arXiv subjects

Kirill Plekhanov

Publications and source records attributed to Kirill Plekhanov.

17 recordsLinked to original sources

arXiv2023

Barren plateaus in quantum tensor network optimization

We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer.

quant-ph↗

arXiv2022

Variational quantum amplitude estimation

We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that shallow circuits can accurately approximate many amplitude amplification steps. We combine the variational approach with maximum likelihood amplitude estimation [Y. Suzuki et al., Quantum Inf. Process. 19, 75 (2020)] in variational quantum amplitude estimation (VQAE). VQAE typically has larger computational requirements than classical MC sampling. To reduce the variational cost, we propose adaptive VQAE and numerically show in 6 to 12 qubit simulations that it can outperform classical MC sampling.

quant-ph↗

arXiv2020

Interaction-stabilized topological magnon insulator in ferromagnets

Condensed matter systems admit topological collective excitations above a trivial ground state, an example being Chern insulators formed by Dirac bosons with a gap at finite energies. However, in contrast to electrons, there is no particle-number conservation law for collective excitations. This gives rise to particle number-nonconserving many-body interactions whose influence on single-particle topology is an open issue of fundamental interest in the field of topological quantum materials. Taking magnons in ferromagnets as an example, we uncover topological magnon insulators that are stabilized by interactions through opening Chern-insulating gaps in the magnon spectrum. This can be traced back to the fact that the particle-number nonconserving interactions break the effective time-reversal symmetry of the harmonic theory. Hence, magnon-magnon interactions are a source of topology that can introduce chiral edge states, whose chirality depends on the magnetization direction. Importantly, interactions do not necessarily cause detrimental damping but can give rise to topological magnons with exceptionally long lifetimes. We identify two mechanisms of interaction-induced topological phase transitions---one driven by an external field, the other by temperature---and show that they cause unconventional sign reversals of transverse transport signals, in particular of the thermal Hall conductivity. We identify candidate materials where this many-body mechanism is expected to occur, such as the metal-organic kagome-lattice magnet Cu(1,3-benzenedicarboxylate), the van der Waals honeycomb-lattice magnet CrI$_3$, and the multiferroic kamiokite (Fe$_2$Mo$_3$O$_8$). Our results demonstrate that interactions can play an important role in generating nontrivial topology.

cond-mat.str-el↗

arXiv2020

Quadrupole spin polarization as signature of second-order topological superconductors

We study theoretically second-order topological superconductors characterized by the presence of pairs of zero-energy Majorana corner states. We uncover a quadrupole spin polarization at the system edges that provides a striking signature to identify topological phases, thereby complementing standard approaches based on zero-bias conductance peaks due to Majorana corner states. We consider two different classes of second-order topological superconductors with broken time-reversal symmetry and show that both classes are characterized by a quadrupolar structure of the spin polarization that disappears as the system passes through the topological phase transition. This feature can be accessed experimentally using spin-polarized scanning tunneling microscopes. We study different models hosting second-order topological phases, both analytically and numerically, and using Keldysh techniques we provide numerical simulations of the spin-polarized currents probed by scanning tips.

cond-mat.mes-hall↗

arXiv2020

Majorana bound states in topological insulators with hidden Dirac points

We address the issue whether it is possible to generate Majorana bound states at the magnetic-superconducting interface in two-dimensional topological insulators with hidden Dirac points in the spectrum. In this case, the Dirac point of edge states is located at the energies of the bulk states such that two types of states are strongly hybridized. Here, we show that well-defined Majorana bound states can be obtained even in materials with hidden Dirac point provided that the width of the magnetic strip is chosen to be comparable with the localization length of the edge states. The obtained topological phase diagram allows one to extract precisely the position of the Dirac point in the spectrum. In addition to standard zero-bias peak features caused by Majorana bound states in transport experiments, we propose to supplement future experiments with measurements of charge and spin polarization. In particular, we demonstrate that both observables flip their signs at the topological phase transition, thus, providing an independent signature of the presence of topological superconductivity. All features remain stable against substantially strong disorder.

cond-mat.mes-hall↗

arXiv2019

Valence bond fluctuations in the Kitaev spin model

We introduce valence bond fluctuations, or bipartite fluctuations associated to bond-bond correlation functions, to characterize quantum spin liquids and their entanglement properties. Using analytical and numerical approaches, we find an identical scaling law between valence bond fluctuations and entanglement entropy in the two-dimensional Kitaev spin model and in one-dimensional chain analogues. We also show how these valence bond fluctuations can locate quantum phase transitions between the three gapped and the gapless Majorana semi-metal phases in the honeycomb model. We then study the effect of a uniform magnetic field along the 111 direction opening a gap in the intermediate phase which becomes topological. We still obtain a robust signal to characterize the transitions towards the three gapped phases. The linear scaling behavior of such bipartite fluctuations in two dimensions is also distinguishable from the one in the Neel magnetic state.

cond-mat.str-el↗

arXiv2019

Magnetically-Confined Bound States in Rashba Systems

A Rashba nanowire is subjected to a magnetic field that assumes opposite signs in two sections of the nanowire, and, thus, creates a magnetic domain wall. The direction of magnetic field is chosen to be perpendicular to the Rashba spin-orbit vector such that there is only a partial gap in the spectrum. Nevertheless, we prove analytically and numerically that such a domain wall hosts a bound state whose energy is at bottom of the spectrum below the energy of all bulk states. Thus, this magnetically-confined bound state is well-isolated and can be accessed experimentally. We further show that the same type of magnetic confinement can be implemented in two-dimensional systems with strong spin-orbit interaction. A quantum channel along the magnetic domain wall emerges with a non-degenerate dispersive band that lies energetically below the bulk states. We show that this magnetic confinement is robust against disorder and various parameter variations.

cond-mat.mes-hall↗

arXiv2019

Hinge states in a system of coupled Rashba layers

We consider a system of stacked tunnel-coupled two-dimensional electron- and hole-gas layers with Rashba spin-orbit interactions subjected to a staggered Zeeman field. The interplay of different intra-layer tunnel couplings results in a phase transition to a topological insulator phase in three dimensions hosting gapless surface states. The staggered Zeeman field further enriches the topological phase diagram by generating a second-order topological insulator phase hosting gapless hinge states. The emergence of the topological phases is proven analytically in the regime of small Zeeman field and confirmed by numerical simulations in the non-perturbative region of the phase diagram. The topological phases are stable against external perturbations and disorder.

cond-mat.mes-hall↗

arXiv2019

Floquet Second-Order Topological Superconductor Driven via Ferromagnetic Resonance

We consider a Floquet triple-layer setup composed of a two-dimensional electron gas with spin-orbit interactions, proximity coupled to an s-wave superconductor and to a ferromagnet driven at resonance. The ferromagnetic layer generates a time-oscillating Zeeman field which competes with the induced superconducting gap and leads to a topological phase transition. The resulting Floquet states support a second-order topological superconducting phase with a pair of localized zero-energy Floquet Majorana corner states. Moreover, the phase diagram comprises a Floquet helical topological superconductor, hosting a Kramers pair of Majorana edge modes protected by an effective time-reversal symmetry, as well as a gapless Floquet Weyl phase. The topological phases are stable against disorder and parameter variations and are within experimental reach.

cond-mat.mes-hall↗

arXiv2019

Topological proximity effects in a Haldane-graphene bilayer system

We reveal a proximity effect between a topological band (Chern) insulator described by a Haldane model and spin-polarized Dirac particles of a graphene layer. Coupling weakly the two systems through a tunneling term in the bulk, the topological Chern insulator induces a gap and an opposite Chern number on the Dirac particles at half-filling resulting in a sign flip of the Berry curvature at one Dirac point. We study different aspects of the bulk-edge correspondence and present protocols to observe the evolution of the Berry curvature as well as two counter-propagating (protected) edge modes with different velocities. In the strong-coupling limit, the energy spectrum shows flat bands. Therefore we build a perturbation theory and address further the bulk-edge correspondence. We also show the occurrence of a topological insulating phase with Chern number one when only the lowest band is filled. We generalize the effect to Haldane bilayer systems with asymmetric Semenoff masses. We propose an alternative definition of the topological invariant on the Bloch sphere.

cond-mat.mes-hall↗

arXiv2018

Driven dissipative dynamics and topology of quantum impurity systems

In this review, we provide an introduction and overview to some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin-boson and related models, which describes a single spin-1/2 coupled to an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin-bath coupling. In these situations, the non-perturbative stochastic Schroedinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_z(t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling to a common bath. In the second part of this review, we discuss quantum engineering of spin-boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose-Einstein condensate, a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott-Superfluid transition.

cond-mat.str-el↗

arXiv2018

Quantum purification spectroscopy

We discuss a protocol based on quenching a purified quantum system that allows to capture bulk spectral features. It uses an infinite temperature initial state and an interferometric strategy to access the Loschmidt amplitude, from which the spectral features are retrieved via Fourier transform, providing coarse-grained approximation at finite times. It involves techniques available in current experimental setups for quantum simulation, at least for small systems. We illustrate possible applications in testing the eigenstate thermalization hypothesis and the physics of many-body localization.

quant-ph↗

arXiv2017

Topological Zak Phase in Strongly-Coupled LC Circuits

We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.

cond-mat.mes-hall↗

arXiv2017

Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model

Recently, the frustrated XY model for spins-1/2 on the honeycomb lattice has attracted a lot of attention in relation with the possibility to realize a chiral spin liquid state. This model is relevant to the physics of some quantum magnets. Using the flexibility of ultra-cold atoms setups, we propose an alternative way to realize this model through the Mott regime of the bosonic Kane-Mele-Hubbard model. The phase diagram of this model is derived using the bosonic dynamical mean-field theory. Focussing on the Mott phase, we investigate its magnetic properties as a function of frustration. We do find an emergent chiral spin state in the intermediate frustration regime. Using exact diagonalization we study more closely the physics of the effective frustrated XY model and the properties of the chiral spin state. This gapped phase displays a chiral order, breaking time-reversal and parity symmetry, but is not topologically ordered (the Chern number is zero).

cond-mat.str-el↗

arXiv2016

Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions

The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band structure associated with chiral edge modes (without the presence of a net unit flux in a unit cell), then referring to the quantum anomalous Hall effect. Focusing on (interacting) boson systems in s-wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition between a uniform superfluid and a BEC (Bose-Einstein Condensate) analog of FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) states, where bosons condense at non-zero wave-vectors. We perform a Ginzburg-Landau analysis of the quantum phase transition on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

cond-mat.quant-gas↗

arXiv2016

On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator

We propose a device architecture capable of direct quantum electro-optical conversion of microwave to optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that electro-optical (vacuum) coupling rates $g_0$ as large as$\sim 2π\, \mathcal{O}(10-100)$ kHz are achievable with currently available technology, due to the small mode volume of the planar microwave resonator. Operating at millikelvin temperatures, such a converter would enable high-efficiency conversion of microwave to optical photons. We analyze the added noise, and show that maximum conversion efficiency is achieved for a multi-photon cooperativity of unity which can be reached with optical power as low as $ \mathcal{O}(1)\,\mathrm{mW} $.

quant-ph↗

arXiv2016

Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light

We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled to an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing to engineer the Jaynes-Cummings lattice and Rabi lattice models. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott-superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin-orbit couplings have been successfully implemented with ultra-cold atoms in optical lattices --- using time-dependent Floquet perturbations periodic in time, for example --- as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries. The Bose-Hubbard model is related to the Jaynes-Cummings lattice model in the large detuning limit between light and matter. In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase.

cond-mat.mes-hall↗