arXiv subjects

Maksym Serbyn

Publications and source records attributed to Maksym Serbyn.

At least 37 records · Page 2Linked to original sources

arXiv2024

Many-body entropies and entanglement from polynomially-many local measurements

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical post-processing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments, and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix which allow us to reconstruct entropies and PT moments from information on local subsystems. This yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements (RMs), providing a practical and common measurement scheme, we prove that our protocol only requires polynomially-many measurements and post-processing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators, and provide numerical evidence that they are satisfied in more general, physically-interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today's quantum platforms.

quant-ph↗

arXiv2024

Tangent space generators of matrix product states and exact Floquet quantum scars

The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator which exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with the error which decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is useful not only for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars -- periodically driven models with quasi-local generators of dynamics that have exact MPS eigenstates in their spectrum.

quant-ph↗

arXiv2024

Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field

Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study [arXiv:2107.03695] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating $g$-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.

cond-mat.supr-con↗

arXiv2023

Deep learning extraction of band structure parameters from density of states: a case study on trilayer graphene

The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.

cond-mat.mes-hall↗

arXiv2023

Recursive greedy initialization of the quantum approximate optimization algorithm with guaranteed improvement

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm, where a quantum computer implements a variational ansatz consisting of $p$ layers of alternating unitary operators and a classical computer is used to optimize the variational parameters. For a random initialization, the optimization typically leads to local minima with poor performance, motivating the search for initialization strategies of QAOA variational parameters. Although numerous heuristic initializations exist, an analytical understanding and performance guarantees for large $p$ remain evasive. We introduce a greedy initialization of QAOA which guarantees improving performance with an increasing number of layers. Our main result is an analytic construction of $2p+1$ transition states - saddle points with a unique negative curvature direction - for QAOA with $p+1$ layers that use the local minimum of QAOA with $p$ layers. Transition states connect to new local minima, which are guaranteed to lower the energy compared to the minimum found for $p$ layers. We use the GREEDY procedure to navigate the exponentially increasing with $p$ number of local minima resulting from the recursive application of our analytic construction. The performance of the GREEDY procedure matches available initialization strategies while providing a guarantee for the minimal energy to decrease with an increasing number of layers $p$.

quant-ph↗

arXiv2023

Many-body localization proximity effect in two-species bosonic Hubbard model

The many-body localization (MBL) proximity effect is an intriguing phenomenon where a thermal bath localizes due to the interaction with a disordered system. The interplay of thermal and non-ergodic behavior in these systems gives rise to a rich phase diagram, whose exploration is an active field of research. In this work, we study a bosonic Hubbard model featuring two particle species representing the bath and the disordered system. Using state of the art numerical techniques, we investigate the dynamics of the model in different regimes, based on which we obtain a tentative phase diagram as a function of coupling strength and bath size. When the bath is composed of a single particle, we observe clear signatures of a transition from an MBL proximity effect to a delocalized phase. Increasing the bath size, however, its thermalizing effect becomes stronger and eventually the whole system delocalizes in the range of moderate interaction strengths studied. In this regime, we characterize particle transport, revealing diffusive behavior of the originally localized bosons.

cond-mat.dis-nn↗

arXiv2023

Superdiffusive Energy Transport in Kinetically Constrained Models

Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a broad superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. Intriguingly, strong deformations of the PXP model by the chemical potential do not restore diffusion, but instead lead to a stable superdiffusive exponent $z\approx3/2$. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.

cond-mat.stat-mech↗

arXiv2022

Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity

Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density of states of multilayer graphene with up to four layers at the single-particle band structure level in the presence of a transverse electric field. Among the considered structures, tetralayer graphene with rhombohedral (ABCA) stacking reaches the highest density of states. We study the phases that can arise in ABCA graphene by tuning the carrier density and transverse electric field. For a broad region of the tuning parameters, the presence of strong Coulomb repulsion leads to a spontaneous spin and valley symmetry breaking via Stoner transitions. Using a model that incorporates the spontaneous spin and valley polarization, we explore the Kohn-Luttinger mechanism for superconductivity driven by repulsive Coulomb interactions. We find that the strongest superconducting instability is in the $p-$wave channel, and occurs in proximity to the onset of Stoner transitions. Interestingly, we find a range of densities and transverse electric fields where superconductivity develops out of a strongly corrugated, singly-connected Fermi surface in each valley, leading to a topologically non-trivial chiral $p+ip$ superconducting state with an even number of co-propagating chiral Majorana edge modes. Our work establishes ABCA stacked tetralayer graphene as a promising platform for observing strongly correlated physics and topological superconductivity.

cond-mat.supr-con↗

arXiv2022

Hilbert space fragmentation and slow dynamics in particle-conserving quantum East models

Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored universality classes of dynamics and invite their further theoretical and experimental studies.

quant-ph↗

arXiv2022

Optimal steering of matrix product states and quantum many-body scars

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states~(MPS). We compare counter-diabatic and leakage minimization approaches to the so-called local steering problem, that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS state in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counter-diabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally we apply our leakage minimization approach to construct quantum scars in the periodically driven non-integrable Ising model.

quant-ph↗

arXiv2022

Crises and chaotic scattering in hydrodynamic pilot-wave experiments

Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g. weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions.

physics.flu-dyn↗

arXiv2022

Avoiding barren plateaus using classical shadows

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBP) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows to avoid WBPs during the optimization process. This paves the way for efficient barren plateau free optimization on near-term devices.

quant-ph↗

arXiv2021

Entanglement and precession in two-dimensional dynamical quantum phase transitions

Non-analytic points in the return probability of a quantum state as a function of time, known as dynamical quantum phase transitions (DQPTs), have received great attention in recent years, but the understanding of their mechanism is still incomplete. In our recent work arXiv:2008.04894, we demonstrated that one-dimensional DQPTs can be produced by two distinct mechanisms, namely semiclassical precession and entanglement generation, leading to the definition of precession (pDQPTs) and entanglement (eDQPTs) dynamical quantum phase transitions. In this manuscript we extend and investigate the notion of p- and eDQPTs in two-dimensional systems by considering semi-infinite ladders of varying width. For square lattices, we find that pDQPTs and eDQPTs persist and are characterized by similar phenomenology as in 1D: pDQPTs are associated with a magnetization sign change and a wide entanglement gap, while eDQPTs correspond to suppressed local observables and avoided crossings in the entanglement spectrum. However, DQPTs show higher sensitivity to the ladder width and other details, challenging the extrapolation to the thermodynamic limit especially for eDQPTs. Moving to honeycomb lattices, we also demonstrate that lattices with odd number of nearest neighbors give rise to phenomenologies beyond the one-dimensional classification.

quant-ph↗

arXiv2021

Unconventional superconductivity in systems with annular Fermi surfaces: Application to rhombohedral trilayer graphene

We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral $p$-wave symmetry, but $d$-wave and extended $s$-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of $T_c$, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above $T_c$, and the proximity of spin singlet superconductivity to the ferromagnetic phase.

cond-mat.supr-con↗

arXiv2021

Propagation of Many-body Localization in an Anderson Insulator

Many-body localization (MBL) is an example of a dynamical phase of matter that avoids thermalization. While the MBL phase is robust to weak local perturbations, the fate of an MBL system coupled to a thermalizing quantum system that represents a "heat bath" is an open question that is actively investigated theoretically and experimentally. In this work we consider the stability of an Anderson insulator with a finite density of particles interacting with a single mobile impurity -- a small quantum bath. We give perturbative arguments that support the stability of localization in the strong interaction regime. Large scale tensor network simulations of dynamics are employed to corroborate the presence of the localized phase and give quantitative predictions in the thermodynamic limit. We develop a phenomenological description of the dynamics in the strong interaction regime, and demonstrate that the impurity effectively turns the Anderson insulator into an MBL phase, giving rise to non-trivial entanglement dynamics well captured by our phenomenology.

cond-mat.dis-nn↗

arXiv2021

Localization of a mobile impurity interacting with an Anderson insulator

Thermalizing and localized many-body quantum systems present two distinct dynamical phases of matter. Recently, the fate of a localized system coupled to a thermalizing system viewed as a quantum bath received significant theoretical and experimental attention. In this work, we study a mobile impurity, representing a small quantum bath, that interacts locally with an Anderson insulator with a finite density of localized particles. Using static Hartree approximation to obtain an effective disorder strength, we formulate an analytic criterion for the perturbative stability of the localization. Next, we use an approximate dynamical Hartree method and the quasi-exact time-evolved block decimation (TEBD) algorithm to study the dynamics of the system. We find that the dynamical Hartree approach which completely ignores entanglement between the impurity and localized particles predicts the delocalization of the system. In contrast, the full numerical simulation of the unitary dynamics with TEBD suggests the stability of localization on numerically accessible timescales. Finally, using an extension of the density matrix renormalization group algorithm to excited states (DMRG-X), we approximate the highly excited eigenstates of the system. We find that the impurity remains localized in the eigenstates and entanglement is enhanced in a finite region around the position of the impurity, confirming the dynamical predictions. Dynamics and the DMRG-X results provide compelling evidence for the stability of localization.

cond-mat.dis-nn↗

arXiv2021

Area-law entangled eigenstates from nullspaces of local Hamiltonians

Eigenstate thermalization in quantum many-body systems implies that eigenstates at high energy are similar to random vectors. Identifying systems where at least some eigenstates are non-thermal is an outstanding question. In this work we show that interacting quantum models that have a nullspace -- a degenerate subspace of eigenstates at zero energy (zero modes), which corresponds to infinite temperature, provide a route to non-thermal eigenstates. We analytically show the existence of a zero mode which can be represented as a matrix product state for a certain class of local Hamiltonians. In the more general case we use a subspace disentangling algorithm to generate an orthogonal basis of zero modes characterized by increasing entanglement entropy. We show evidence for an area-law entanglement scaling of the least entangled zero mode in the broad parameter regime, leading to a conjecture that all local Hamiltonians with the nullspace feature zero modes with area-law entanglement scaling, and as such, break the strong thermalization hypothesis. Finally, we find zero-modes in constrained models and propose setup for observing their experimental signatures.

quant-ph↗

arXiv2021

Entanglement transitions from restricted Boltzmann machines

The search for novel entangled phases of matter has lead to the recent discovery of a new class of ``entanglement transitions'', exemplified by random tensor networks and monitored quantum circuits. Most known examples can be understood as some classical ordering transitions in an underlying statistical mechanics model, where entanglement maps onto the free energy cost of inserting a domain wall. In this paper, we study the possibility of entanglement transitions driven by physics beyond such statistical mechanics mappings. Motivated by recent applications of neural network-inspired variational Ansätze, we investigate under what conditions on the variational parameters these Ansätze can capture an entanglement transition. We study the entanglement scaling of short-range restricted Boltzmann machine (RBM) quantum states with random phases. For uncorrelated random phases, we analytically demonstrate the absence of an entanglement transition and reveal subtle finite size effects in finite size numerical simulations. Introducing phases with correlations decaying as $1/r^α$ in real space, we observe three regions with a different scaling of entanglement entropy depending on the exponent $α$. We study the nature of the transition between these regions, finding numerical evidence for critical behavior. Our work establishes the presence of long-range correlated phases in RBM-based wave functions as a required ingredient for entanglement transitions.

cond-mat.dis-nn↗