge of identifying suitable problems that can take advantage of such devices in spite of their present-day limitations. In solid-state materials, fractional quantum Hall (FQH) phases continue to attract attention as hosts of emergent geometrical excitations analogous to gravitons, resulting from the non-perturbative interactions between the electrons. However, the direct observation of such excitations remains a challenge. Here, we identify a quasi-one-dimensional model that captures the geometric properties and graviton dynamics of FQH states. We then simulate geometric quench and the subsequent graviton dynamics on the IBM quantum computer using an optimally-compiled Trotter circuit with bespoke error mitigation. Moreover, we develop an efficient, optimal-control-based variational quantum algorithm that can efficiently simulate graviton dynamics in larger systems. Our results open a new avenue for studying the emergence of gravitons in a new class of tractable models on the existing quantum hardware.

quant-ph↗

arXiv2022

Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains

Persistent oscillatory dynamics in non-equilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the $\mathbb{Z}_2$ symmetry of the external periodic drive, while QMBS span a subspace of non-thermalizing eigenstates forming an su(2) algebra representation. Here we ask a basic question: is there a physical system that allows to tune between these two dynamical phenomena? In contrast to much previous work, we investigate the possibility of a \emph{continuous} time crystal (CTC) in undriven, energy-conserving systems exhibiting prethermalization. We introduce a long-range XYZ spin model and show that it encompasses both a CTC phase as well as QMBS. We map out the dynamical phase diagram using numerical simulations based on exact diagonalization and time-dependent variational principle in the thermodynamic limit. We identify a regime where QMBS and CTC order co-exist, and we discuss experimental protocols that reveal their similarities as well as key differences.

cond-mat.str-el↗

arXiv2021

Correspondence principle for many-body scars in ultracold Rydberg atoms

The theory of quantum scarring -- a remarkable violation of quantum unique ergodicity -- rests on two complementary pillars: the existence of unstable classical periodic orbits and the so-called quasimodes, i.e., the non-ergodic states that strongly overlap with a small number of the system's eigenstates. Recently, interest in quantum scars has been revived in a many-body setting of Rydberg atom chains. While previous theoretical works have identified periodic orbits for such systems using time-dependent variational principle (TDVP), the link between periodic orbits and quasimodes has been missing. Here we provide a conceptually simple analytic construction of quasimodes for the non-integrable Rydberg atom model, and prove that they arise from a "requantisation" of previously established periodic orbits when quantum fluctuations are restored to all orders. Our results shed light on the TDVP classical system simultaneously playing the role of both the mean-field approximation and the system's classical limit, thus allowing us to firm up the analogy between the eigenstate scarring in the Rydberg atom chains and the single-particle quantum systems.

quant-ph↗

arXiv2020

Quantum scars as embeddings of weakly "broken" Lie algebra representations

We present an interpretation of scar states and quantum revivals as weakly "broken" representations of Lie algebras spanned by a subset of eigenstates of a many-body quantum system. We show that the PXP model, describing strongly-interacting Rydberg atoms, supports a "loose" embedding of multiple $\mathrm{su(2)}$ Lie algebras corresponding to distinct families of scarred eigenstates. Moreover, we demonstrate that these embeddings can be made progressively more accurate via an iterative process which results in optimal perturbations that stabilize revivals from arbitrary charge density wave product states, $|\mathbb{Z}_n\rangle$, including ones that show no revivals in the unperturbed PXP model. We discuss the relation between the loose embeddings of Lie algebras present in the PXP model and recent exact constructions of scarred states in related models.

cond-mat.str-el↗

arXiv2019

Systematic construction of scarred many-body dynamics in 1D lattice models

We introduce a family of non-integrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically-constrained many-body system. We numerically demonstrate that this construction yields new families of models with robust wave-function revivals, and it includes kinetically-constrained quantum clock models as a special case. We show that scarring dynamics in these models can be decomposed into a period of nearly free clock precession and an interacting bottleneck, shedding light on their anomalously slow thermalization when quenched from special initial states.

cond-mat.stat-mech↗

arXiv2019

Getting CICY High

Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low $h^{1,1}$ geometries for training and validate on geometries with large $h^{1,1}$. Neural networks and Support Vector Machines successfully predict trends in the number of Kähler parameters of CICY threefolds. The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher $h^{1,1}$.

hep-th↗

arXiv2018

Machine Learning CICY Threefolds

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.

hep-th↗