This course is an introduction to some approaches for exactly preparing multi-qubit states on a quantum computer. In Lecture 1, we begin with a brief review of quantum circuits; we then consider the GHZ state, and its preparation in constant depth. In Lecture 2, we introduce matrix product states and sequential state preparation; we consider the example of AKLT states, and their preparation in...
This course is an introduction to some approaches for exactly preparing multi-qubit states on a quantum computer. In Lecture 1, we begin with a brief review of quantum circuits; we then consider the GHZ state, and its preparation in constant depth. In Lecture 2, we introduce matrix product states and sequential state preparation; we consider the example of AKLT states, and their preparation in...
This course is an introduction to some approaches for exactly preparing multi-qubit states on a quantum computer. In Lecture 1, we begin with a brief review of quantum circuits; we then consider the GHZ state, and its preparation in constant depth. In Lecture 2, we introduce matrix product states and sequential state preparation; we consider the example of AKLT states, and their preparation in...
The rational Calogero-Sutherland-Moser model is originally a system of identical particles scattering on the line with inverse-square potential. There are also trigonometric, hyperbolic and elliptic version of this model. The integrability of the model follows from the presence of a Lax pair.
The Calogero system of type $A$ admits the so-called $R$-matrix Lax pair presentation, the matrix...
The Eigenstate Thermalization Hypothesis (ETH) provides a foundational framework for understanding thermalization in quantum ergodic systems and, with appropriate generalizations, for characterizing equilibration in integrable models. However, numerical verification of ETH has traditionally relied on exact diagonalization (ED), which severely limits accessible system sizes.
In this work, we...
We present a systematic approach to unitarise the Bethe Ansatz, enabling the construction of quantum circuits that exactly prepare eigenstates of a class of integrable models. The key step is a change of basis in the auxiliary space of the algebraic Bethe Ansatz to the ‘F-basis’, known from the theory of integrable models. The F-basis, which ensures symmetry under exchange of auxiliary qubits,...
While in the general framework of quantum resource theories one typically only distinguishes between operations that can or cannot generate the resource of interest, in a many-body setting one can further characterize quantum operations based on underlying geometrical constraints. For instance, a natural question is to understand the power of resource-generating operations that preserve...
In the first part of the talk we will investigate the finite-volume spectra the nonrelativistic Calogero-Moser quantum systems, which can be solved analytically. We will compare the analytically calculated spectra from the finite-volume Calogero-Moser systems to the wavenumbers obtained from the corresponding Bethe ansatz equations. The eigenstates are also calculated numerically using the...
The emergence of hydrodynamics is one of the deepest phenomena in many-body systems. Arguably, the hydrodynamic equations are also the most important tools for predicting large-scale behaviour. Understanding how such equations emerge from microscopic deterministic dynamics is a century-old problem, despite recent progress in fine-tuned integrable systems. Due to the universality of...
I will introduce a method to compute the minimal form factors of diagonal integrable field theories perturbed by generalized $T \bar{T}$-perturbations that is going to appear in the next few months in a new paper with O. Castro-Alvaredo and S. Negro. Building on our previous results, these MFFs are constructed in such a way as to not allow for any free parameters, an issue that plagued...
Confinement is a central concept in the theory of strong interactions, which leads to the absence of quarks (and gluons) from the spectrum of experimentally observed particles. The underlying mechanism is based on a linear potential, which can also be realised in condensed matter systems. A one-dimensional example with a great analogy to quantum chromodynamics is the mixed-field three-state...
Integrable systems provide a rare opportunity to exactly understand the physics of complex systems, especially in the case of many-body quantum systems, where exponential complexity of simulation severely limits the effectiveness of brute-force approaches. With the recent rapid progress of quantum computers, integrable circuits have increasingly come into focus. While integrability is...
We investigate dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of random Erdős-Rényi networks of size $N$. We analytically show that dynamical critical points are independent of the edge generation probability $p$, and matches that of the integrable fully connected network ($p=1$). This is due to the $O(N^{-1/2})$ bound on the overlap between the...
Novel approach to integrable one-dimensional many-body systems with or without interactions is Generalized Hydrodynamics (GHD). According to GHD, excitations in the system can be described by quasi particles. The key postulate of the GHD is the assumption of a mesoscopic scale for time and space (fluid cells) which state maximizes local entropy. GHD provides evolution of the system over large...
The Blume-Capel model, a spin chain system exhibiting a tricritical point described by a conformal field theory with central charge $c=7/10$, serves as a rich framework for studying its thermal perturbation, the $E_7$ integrable quantum field theory. In my work, I investigate both numerical and analytical aspects of the $E_7$ model, aiming to validate theoretical predictions and explore new...
The characterization of ensembles of random states over many qubits and their realization by quantum circuits are important tasks in quantum-information theory. In this work, we study ensembles of states 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...
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. We discuss a classification of three-state cellular automata (with a stable ‘vacuum’ state and ‘particles’ with ± charges). The classification is aided by the automata’s different transformation proper- ties under discrete...
A large class of free fermionic spin chain models have been found recently, that are not soluble by a Jordan-Wigner transformation, but by some more complex construction introduced in the original work of Fendley, that rather resembles the methods to solve integrable systems. In the present work we relied on these techniques to calculate the correlation functions of some local operators in...
Quantum integrable models possess a sufficiently large number of conserved quantities in involution. As a result, these models often admit mathematical methods that enable the construction of exact solutions, even in the presence of complex physical properties such as nonlinearity and dispersion. Consequently, they are of great interest across various areas of theoretical and mathematical...
I present recent progress in computing finite-temperature dynamical correlation functions in the 1+1 dimensional Ising field theory, an integrable quantum field theory. Leveraging the fact that in the Ising model, the finite-temperature form factor expansion can be recast as a Fredholm determinant, I develop a numerical approach based on evaluating these determinants. This representation is...
We derive a systematic construction for form factors of relevant fields in the thermal perturbation of the tricritical Ising model, an integrable model with scattering amplitudes described by the $E_7$ bootstrap. We find a new type of recursive structure encoding the information in the bound state fusion structure, which fully determines the form factors of the perturbing field and the...
We present results from plaquette models with ground states coming from both linear and nonlinear constraint rules. For the linear case, we study the triangular plaquette spin model, which we also study in the presence of an external longitudinal magnetic field. For the latter case, we study spin models whose ground state constraints come from nonlinear elementary cellular automaton rules. We...
We consider quantum or classical many-body Hamiltonian systems characterized by integrable
contact interactions supplemented by a generic two-body potential, potentially long-range. We
show how the hydrodynamics of local observables is given in terms of a generalised version of Bogoliubov–Born–Green–Kirkwood–Yvon
hierarchy, which we denote as gBBGKY, which is built for the
densities, and...
Generalised Hydrodynamics (GHD) has proven successful to describe thermodynamics and hydrodynamics of integrable systems (See see Castro-Alvaredo, O. et al. Phys. Rev. X 6, 041065 (2016)). These systems present infinitely many constants of motion in involution and thus do not relax to a classical Gibbs Ensemble, but to a Generalised Gibbs Ensemble (GGE), taking into account all these...
Integrable systems feature an infinite number of conserved charges and on hydrodynamic scales are described by generalised hydrodynamics (GHD). This description breaks down when the integrability is weakly broken and sufficiently large space-time-scales are probed. The emergent hydrodynamics depends then on the charges conserved by the perturbation.
In my contribution I will focus on...
Mathematical models of non-abelian anyons can be constructed using the data of fusion categories. In this context anyon species are labelled by objects in the category, and projectors can be constructed which describe the fusion of neighbouring anyons into a third anyon. The boost operator formalism provides a robust way to construct and classify integrable models based on fusion categories....
The Lie symmetries of the Pais-Uhlenbeck Oscillator (PUO) are identified. They are then used to generate the Bi-Hamiltonian structure of this system. We then study how we might leverage this Bi-Hamiltonian
structure to mitigate the pathologies associated with theories where, as in the case of the PUO, the lagrangian admits time derivatives of order two or higher. Theories of this nature are...
In this talk, we will discuss [arxiv:2502.19504]: Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits (QCs). 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...
The study of correlation functions of integrable models at their free fermion points often leads to expressions involving Fredholm determinants of integrable integral operators. This occurs, for example, in dynamical two-point correlation functions of the impenetrable Bose gas, the XY and XX spin chains at finite temperature. In this talk, we address the problem of obtaining the long-time and...
In this talk, I will discuss the nonequilibrium dynamics in a quantum Ising chain where the transverse field slowly rotates. The corresponding magnetization oscillations are found to be non-thermalized and can be explained by contributions from different particle excitations in the quantum E_8 integrable model. For the details of the talk, firstly, I will provide a brief introduction to the...
We investigate the entanglement properties of the Quantum Six-Vertex Model on a cylinder, focusing on the Shannon-Renyi entropy in the limit of Renyi order $n = \infty$.
This entropy, calculated from the ground state amplitudes of the equivalent XXZ spin-1/2 chain, allows us to determine the Renyi entanglement entropy of the corresponding Rokhsar-Kivelson wavefunctions, which describe the...
In this talk, I will discuss how to study the probabilities of observing unusually large or small particle currents in the context of the totally asymmetric simple exclusion process (TASEP) on a ring. To do this, we will revisit the large deviation function derived in a seminal paper by Derrida and Lebowitz (Phys.Rev.Lett.80,209(1998). We adapt their approach for the TASEP with accelerated...
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics.
It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments.
The entanglement dynamics emerging from long-range correlated states is far less studied,...
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics.
It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments.
The entanglement dynamics emerging from long-range correlated states is far less studied,...
The sine-Gordon theory is a paradigmatic integrable field theory, relevant for the description of many 1D gapped systems. Despite its integrable nature, calculating finite temperature physical quantities, such as correlation functions, remains a challenge. The titular method of random surfaces is a Monte Carlo-based numerical algorithm that makes it possible to get non-perturbative results at...
It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack...
In this talk, I explain the structure of the local consrvetaion law in several interacting integrable systems.
Quantum integrable systems are exactly solvable by the Bethe ansatz.
Behind their exact solvability, there is an infinite number of local conserved quantities $\{Q_{k}\}_{k=2,3,4,\ldots}$.
Although the existence of $Q_{k}$ itself is guaranteed from the quantum inverse scattering...
This poster presents a novel class of subleading Regge trajectories (with non-orthogonal intercepts) in $\mathcal{N}=4$ SYM using the Quantum Spectral Curve (QSC), an integrability-based technique. I show how the standard application of the QSC, valid for leading trajectories, fails for the examined cases, and propose some crucial modifications to the method, which pass non-trivial consistency...
From a many-body perspective, classical integrable systems fall into two broad categories: fluids and chains. The former are particle-based and their hydrodynamics closely mirrors that of quantum models. Chain systems, on the other hand, behave like integrable wave equations, with their long-time dynamics separating into solitons and dispersive radiation. While soliton gases are relatively...
One of the more recent concepts in condensed matter theory are symmetry-protected topological (SPT) phases. Although the core of the theory exists, particular models as well as models outside the basic paradigm are not studied well yet. Here we study the topological modes protected by the $Z_N^{\otimes 3}$ symmetries in two-dimensional systems. A class of models with massless excitations...
The Lieb-Liniger model is a fundamental example of an interacting integrable system, describing bosons in one dimension with point-like interactions. A key challenge in its study is solving the linear integral equations that govern the rapidity density and its moments. In this talk, I will present a trans-series approach to solving these equations, which systematically encodes both...
The $J_1$-$J_2$ spin chain is one of the canonical models of quantum magnetism, and has long been known to host a critical antiferromagnetic phase with power-law decay of spin correlations.
Using the matrix product state path integral to capture the effects of entanglement near the saddle points, we argue here that there are, in fact, two distinct critical phases: the 'Affleck-Haldane'...
In our work, we consider a two-component fermionic system on a lattice with anticorrelated disorder. Due to the locality of interspecies attractive interaction, it turns out that the disorder for composite pairs is supressed. This makes the transport of pairs to be possible. Within our study, we investigate the temperature dependence of particle 'conductivity'.
