# Dynamics, criticality, and universality in random quantum circuits

We will use MeetAnyway for the poster sessions. All the posters will be presented during both poster sessions
- Thursday, 6:30 - 8 p.m., Friday, 1:30 - 3 p.m..
The times given in the schedule are according to Central European Summer Time (CEST).

### Thermalization and scrambling in dual-unitary circuits

Claeys, Pieter W.

Dual-unitary quantum circuits can be used to construct 1 + 1 dimensional lattice models for which all dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space. Considering time-ordered correlators, we present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic), a generalized Gibbs ensemble (non-ergodic), and prethermalization to the latter before thermalization to the former in a non-ergodic model with a small ergodicity-inducing perturbation. Out-of-time-order correlations (OTOCs), a measure for operator spreading and scrambling, can similarly be calculated, where dual-unitary circuit models exhibit a maximal butterfly velocity and exponential decay away from the light cone.

### Measurement-induced criticality in (2+1)-dimensional hybrid quantum circuits

Dalmonte & Turkeshi, Marcello & Xhek

### The frustration of being odd

Franchini, Fabio

Boundary conditions are not expected to play any role in the bulk, local properties of large systems. At the same time, we know that frustrated systems present features that cannot be explained using the toolbox of non-frustred one. We consider one-dimensional chains with frustrated boundary conditions (FBC, i.e., periodic boundary conditions with an odd number of lattice sites) and show that they destroy the local order that characterizes these system under normal circumstances. In fact, different local orders can emerge under FBC, which are separated by a BC-Induced Quantum Phase Transition. Although these results could be surprising, their origin is quite simple and natura, but can also be supported by rigourus, non-perturbative calculations.

### Many-body quantum chaos and the local pairing of Feynman histories

Garratt, Samuel

We study many-body quantum dynamics using Floquet quantum circuits in one space dimension as simple examples of systems with local couplings that support ergodic phases. Physical properties can be expressed in terms of multiple sums over Feynman histories, which for these models are many-body orbits in Fock space. A natural simplification of these sums is the diagonal approximation, where the only terms that are retained are ones in which each orbit is paired with a partner that carries the complex conjugate weight. We examine when the diagonal approximation holds, its consequences in calculations of physical properties, and the nature of the leading corrections to it. We show that properties are dominated at long times by contributions to orbit sums in which each orbit is paired locally with a conjugate, as in the diagonal approximation, but that in large systems these dominant contributions consist of many spatial domains, with distinct local pairings in neighbouring domains. The existence of these domains is reflected in deviations of the spectral form factor from RMT predictions, and of matrix element correlations from ETH predictions; deviations of both kinds diverge with system size. We demonstrate that our physical picture of orbit-pairing domains has a precise correspondence in the spectral properties of a transfer matrix that acts in the space direction to generate the ensemble-averaged spectral form factor. arXiv:2008.01697

### Non-abelian fluctuating hydrodynamics and nature of diffusion in isotropic Heisenberg chains

Glorioso, Paolo

After thermalization, it is generally believed that spin transport in non-integrable spin chains is governed by standard diffusion. There is however an old debate, revived in recent literature, questioning whether this expectation is correct, claiming that the diffusion constant of certain SU(2) spin chains diverges logarithmically in time. I will address this debate using recently developed techniques in fluctuating hydrodynamics, with particular focus on the classical isotropic Heisenberg model.

### Alternative spacetimes in the solid state physics

Jafari, Seyed Akbar

We show that solids hosting tilted Dirac cone in their spectrum provide an effective spacetime structure. The structure of the spacetime is encoded in the tilt parameter which can be controlled by electric fields. We study properties of such spacetimes, and their spectroscopic signatures. We point some novel solid- state phenomena that are caused by the new spacetime structure including: (1) Enhancement of magnetic fields, (2) generation of charged Andreev modes, (3) formation of a novel TE mode, (4) new plasmon polarities, (5) synthetic gauge fields and spin orbit interactions, (7) generation of electricity from temporal variation of temperature.

### The Possibilities of the Interdisciplinary Strategy for Quantum Information/Photonic Optimization

Jayaraj, Shwetha

With the esteemed honor of the Max Planck Institute for the invitation to present my poster at the conference, I will provide a practical prototype of how the interdisciplinary strategy has proven effective at the New York Institute of Technology in building efficient physical models in both classical circuit optimization but especially in quantum architecture dynamics. Firstly, by outlining NYIT's original Storm Station solar-powered structure constructed to aid in climate crisis events in Puerto Rico deployed using a uniquely interdisciplinary collaboration to multipurpose modules. And secondly, leading into potential optimizations that can be achieved utilizing quantum-based architecture on both the NYIT Storm Station project but also on an interdisciplinary scale overall. Effective methodologies of quantum computing and the necessary gate logic that accompanies the theoretical field should not be lost on the rest of the moving components in the classical system, an idea that might seem initially commonplace but may not easily be implemented in practice with working professionals. A display of how NYIT Manhattan & its student-facilitated interdisciplinary quantum research group (the QRG) will be presented along with a critical analysis between free-form think tank structures and discipline-specific approaches in quantum computing frameworks which invites room for open discussion as well as further research.

### Correlations in Perturbed Dual-Unitary Circuits: Efficient Path-Integral Formula

Kos, Pavel

Interacting many-body systems with explicitly accessible correlation functions are extremely rare, especially in the absence of integrability. Recently, we identified a remarkable class of such systems: dual-unitary quantum circuits [B. Bertini, P. Kos, T. Prosen PRL 123, 210601 (2019)]. Dual-unitarity, however, requires fine-tuning and the degree of generality of the observed dynamical features remained unclear. In my poster, based on arXiv:2006.07304 [P. Kos, B. Bertini, T. Prosen], we address this question by studying perturbed dual-unitary quantum circuits. First, we show that random deviations from dual-unitarity preserve the dual-unitary form of the correlations. Then, considering fixed perturbations, we show how the correlation functions are expressed in terms of one-dimensional transfer matrices. These matrices are contracted over generic paths connecting the origin to a fixed endpoint inside the causal light cone. The correlation function is given as a sum over all such paths.

### Conformal invariance and quantum non-locality in hybrid quantum circuits

Li, Yaodong

We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition, by revealing space-time conformal covariance of entanglement entropies and mutual information for various subregions at different circuit depths. While the evolution takes place in real time, the spacetime manifold of the circuit appears to host a Euclidean field theory with imaginary time. Throughout the paper we investigate Clifford circuits with several different boundary conditions by injecting physical qubits at the spatial and/or temporal boundaries, all giving consistent characterizations of the underlying "Clifford CFT". We emphasize (super)universal results that are consequences solely of the conformal invariance and do not depend crucially on the precise nature of the CFT. Among these are the infinite entangling speed as a consequence of measurement-induced quantum non-locality, and the critical purification dynamics of a mixed initial state.

### Mean-field entanglement transitions in random tree tensor networks

Lopez Piqueres, Javier

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. We verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

### Measurement-induced entanglement transitions in many-body localized systems

Lunt, Oliver

The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume-law to an area-law at a critical measurement probability $p_{c}$. Interestingly, there is a distinction in the value of $p_{c}$ depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, $p_{c} > 0$, whereas for weakly chaotic systems, such as integrable models, $p_{c} = 0$. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with $p_{c} > 0$ when the measurement basis is scrambled and $p_{c} = 0$ when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at $p_{c} > 0$, we use finite-size scaling to obtain the critical exponent $\nu = 1.3(2)$, close to the value for 2+0D percolation. We also find a dynamical critical exponent of $z = 0.98(4)$ and logarithmic scaling of the R\'{e}nyi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.

### Quantum transport on generalized scale-free networks

Maciel, Cássio

A large variety of studies on quantum transport, that emerged in the last years, whether in physics, chemistry or in the construction of quantum algorithms, present elements of great scientific interest. In this work we study quantum transport in generalized scale-free networks (GSFNs) through continuous-time quantum walks (CTQWs). The efficiency of the transport is monitored through the exact and the average return probabilities. The latter depends only on the eigenvalues and eigenvectors of the connectivity matrix. For GSFNs three parameters govern their growth: the maximum and minimum degrees, i.e., the liminting number of links emerging from every node, and γ that measures the density of connections in the network. We observe a nontrivial interplay between strong localization effects, due to starlike segments, and good spreading because of the linear segments. We show that the quantum transport on GSFNs can be increased by varying the minimum or the maximum allowed degrees. The same quantum efficiency is reached by considering various combinations of the construction parameters of the network, which normally show different topological features.

### Dynamic and Steady State Flow Properties of Cholesteric type Mesophases

Dynamic and steady state flow properties for derivatives of cholesterol have been determined. An attempt to analyze flow behavior of cholesteric type liquid crystal mesogens with an aim to the application as additives in modern lubricants was done. Cholesteryl ethoxy ethoxy ethyl carbonate, Cholesteryl bromide (here after referred as CB,CEEEC) were investigated using AR G2 rheometer. The onset of nonlinearity is obtained at low percentage of strains in CB than CEEEC. The viscoelastic properties of both mesogens were shown to be strongly temperature dependent. In CB, the temperature scans on G′ and G′′ discovered an anomaly which might be an indication of Smectic phase. The frequency behaviour of the mesogen CEEEC is characterized by a prevalent viscous behaviour (G”>G’), while for CB a crossover of where the storage modulus dominates the loss modulus and level off at higher frequencies is observed. In steady state experiment shear thinning followed by Newtonian flow is found in CB and Newtonian flow behavior is seen in CEEEC. This workis intended to scientifically highlight flow behaviour of these two flow-aligning thermotropic cholesterol type mesogens and their importance in the field of lubrication. Such a characterization may perhaps provide operational parameters for the preparation of lubricants and additives in Tribology. Key words: VIscoelastic, Shear thinning, lubrication, Tribology.

### Operator Spreading in the Memory Matrix Formalism

McCulloch, Ewan

Quantum information is conserved under unitary dynamics, and can be viewed as a hydrodynamical slow mode. We re-frame operator spreading within the memory matrix formalism by including this often overlooked slow mode. This formalism yields a succinct expression for the butterfly velocity and shows that the biased diffusion of operators in ergodic systems is arguably the simplest scenario consistent with unitary dynamics. We present the formalism developed for Floquet circuits and Hamiltonian models and present results for a Floquet circuit without symmetry.

### Integrable quantum many-body sensors for AC field sensing

Mishra, Utkarsh

Quantum sensing is inevitably an elegant example for supremacy of quantum technologies over their classical counterparts. One of the desired endeavor of quantum metrology is AC field sensing. Here, by the means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the critical ground states, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving precision for sensing the amplitude well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. This shows the potential of integrable many-body systems for providing quantum enhanced precision in AC field sensing.

### Simulating semi-infinite generalized Aubry-Andr\'{e} or Harper (AAH) model using continued fractions

Odavić, Jovan

Using continued fractions and recurrence relations for the related convergents we derive an expression for the reservoir self-energy which enables numerical simulation of the semi-infinite AAH model within the Matsubara Green's functions formalism at zero temperature. To demonstrate the effectiveness of the derived expression we compute the local and total density of states, density per lattice site and demonstate the existance of a phase transion using Inverse Participation Ration measure in the thermodynamic limit.

### Universality of entanglement transitions from stroboscopic to continuous measurements

Romito, Alessandro

Quantum measurements can induce an entanglement transition between extensive and sub-extensive scaling of the entanglement entropy. This transition is of great interest since it illuminates the intricate physics of thermalization and control in open interacting quantum systems. Whilst this transition is well established for stroboscopic measurements in random quantum circuits, a crucial link to physical settings is its extension to continuous observations, where for an integrable model it has been shown that a sub-extensive scaling appears for arbitrarily weak measurements. Here we study a one-dimensional quantum circuit evolving under random unitary transformations and generic positive operator-valued measurements of variable strength. We first show that, for stroboscopic measurements, there is a consistent phase boundary in the space of the measurement strength and the measurement probability, clearly demonstrating a critical value of the measurement strength below which the system is always ergodic, irrespective of the measurement probability. Then, we demonstrate that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable, and show that it is smoothly connected to the transition in the stroboscopic models. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.

### Measurement-induced phase transitions in all-to-all quantum circuits and quantum trees

We present some analytical and numerical results on entanglement transitions in all-to-all quantum circuits with measurements. Exploiting the underlying locally tree-like structure of the space-time graph, we quantify the quantum information flowing through the circuit via the entanglement between the apex and base of the tree. The tree-like structure of the graph allows for a recursive solution to the problem which analytically solvable in some cases yielding exact results for the location of the critical point and scaling near the critical point. Away from these cases, we present numerical results which confirm the universality of our results.

Ruhman, Jonathan

### Spectral Transitions and Universal Steady-States in Random Kraus Maps and Circuits

Sá, Lucas

We study the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we analyze both fully connected models and their local Floquet circuit counterparts. Quite remarkably, the statistical properties of the spectrum and steady-state of local Kraus circuits are qualitatively the same as those of nonlocal Kraus maps, indicating that the latter---for which a large-N RMT model is amenable to exact analytic computations---already capture realistic and universal properties of generic open quantum systems. We find the spectrum of the Kraus maps to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The steady-state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady-state is characterized by uncorrelated eigenvalues; at large-enough dissipation, the steady-state is well described by a random Wishart matrix. The steady-state properties thus coincide with those of random Lindbladian dynamics, indicating their universality. Based on L. Sá, P. Ribeiro, T. Can, and T. Prosen, arXiv:2007.04326.

### Out-of-time-ordered-correlator quasi-probabilities for the quantum kicked top

Shammah, Nathan

The cumulative nonclassicality of the quasi-probability distribution (QPD) behind the out-of-time-ordered correlator (OTOC) [1] exhibits different timescales for spin chains. These timescales have been conjectured to be useful for distinguishing integrable and non-integrable Hamiltonians [2]. We further investigate the QPD for the quantum kicked top model, and use the time scales of its nonclassicality to understand the relationship between entanglement and chaos for different parameter regimes. [1] N.Yunger Halpern, B.Swingle, and J.Dressel, "The quasiprobability behind the out-of-time-ordered correlator", PRA 97.4 042105 (2018) [2] J. R. Gonzalez Alonso, N. Yunger Halpern, and J. Dressel, "Out-of-Time- Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling", PRL 122.4 040404 (2019)

### The minimal cut problem in all-to-all circuits with measurement

Skinner, Brian

The simplest toy model for the entanglement transition in a quantum circuit is the problem of the “minimal cut”, in which the entanglement entropy of a subregion is described by the number of legs of the circuit that must be broken in order to separate one subregion from the rest of the system. This toy model serves as an upper bound for the entanglement entropy that becomes exact in certain limits. Here we present a solution to the minimal cut problem in “all-to-all” circuits with measurements, for which pairwise unitary operators can directly couple any two spins to each other and measurements are of single spins. In this case the entanglement transition is associated with a minimal cut separating the initial and final times of the circuit. We present a derivation of the critical measurement rate and critical exponents for this problem, and confirm our results with numeric simulations.

### Effects of integrability on the measurement-induced entanglement transitions

Szyniszewski, Marcin

We investigate a range of random quantum circuit models subject to unitary Hamiltonian dynamics and projective measurements. For random unitary evolution, these circuits are known to exhibit a phase transition between the volume-law and the area-law entanglement behaviour. In this work, however, the employed Hamiltonian is that of a nonrandom integrable spin chain. We examine standard entanglement transition measures, such as entanglement entropy and tripartite mutual information, and determine the fate of the transition as a function of the model parameters and the details of the applied measurements. Our work gives insights into how the interplay between integrability and quantum measurements impacts entanglement dynamics.

### Entanglement of Local Operators and the Butterfly Effect

Tan, Mao Tian

We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a “membrane theory” in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an O(1) amount of information is found to be delocalized by local operators in integrable systems such as free fermions and Clifford circuits.

### Entanglement entropy scaling transition under competing monitoring protocols

Van Regemortel, Mathias

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second one destroys the coherence via dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides novel insights into the occurrence of a measurement-induced phase transition within a continuous monitoring protocol.

### Simultaneous quantum communication and multiple entangling gate operations across spin-chain channel

Yousefjani, Rozhin

The time evolution of spin chains has been extensively studied for both transferring quantum states and implementing quantum gates between distant registers of a quantum computer. Nonetheless, in most of the proposed protocols, operations can only be performed between a pair of channel users (qubits) at each time. This bottleneck significantly limits the rate of operation in quantum computers because communication and gate implementation between channel users can only be carried out sequentially. Here, we make an essential step towards overcoming these obstacles. In the first step, we develop a novel protocol that allows multiple users to simultaneously communicate in two-way through a common spin chain channel. In the next step, by extending our protocol, we establish parallel two-qubit entangling gate operations.

### Fault-tolerant qudit Hamiltonian engineering and quantum sensing beyond the interaction limit

Zhou, Hengyun

In this work, we develop robust techniques for Hamiltonian engineering in both interacting qubit and qudit systems. By devising systematic rules for the transformation of spin Hamiltonians under global manipulation and their associated imperfections, we are able to develop robust pulse sequences that enable the first demonstration of quantum sensing beyond the spin-spin interaction limit in the solid state, exploration of quench dynamics in a long-range XXZ spin model, and novel types of spin-1 Hamiltonians that may host quantum many-body scars.