Many-body Theory Research Articles

Federated Learning with tensor networks: a quantum AI framework for healthcare

Abstract The healthcare industries frequently handle sensitive and proprietary data, and due to strict
privacy regulations, they are often reluctant to share data directly. In today’s context, Federated
Learning (FL) stands out as a crucial remedy, facilitating the rapid advancement of distributed machine
learning while effectively managing critical concerns regarding data privacy and governance.
The fusion of federated learning and quantum computing represents a groundbreaking interdisciplinary
approach with immense potential to revolutionize various industries, from healthcare to
finance. In this work, we propose a federated learning framework based on quantum tensor networks
that takes advantage of the principles of many-body quantum physics. Currently, there are
no known classical tensor networks implemented in federated settings. Furthermore, we investigated
the effectiveness and feasibility of the proposed framework by conducting a differential privacy analysis
to ensure the security of sensitive data across healthcare institutions. Experiments on popular
medical image datasets show that the federated quantum tensor network model achieved a mean
receiver-operator characteristic area under the curve (ROC-AUC) of 91-98%, outperforming several
state-of-the-art federated learning methods while using fewer parameters. Experimental results
demonstrate that the quantum federated global model, consisting of highly entangled tensor network
structures, showed better generalization and robustness and achieved higher testing accuracy,
surpassing the performance of locally trained clients under unbalanced data distributions among
healthcare institutions.

Fading ergodicity

Eigenstate thermalization hypothesis (ETH) represents a breakthrough in many-body physics since it allows us to link thermalization of physical observables with the applicability of random matrix theory (RMT). Recent years were also extremely fruitful in exploring possible counterexamples to thermalization, ranging, among others, from integrability, single-particle chaos, many-body localization, many-body scars, to Hilbert-space fragmentation. In all these cases the conventional ETH is violated. However, it remains elusive how the conventional ETH breaks down when one approaches the boundaries of ergodicity, and whether the range of validity of the conventional ETH coincides with the validity of RMT-like spectral statistics. Here we bridge this gap and we introduce a scenario of the ETH breakdown in many-body quantum systems, dubbed fading ergodicity regime, which establishes a link between the conventional ETH and nonergodic behavior. We conjecture this scenario to be relevant for the description of finite many-body systems at the boundaries of ergodicity, and we provide numerical and analytical arguments for its validity in the quantum sun model of ergodicity-breaking phase transition. For the latter, we provide evidence that the breakdown of the conventional ETH is not associated with the breakdown of the RMT-like spectral statistics. Published by the American Physical Society 2024

SU(N) magnetism with ultracold molecules

Abstract Quantum systems with SU(N) symmetry are paradigmatic settings for quantum many-body physics. They have been studied for the insights they provide into complex materials and their ability to stabilize exotic ground states. Ultracold alkaline-earth atoms were predicted to exhibit SU(N) symmetry for N = 2I +1 = 1, 2, . . . , 10, where I is the nuclear spin. Subsequent experiments have revealed rich many-body physics. However, alkaline-earth atoms realize this symmetry only for fermions with repulsive interactions. In this paper, we predict that ultracold molecules shielded from destructive collisions with static electric fields or microwaves exhibit SU(N) symmetry, which holds because deviations of the s-wave scattering length from the spin-free values are only about 3% for CaF with static-field shielding and are estimated to be even smaller for bialkali molecules. They open the door to N as large as 32 for bosons and 36 for fermions. They offer important features unachievable with atoms, including bosonic systems and attractive interactions.

Learning quantum properties from short-range correlations using multi-task networks

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

Moiré-engineered light-matter interactions in MoS2/WSe2 heterobilayers at room temperature

Moiré superlattices in van der Waals heterostructures represent a highly tunable quantum system, attracting substantial interest in both many-body physics and device applications. However, the influence of the moiré potential on light-matter interactions at room temperature has remained largely unexplored. In our study, we demonstrate that the moiré potential in MoS2/WSe2 heterobilayers facilitates the localization of interlayer exciton (IX) at room temperature. By performing reflection contrast spectroscopy, we demonstrate the importance of atomic reconstruction in modifying intralayer excitons, supported by the atomic force microscopy experiment. When decreasing the twist angle, we observe that the IX lifetime becomes longer and light emission gets enhanced, indicating that non-radiative decay channels such as defects are suppressed by the moiré potential. Moreover, through the integration of moiré superlattices with silicon single-mode cavities, we find that the devices employing moiré-trapped IXs exhibit a significantly lower threshold, one order of magnitude smaller compared to the device utilizing delocalized IXs. These findings not only encourage the exploration of many-body physics in moiré superlattices at elevated temperatures but also pave the way for leveraging these artificial quantum materials in photonic and optoelectronic applications.

Interaction-Induced Multiparticle Bound States in the Continuum.

Bound states in the continuum (BICs) are localized modes residing in the radiation continuum. They were first predicted for single-particle states, and became a general feature of many wave systems. In many-body quantum physics, it is still unclear what would be a close analog of BICs, and whether interparticle interaction may induce BICs. Here, we predict a novel type of multiparticle states in the interaction-modulated Bose-Hubbard model that can be associated with the BIC concept. Under periodic boundary conditions, a so-called quasi-BIC appears as a bound pair residing in a standing wave formed by the third particle. Under open boundary conditions, such a hybrid state becomes an eigenstate of the system. We demonstrate that the Thouless pumping of the quasi-BICs can be realized by modulating the onsite interactions in space and time. Surprisingly, while the center of mass of the quasi-BIC is shifted by a unit cell in one cycle, the bound pair moves in the opposite direction with the standing wave.

A Review on Study Short-Range Correlations and the Isospin Dependence

High-energy electron scattering can be considered a crucial tool for interpreting the function of high-momentum nucleons (and quarks) in nuclei and offers a clean, accurate probing for investigations of hadronic and nuclear organization. The intense repulsion of nuclear contact at small distances is the source of short-range interactions in nuclei and nuclear matter. These connections have been verified in several nuclear tests using hadronic and electroweak probes. Improved knowledge of the underlying structure of these high-momentum and short-range arrangements in nuclei will be crucial for a variety of high-energy observables. The short-range correlations also appear to be associated with changes in the quark distributions in nuclei. Over the past ten years, there has been a significant concentration on both theoretical and experimental efforts aimed at characterizing short-range correlations, namely their isospin dependence. In this review, it will employ a theoretical framework rooted in many-body Green's functions theory. Specifically, review focus on the one-body momentum distributions as a fundamental variable. The objective is to provide a concise overview of the latest research findings in the field.

Commutative families in DIM algebra, integrable many-body systems and q, t matrix models

We extend our consideration of commutative subalgebras (rays) in different representations of the W1+∞ algebra to the elliptic Hall algebra (or, equivalently, to the Ding-Iohara-Miki (DIM) algebra Uq,tgl̂̂1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {U}_{q,t}\\left({\\hat{\\hat{\\mathfrak{gl}}}}_1\\right) $$\\end{document}). Its advantage is that it possesses the Miki automorphism, which makes all commutative rays equivalent. Integrable systems associated with these rays become finite-difference and, apart from the trigonometric Ruijsenaars system not too much familiar. We concentrate on the simplest many-body and Fock representations, and derive explicit formulas for all generators of the elliptic Hall algebra en,m. In the one-body representation, they differ just by normalization from znqmD̂\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {z}^n{q}^{m\\hat{D}} $$\\end{document} of the W1+∞ Lie algebra, and, in the N -body case, they are non-trivially generalized to monomials of the Cherednik operators with action restricted to symmetric polynomials. In the Fock representation, the resulting operators are expressed through auxiliary polynomials of n variables, which define weights in the residues formulas. We also discuss q, t-deformation of matrix models associated with constructed commutative subalgebras.

Electric conductivity of hot and dense nuclear matter

Transport coefficients play an important role in characterising hot and dense nuclear matter, such as that created in ultra-relativistic heavy-ion collisions (URHIC). In the present work we calculate the electric conductivity of hot and dense hadronic matter by extracting it from the electromagnetic spectral function, through its zero energy limit at vanishing 3-momentum. We utilise the vector dominance model (VDM), in which the photon couples to hadronic currents predominantly through the ρ meson. Therefore, we use hadronic many-body theory to calculate the ρ-meson's self-energy in hot and dense hadronic matter, by dressing its pion cloud with π-ρ, π-σ, π-K, N-hole, and Δ-hole loops. We then introduce vertex corrections to maintain gauge invariance. Finally, we analyze the low-energy transport peak as a function of temperature and baryon chemical potential, and extract the conductivity along a proposed phase transition line.

An extremely bad-cavity laser

Lasing in the bad-cavity regime has promising applications in quantum precision measurement and frequency metrology due to the reduced sensitivity of the laser frequency to cavity-length fluctuations. Thus far, relevant studies have been mainly focused on conventional cavities whose finesse is high enough that the resonance linewidth is sufficiently narrow compared to the cavity’s free spectral range, though still in the bad-cavity regime. However, lasing output from the cavity whose finesse is close to the limit of 2 has never been experimentally accessed. Here, we demonstrate an extremely bad-cavity laser, analyze the physical mechanisms limiting cavity finesse, and report on the worst-ever laser cavity with finesse reaching 2.01. The optical cavity has a reflectance close to zero and only provides weak optical feedback. The laser power can be as high as tens of μW and the spectral linewidth reaches a few kHz, over one thousand times narrower than the gain bandwidth. In addition, the measurement of cavity pulling reveals a pulling coefficient of 0.0148, the lowest value ever achieved for a continuous-wave laser. Our findings open up an unprecedentedly innovative perspective for future new ultra-stable lasers, which could possibly trigger future discoveries in optical clocks, cavity QED, continuous-wave superradiant laser, and explorations of quantum many-body physics.

Extracting the crystal electric field levels of Ce-4f1 states in CeB6 by atomic multiplet simulations

The crystal electric field (CEF) is vital in defining the low-energy electronic structure of lanthanide compound, and thus very essential in understanding the many-body physics of the strongly correlated 4 f electrons. Many efforts have been made to determine the low-energy electronic structure of the intrinsically correlated material CeB6 and its derived compounds. In this paper, we performed atomic multiplet (AM) simulations on the Ce-4f1 states in CeB6 and directly fitted them with previously reported resonant inelastic x-ray scattering spectroscopy (RIXS). The simulation results suggest that the discrepancy of excitations energies extracted from Raman spectroscopy and RIXS is a result of intrinsic varied crystal electric field strength, which can be reconciled by considering the enhanced CEF by eliminating the insulating scenario.

Graphene with suitable-size nitrogen-doped cavity being an excellent photocatalyst for proton-coupled electron transfer in water splitting

Aiming to attain porous carbon nitride photocatalysts with high specific surface area, abundant active sites, broad absorption range and effective electron-hole separation, we remove carbon rings from graphene and replace all the edge carbon atoms of the cavity with nitrogen atoms. The accurate electronic structures and exciton properties of the proposed materials are revealed by the ab initio many-body Green's function theory. Computational results show that the absorption of the designed materials can cover both the visible and the near-infrared light region. The exciton binding energies of the materials are one order of magnitude lower than those of the typical two-dimensional photocatalyst graphitic carbon nitride. Due to the formation of hydrogen bonds between pyridinic nitrogen atoms and water molecules during water splitting, the key excited-state proton-coupled electron transfer reactions are barrierless. These findings could serve as guidelines for the realization of high-performance metal-free two-dimensional photocatalysts.

(C5H9NH3)2CuBr4 : A metal-organic two-ladder quantum magnet

Low-dimensional quantum magnets are a versatile materials platform for studying the emergent many-body physics and collective excitations that can arise even in systems with only short-range interactions. Understanding their low-temperature structure and spin Hamiltonian is key to explaining their magnetic properties, including unconventional quantum phases, phase transitions, and excited states. We study the metal-organic coordination compound (C5H9NH3)2CuBr4 and its deuterated counterpart, which upon its discovery was identified as a candidate two-leg quantum (S=12) spin ladder in the strong-leg coupling regime. By growing large single crystals and probing them with both bulk and microscopic techniques, we deduce that two previously unknown structural phase transitions take place between 136 and 113 K. The low-temperature structure has a monoclinic unit cell that gives rise to two inequivalent spin ladders. We further confirm the absence of long-range magnetic order down to 30 mK and investigate the implications of this two-ladder structure for the magnetic properties of (C5H9NH3)2CuBr4 by analyzing our own specific-heat and susceptibility data. Published by the American Physical Society 2024

Interfacial negative biexcitons in a monolayer WS2/InGaN quantum dots heterostructure

In this work, we fabricated a Van der Waals heterostructure of monolayer (ML) WS2 and InGaN quantum dots (QDs). This heterostructure is divided into coupled and uncoupled regions based on the thickness of the inserted hBN layer. Upon measuring its PL spectra, we identified an interfacial negative biexciton, which consists of a trion in ML WS2 and an exciton in QDs, in the coupled region. This interfacial negative biexciton features the negative charge of the trion and the quantum confinement of QDs, with its relative intensity showing a strong dependence on the excitation photon energy and featuring a significant threshold. Our work highlights the effective coupling within the mixed-dimensional heterostructure, offering new prospects for the study of many-body physics.

Machine learning on quantum experimental data toward solving quantum many-body problems

Advancements in the implementation of quantum hardware have enabled the acquisition of data that are intractable for emulation with classical computers. The integration of classical machine learning (ML) algorithms with these data holds potential for unveiling obscure patterns. Although this hybrid approach extends the class of efficiently solvable problems compared to using only classical computers, this approach has been only realized for solving restricted problems because of the prevalence of noise in current quantum computers. Here, we extend the applicability of the hybrid approach to problems of interest in many-body physics, such as predicting the properties of the ground state of a given Hamiltonian and classifying quantum phases. By performing experiments with various error-reducing procedures on superconducting quantum hardware with 127 qubits, we managed to acquire refined data from the quantum computer. This enabled us to demonstrate the successful implementation of theoretically suggested classical ML algorithms for systems with up to 44 qubits. Our results verify the scalability and effectiveness of the classical ML algorithms for processing quantum experimental data.

Quantum Spin Dynamics Due to Strong Kitaev Interactions in the Triangular-Lattice Antiferromagnet CsCeSe_{2}.

The extraordinary properties of the Kitaev model have motivated an intense search for new physics in materials that combine geometrical and bond frustration. In this Letter, we employ inelastic neutron scattering, spin wave theory, and exact diagonalization to study the spin dynamics in the perfect triangular-lattice antiferromagnet (TLAF) CsCeSe_{2}. This material orders into a stripe phase, which is demonstrated to arise as a consequence of the off-diagonal bond-dependent terms in the spin Hamiltonian. By studying the spin dynamics at intermediate fields, we identify an interaction between the single-magnon state and the two-magnon continuum that causes decay of coherent magnon excitations, level repulsion, and transfer of spectral weight to the continuum that are controlled by the strength of the magnetic field. Our results provide a microscopic mechanism for the stabilization of the stripe phase in TLAF and show how complex many-body physics can be present in the spin dynamics in a magnet with strong Kitaev coupling even in an ordered ground state.

MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics.

The MPSDynamics.jl package provides an easy-to-use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system-environment observables.

Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi Point Strange Correlators

In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications, such as secret-sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., linelike subsystems in the two-dimensional cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is that has either fractal and linelike subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in a square lattice can be locally simulated by an HOCA-generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call . We propose a universal procedure to design the spatial configuration of the multi point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long-range behavior in a short-range entangled state. Our HOCA approaches and multi point strange correlators pave the way for a unified paradigm to design, classify, and detect phases of matter with symmetries supported on a great variety of subsystems, and also provide potential useful perspective in surpassing the computational irreducibility of HOCA in a quantum mechanical way. Published by the American Physical Society 2024

Time-reversal in a dipolar quantum many-body spin system

Time reversal in a macroscopic system contradicts daily experience. It is practically impossible to restore a shattered cup to its original state by just time reversing the microscopic dynamics that led to its breakage. Yet, with the precise control capabilities provided by modern quantum technology, the unitary evolution of a quantum system can be reversed in time. Here, we implement a time-reversal protocol in a dipolar interacting, isolated many-body spin system represented by Rydberg states in an atomic gas. By changing the states encoding the spin, we flip the sign of the interaction Hamiltonian, and demonstrate the reversal of the relaxation dynamics of the magnetization by letting a demagnetized many-body state evolve back in time into a magnetized state. We elucidate the role of atomic motion using the concept of a Loschmidt echo. Finally, by combining the approach with Floquet engineering, we demonstrate time reversal for a large family of spin models with different symmetries. Our method of state transfer is applicable across a wide range of quantum simulation platforms and has applications far beyond quantum many-body physics, reaching from quantum-enhanced sensing to quantum information scrambling. Published by the American Physical Society 2024

Quantum inception score

Motivated by the great success of classical generative models in machine learning, enthusiastic exploration of their quantum version has recently started. To depart on this journey, it is important to develop a relevant metric to evaluate the quality of quantum generative models; in the classical case, one such example is the (classical) inception score (cIS). In this paper, as a natural extension of cIS, we propose the quantum inception score (qIS) for quantum generators. Importantly, qIS relates the quality to the Holevo information of the quantum channel that classifies a given dataset. In this context, we show several properties of qIS. First, qIS is greater than or equal to the corresponding cIS, which is defined through projection measurements on the system output. Second, the difference between qIS and cIS arises from the presence of quantum coherence, as characterized by the resource theory of asymmetry. Third, when a set of entangled generators is prepared, there exists a classifying process leading to the further enhancement of qIS. Fourth, we harness the quantum fluctuation theorem to characterize the physical limitation of qIS. Finally, we apply qIS to assess the quality of the one-dimensional spin chain model as a quantum generative model, with the quantum convolutional neural network as a quantum classifier, for the phase classification problem in the quantum many-body physics. Published by the American Physical Society 2024