Schedule for: 25w5429 - Exact Solutions in Quantum Information: Entanglement, Topology, and Quantum Circuits

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Meet and Greet at BIRS Lounge (PDC 2nd Floor)

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

Quantum entanglement possesses a rich collective structure that remains poorly understood in quantum matter and architectures. Here we study genuine multiparty entanglement (GME) in two families of systems in and out of equilibrium. First, we find that in quantum spin liquids GME is 1) absent at short scales (“entanglement frustration”), 2) predominantly present in loopy subregions. Second, we study hybrid quantum circuits that realize measurement-induced transitions. In a solvable 1d model, we show that GME decays algebraically for any number of parties, and we give the exponents via logarithmic conformal field theory. We further present estimates for such new “entanglement exponents” in generic Haar-random circuits.

Quantum information processing, at its core, is effected through unitary transformations applied to states on the Bloch sphere, the standard geometric realization of a two-level, single-qubit system. That said, in viewing the application of a logic gate as a continuous dynamical process, it is natural to replace the original Hilbert space of the problem with a finite-rank Hermitian vector bundle, through which unitary transformations may be achieved in a natural geometric way via parallel transport along a connection. It then follows that the construction of quantum circuits is captured in a topological quantum field theory (TQFT), decorated with flat bundles. At the same time, an extension to the classification of topological quantum matter — relying upon hyperbolic geometries — that has emerged in my collaborative work with theoretical physicists and experimentalists suggests that this setup may be actualizable as a physical platform for computation.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

We have initiated a study of dynamical two-point functions of arbitrary local operators in integrable lattice models by means of `thermal form factor series'. These are obtained as expansions in a basis of eigenstates of an appropriately defined `quantum transfer matrix'. The latter is different from the transfer matrix that generates the Hamiltonian. The quantum transfer matrix rather is an abstract object that generates lattice path integral representations of the partition function and of correlation functions of quantum chains. For integrable quantum chains it can be constructed in such a way that its spectrum and eigenstates can be calculated by `integrable methods' such as the algebraic Bethe Ansatz. After explaining the general formalism, I shall show that thermal form factor series provide explicit representations of dynamical two-point correlation functions of the XXZ quantum spin chain in the thermodynamic limit that are efficient for numerical and asymptotic analysis. Concrete examples of spectral functions and of current-current functions that determine the transport properties of the spin chain will be considered.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Different variants of partial orders among quantum states arise naturally in the context of various quantum resources. For example, in discrete variable quantum computation, stabilizer operations naturally produce an order between input and output states; in technical terms this order is vector majorization of discrete Wigner functions in discrete phase space. In the continuous variable case, a natural counterpart would be continuous majorization of Wigner functions (Wigner majorization) in quantum phase space. In this talk, I will discuss recent developments in the theory of Wigner majorization between N-mode bosonic states. These include a generalization of continuous majorization to states with finite Wigner negativity. Moreover, I will address the question of which type of quantum operation connects two states if a Wigner majorization relation exists between them. Finally, I will discuss the implications of these findings in view of applications in resource theories.

As it is essential to have a quantum theory of gravity for understanding the fundamental principles underlying black hole thermodynamics, constructing and studying quantum gravity has been a constant desire in modern theoretical physics. I will construct the explicit framework to build a formalism to construct a lattice model of space time and quantum gravity. I will present explicit toy models of quantum gravity with this framework. I will utilize quantum gravity in the semi-classical regime by taking quantum field theory as its framework and demonstrate that the notion of entanglement, which is central in the quantum nature of physics, plays an important role in studying quantum gravity.

In the context of out-of-equilibrium many-body quantum systems, increasing attention has been recently devoted to the problem of characterizing how symmetries evolve in time under unitary dynamics. The main questions are whether symmetries are dynamically restored in local subsystems and how the time scales involved depend on the initial states and the dynamical features. In this talk, I will discuss the case of a symmetry initially unbroken under a random unitary evolution that does not preserve it, employing the entanglement asymmetry as a versatile and computable probe of symmetry breaking in extended quantum systems. I will consider both local and non-local random unitary circuits, finding qualitative differences on the equilibration timescales depending on the subsystem size and the locality of the interactions. These results give a phenomenological overview of the evolution of symmetries in typical non-integrable dynamics.

Quantum entanglement, symmetries and defects are captivating topics in quantum physics and quantum information science, where analytical methods enabling exact solutions along with robust numerical techniques can be employed to address a range of interesting problems. In this talk, I will briefly illustrate two examples which connect these three different subjects. The first example concerns the symmetry resolution of quantum entanglement, which captures the refined structure of entanglement in quantum systems with global symmetries. In particular, I will briefly describe a computational framework suitable for tracking the dynamical evolution of symmetry resolved entanglement and symmetry charge full-counting statistics in symmetry-preserving out-of-equilibrium settings. The second example concerns topological defects in quantum systems, which play interesting and important roles in the construction of long-lived physical quantities. This talk is mainly based on arXiv: 2412.14165 and arXiv: 2410.17317.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We describe an efficient, fully fault-tolerant implementation of Measurement-Based Quantum Computation (MBQC) in the 3D cluster state. The two key novelties are (i) the introduction of a lattice defect in the underlying cluster state and (ii) the use of the Rudolph-Grover rebit encoding. Concretely, (i) allows for a topological implementation of the Hadamard gate, while (ii) does the same for the phase gate. Furthermore, we develop general ideas towards circuit compaction and algorithmic circuit verification, which we implement for the Reed-Muller code used for magic state distillation. Our performance analysis highlights the overall improvements provided by the new methods.

We study the open quantum system dynamics (in the Trotterized limit) of an integrable quantum circuit of a spin- 1/2 impurity interacting at the edge with a qubit chain in the presence of onsite dephasing noise. Using a combination of Bethe Ansatz (BA) and exact diagonalization (ED), we study the dynamics of both the bulk and the impurity for the XXX (Heisenberg) and the XX qubit chains in the presence and absence of bulk noise. In the absence of noise, we show that the impurity exhibits two distinct phases, the bound mode phase where the impurity keeps oscillating in time, and the Kondo phase where it decays with Kondo time tK . Turning on the bulk dephasing noise, we find for the two models that in the long time limit in both regimes the quantum Zeno effect takes place where the dynamics of the impurity magnetization slows down as the noise strength γ increases. The opposite effect is seen for short times ($t\ll 1/\gamma)$ in the bound mode regime where the impurity magnetization decays faster as the noise strength increases. We show that the Zeno effect slowing down the impurity dynamics in the long time limit is driven by the change in bulk dynamics from ballistic (KPZ) universality class in the XX (XXX) chain to diffusive dynamics in the presence of the noise.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

We consider the square lattice S=½ quantum compass model (QCM) parameterized by Jx, Jz, under an in-plane field. At the special field value, (hx*,hz*)=2S(Jx,Jz), we show that the QCM Hamiltonian may be written in a form such that two simple product states can be identified as exact ground-states, below a gap. Exact excited states can also be found. The presence of the gap implies that the exactly solvable point is part of an extended phase distinct from the low field and high field phases. Our findings are important for understanding the field dependent phase diagram of materials with predominantly directionally-dependent Ising interactions, and duality relations connects the QCM model to the Xu-Moore model and the toric code. Similar exact ground-states can be found for one dimensional Kitaev Spin chains with Periodic BC, however, open BC leads to a ground-state with a single soliton.

In recent years the role of symmetries and their breaking has been investigated in the context of entanglement. In particular, it has been possible to define symmetry resolved entanglement measures. These are measures of entanglement associated to symmetry sectors of a particular theory. In this talk I will introduce the main properties and definition of these measures and discuss some special examples that feature in my own research. I will focus mostly on the contribution to entanglement of localised excitations above the ground state of an integrable quantum field theory.

In this talk, I will discuss the interplay of confinement, string breaking and entanglement asymmetry on a 1D quantum Ising chain. In particular, I show that while the introduction of confinement through a longitudinal field typically suppresses entanglement, it can also serve to increase it beyond a bound set for free particles. I will also describe the interplay of entanglement asymmetry and with conservation laws associated with link variables, comparing two approaches to deal with the non-locality of the link variables, either directly or following a Kramers-Wannier transformation that maps bond variables (kinks) to site variables (spins).

Digital quantum devices have emerged as powerful platforms for exploring the non-equilibrium dynamics of quantum many-body systems. Integrable systems represent useful benchmarks for validating noisy experimental setups. Moreover, breaking integrability can lead to surprising dynamical phenomena, unveiling new insights into quantum dynamics. In this talk, I will present two illustrative examples: first, how breaking integrability can result in anomalously slow thermalization, and second, how proximity to (digital) integrable dynamics sheds light on the origin of quantum many-body scars.

We study the phase diagram of an extended parafermion chain, which, in addition to terms coupling parafermions on neighbouring sites, also possesses terms involving four sites. Via a Fradkin–Kadanoff transformation the parafermion chain is shown to be equivalent to the non-chiral Z3 axial next-nearest neighbour Potts model. The phase diagram contains several gapped phases, including a topological phase where the system possesses three (nearly) degenerate ground states, and a gapless Luttinger-liquid phase. Furthermore, we apply Witten’s conjugation argument to spin chains. The approach allows us to treat two 3-invariant frustration-free parafermion chains, recently derived by Iemini et al. [2] and Mahyaeh and Ardonne [3], respectively, in a unified framework. References: Jurriaan Wouters, Hosho Katsura and Dirk Schuricht, SciPost Phys. Core 4, 027 (2021) Jurriaan Wouters, Fabian Hassler, Hosho Katsura and Dirk Schuricht, SciPost Phys. Core 5, 008 (2022)

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

In this talk, I will explore the pioneering technology of QuEra, focusing on its neutral-atom quantum computers. QuEra's approach combines analog and digital quantum computing, leveraging the strengths of neutral atoms for high coherence and unique qubit manipulation. The presentation will cover QuEra's ambitious roadmap, which includes significant milestones in quantum error correction and scalability for gate-based computing, as well as recent applications obtained in analog quantum computing for quantum simulation, optimization, and machine learning.

The ‘operator entanglement’ is an indicator of the complexity of quantum operators, and of their approximability by Matrix Product Operators (MPO) in 1D quantum systems. I will discuss the ‘entanglement barrier’: the fact that the OE of a reduced density matrix initially grows linearly as entanglement builds up between the local degrees of freedom, then reaches a maximum, and ultimately decays to a small finite value as the reduced density matrix converges to a simple stationary state through standard thermalization mechanisms. This ‘entanglement barrier’ can be obtained in various models, and it has recently been found in experimental data in the trapped ion setup of [Brydges et al., Science 364, 260 (2019)], by performing a new analysis of the data using the randomized measurement toolbox. I will also briefly discuss the influence of chaotic vs. integrable dynamics, as well as dissipation, on the shape of the ‘entanglement barrier’.

We discuss the entanglement between two critical spin chains induced by the Bell-state measurements, when each chain was independently in the ground state before the measurement. This corresponds to a many-body version of “entanglement swapping”. We employ a boundary conformal field theory (CFT) approach and describe the measurements as conformal boundary conditions in the replicated field theory. We show that the swapped entanglement exhibits a logarithmic scaling, whose coefficient takes a universal value determined by the scaling dimension of the boundary condition changing operator. We apply our framework to the critical spin-1/2 XXZ chain and determine the universal coefficient by the boundary CFT analysis, which is verified by a numerical calculation. This talk is based on M. Hoshino, M. O., and Y. Ashida, arXiv:2406.12377

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Constrained dynamics in quantum many-body systems have attracted a great deal of attention in recent years. In many cases, the restricted mobility of elementary excitations can be understood in terms of higher symmetries beyond charge conservation. For instance, the exact conservation of a dipole-moment operator can impose that isolated single-particle excitations become immobile, while pairs of excitations are mobile. In this talk I will discuss how signatures of constrained dynamics can be observed in a quasi-one-dimensional model where the dipole symmetry is not exact, but emerges in the low-energy sector. Specifically, we study a deformation of the exactly solvable Bariev model on a two-leg ladder, whose phase diagram features a Tomonaga-Luttinger liquid phase of bound pairs. Using a combination of field theory methods and numerical simulations, we show that the single-particle defects in this phase show remarkably slow relaxation dynamics. We propose a protocol to observe the effects of the approximate dipole symmetry using hardcore bosons in optical lattices or Rydberg atom arrays.

Quantum n-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Con- sequently, there is significant interest in developing methods to prepare and manipulate Dicke states, which form a basis for the subspace of fully symmetric states. Two simple protocols for transforming Dicke states are considered. An algebraic characterization of the operations that these protocols induce is obtained in terms of the Weyl algebra $W(2)$ and $su(2)$. Fixed points under the application of the combination of both protocols are explicitly determined. Connec- tions with the binary Hamming scheme, the Hadamard transform, and Krawtchouk polynomials are highlighted.

Non-thermal energy eigenstates of thermalizing isolated quantum systems have been intensively studied these days, as counter examples for the strong eigenstate thermalization hypothesis. These states called “quantum many-body scars (QMBS)” exhibit specific properties such as low entanglement entropies or persistent oscillations. Nowadays, it is believed that, based on many numerical evidence, these exceptional non-thermal states emerge when the Hamiltonian has a relatively small invariant subspace, which weakly violate ergodicity in the Hilbert space. In this talk, we demonstrate that weak violations of ergodicity can be achieved by embedding selected integrable models into the larger Hilbert spaces of otherwise chaotic systems. The integrable subspaces lack a tensor product structure with respect to any spatial bipartition, distinguishing them from trivial embedding cases. Interestingly, models constructed in this manner can be viewed as perturbations of systems exhibiting Hilbert space fragmentation, where the perturbations eliminate the fragmentation. Furthermore, we show that this approach to constructing weakly ergodicity-breaking models can also be extended to quantum circuits.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

In recent years, a new kind of symmetry has found many surprising applications in quantum field theory and many-body quantum systems. These symmetries are generated by conserved operators that do not come with an inverse, and therefore do not form a group. We will discuss the tensor network presentation for exact non-invertible symmetries of various lattice models, ranging from the Ising model to discrete lattice gauge theories.

Quantum simulations are recently gaining growing attention across various scientific communities, that range from condensed matter to high-energy physics, encompassing experimental and theoretical approaches. The main challenge often consists in mapping a quantum system – whether a single-particle, many-body system, or field theory – onto a system of interacting qubits, which are the fundamental units of quantum computation. Although the overarching goal of quantum simulations appear simple, this field can be approached from many different perspectives, with numerous and compelling methods emerging. During this workshop, I would like to contribute to the ongoing discussion by presenting a recent paper [arXiv:2407.01669], co-authored with Giuseppe Mussardo and Andrea Trombettoni. I will focus on the problem of measurement in the context of a digital simulation, considering some simple quantities in scattering theory, such as reflection and transmission amplitudes of a one-dimensional particle interacting with a short-ranged potential. The quantum algorithm we are proposing involves coupling the quantum register to an ancillary qubit, whose measurement allows us to tomographically reconstruct not only the absolute values, but also the relative phase between reflection and transmission amplitudes.

In systems with particle number conservation, the symmetry-resolved entanglement components are not extensive. However, when two independent subsystems are combined, minimal bounds can be derived for the entanglement components. These results can be applied to obtain bounds on the entanglement components for any Gaussian system. In such systems which have symmetry-protected topology, the eigenvalues of the density matrix are restricted to an interval. Using these restrictions and tools from majorization theory, we show that the symmetry-resolved entanglement components have topologically protected minima.

Exact solutions are available for a number of models of great interest in quantum mechanics, including some with promise for quantum information processing. In practice however, such formal exact solutions are challenging to translate into detailed quantitative predictions: any connection between the underlying system and its measurable quantities relies on knowing how physical operators and model (eigen)states "talk" to each other, this being quantitatively encoded in operator matrix elements. If obtained, these can then be "cooked" into correlation functions via Lehmann representations, but summing contributions is generally out of reach. This talk will focus on the matrix elements themselves: for given observables, their dependence on states and excitations will be discussed, as well as how sensitive they are to various modifications of the details of the states. An approach towards regularizing microscopic states into field theory-like entities will be discussed, with potential use in computing correlations and managing (numerical) renormalization approaches to in- and out-of-equilibrium situations.

We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, $\sigma_n^x$ and $\sigma_n^y$, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the XX model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We show that performing weak measurements on the quantum critical ground state of 1D Hamiltonians can give rise to highly complex novel scaling behavior due to the intrinsic indeterministic ('random') nature of measurements. We illustrate this for the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by performing weak measurements in (a) with the local energy and in (b) with the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis, we find that the scaling behavior of each problem is governed by a new, measurement-dominated RG fixed point that we study within an $\epsilon$ expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured ground state, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (log-CFTs); (iii): universal 'effective central charges' c^{eff)_n for the prefactors of the logarithm of subsystem size of the n^th R\enyi entropies, which are independent of each other for different n, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy' [PRL 67, 161 (1991)] S_{eff} which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. -- A subset of these results have so-far also been obtained within the \epsilon expansion for the measurement-dominated critical point in the critical Ising case (b). [based on: arXiv:2409.02107]

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.