Showing papers on "Ising model published in 2021"

Self-organized error correction in random unitary circuits with measurement

Abstract: Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a subthermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. We quantify these notions by identifying a power-law decay of the mutual information I({x}:A¯)∝x−3/2 in the volume-law-entangled phase, between a qudit located a distance x from the boundary of a region A, and the complement A¯, which implies that a measurement of this qudit will retrieve very little information about A¯. We also find a universal logarithmic contribution to the volume law entanglement entropy S(2)(A)=κLA+32logLA which is intimately related to the first observation. We obtain these results by relating the entanglement dynamics to the imaginary time evolution of an Ising model, to which we apply field-theoretic and matrix-product-state techniques. Finally, exploiting the error-correction viewpoint, we assume that the volume-law state is an encoding of a Page state in a quantum error-correcting code to obtain a bound on the critical measurement strength pc as a function of the qudit dimension d: pclog[(d2−1)(pc−1−1)]≤log[(1−pc)d]. The bound is saturated at pc(d→∞)=1/2 and provides a reasonable estimate for the qubit transition: pc(d=2)≤0.1893.

Two-fold symmetric superconductivity in few-layer NbSe2

Abstract: The strong Ising spin–orbit coupling in certain two-dimensional transition metal dichalcogenides can profoundly affect the superconducting state in few-layer samples. For example, in NbSe2, this effect combines with the reduced dimensionality to stabilize the superconducting state against magnetic fields up to ~35 T, and could lead to topological superconductivity. Here we report a two-fold rotational symmetry of the superconducting state in few-layer NbSe2 under in-plane external magnetic fields, in contrast to the three-fold symmetry of the lattice. Both the magnetoresistance and critical field exhibit this two-fold symmetry, and it also manifests deep inside the superconducting state in NbSe2/CrBr3 superconductor-magnet tunnel junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behaviour to the mixing between two closely competing pairing instabilities, namely the conventional s-wave instability typical of bulk NbSe2 and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results demonstrate the unconventional character of the pairing interaction in few-layer transition metal dichalcogenides and highlight the exotic superconductivity in this family of two-dimensional materials. A two-fold rotational symmetry is observed in the superconducting state of NbSe2. This is strikingly different from the three-fold symmetry of the lattice, and suggests that a mixed conventional and unconventional order parameter exists in this material.

Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition

Abstract: It is well known that by repeatedly measuring a quantum system it is possible to completely freeze its dynamics into a well defined state, a signature of the quantum Zeno effect. Here we show that for a many-body system evolving under competing unitary evolution and variable-strength measurements the onset of the Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising chain with continuous monitoring of the transverse magnetization as paradigmatic example we show that for weak measurements the entanglement produced by the unitary dynamics remains protected, and actually enhanced by the monitoring, while only above a certain threshold the system is sharply brought into an uncorrelated Zeno state. We show that this transition is invisible to the average dynamics, but encoded in the rare fluctuations of the stochastic measurement process, which we show to be perfectly captured by a non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an imaginary valued transverse field. We provide analytical results based on the fermionization of the non-Hermitian Hamiltonian in supports of our exact numerical calculations.

100,000-spin coherent Ising machine.

Abstract: Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solvi...

Kramers-Wannier-like duality defects in (3 + 1)d gauge theories.

Abstract: We introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at $\theta = \pi$, $\mathcal{N}=1$ SO(3) super YM, and $\mathcal{N}=4$ SU(2) super YM at $\tau = i$. We also introduce an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories.

A Probabilistic Compute Fabric Based on Coupled Ring Oscillators for Solving Combinatorial Optimization Problems

Abstract: Nondeterministic polynomial time hard (NP-hard) combinatorial optimization problems (COPs) are intractable to solve using a traditional computer as the time to find a solution increases very rapidly with the number of variables. An efficient alternative computing method uses coupled spin networks to solve COP. This work presents a first-of-its-kind coupled ring oscillator (ROSC)-based scalable probabilistic Ising computer to solve NP-hard COPs. An integrated coupled oscillator network was designed with 560 ROSCs that mimic a coupled spin network. Each ROSC can be coupled to any of its neighbors using programmable back-to-back (B2B) inverter-based coupling mechanism. The ROSC-based spins and B2B inverter-based coupling were optimized to work under a wide range of system noise as well as voltage and temperature variations. Randomly generated 1000 max-cut problems were mapped and solved in the hardware. The integrated Ising computer produced satisfactory solutions of max-cut problems when compared with commercial software running on a CPU. Experiments show that the integrated CMOS-based Ising computer can find the solution to NP-hard problems with an accuracy of 82%–100%. In addition, the repeated measurements of the same problem showed that the Ising computer can traverse through several local minima to find high-quality solutions under various voltage and temperature variation conditions. The experimental results show that ROSCs are a potential candidate for a dedicated hardware accelerator aiming to solve a wide range of COPs.

Quantum computing for quantum tunneling

Abstract: We demonstrate how quantum field theory problems can be practically encoded by using a discretization of the field theory problem into a general Ising model, with the continuous field values being encoded into Ising spin chains. To illustrate the method, and as a simple proof of principle, we use a (hybrid) quantum annealer to recover the correct profile of the thin-wall tunnelling solution. This method is applicable to many nonperturbative problems.

Topological persistence machine of phase transitions

Abstract: The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science, such as the glass-liquid transition. However, data obtained from physical states may not have explicit shapes as structural materials. We thus propose a general framework, termed ``topological persistence machine,'' to construct the shape of data from correlations in states, so that we can subsequently decipher phase transitions via qualitative changes in the shape. Our framework enables an effective and unified approach in phase transition analysis. We demonstrate the efficacy of the approach in detecting the Berezinskii-Kosterlitz-Thouless phase transition in the classical XY model and quantum phase transitions in the transverse Ising and Bose-Hubbard models. Interestingly, while these phase transitions have proven to be notoriously difficult to analyze using traditional methods, they can be characterized through our framework without requiring prior knowledge of the phases. Our approach is thus expected to be widely applicable and will provide practical insights for exploring the phases of experimental physical systems.

Thermodynamic properties and hysteresis loops in a hexagonal core-shell nanoparticle.

Abstract: We applied Monte Carlo simulation to investigate the thermodynamic properties and hysteresis loops of the hexagonal core-shell nanoparticle described by a ferrimagnetic mixed-spin (3/2, 5/2) Ising model. The results revealed the significance of the single-ion anisotropy, exchange coupling, external magnetic field in dominating various thermodynamic quantities and hysteresis loops. We obtained the variation of the critical temperature with various parameters. Under certain parameter conditions, the system may exhibit rich multiple-loop hysteresis behaviors, depending on the competition among the physical parameters.

An Ising Hamiltonian solver based on coupled stochastic phase-transition nano-oscillators

Abstract: Combinatorial optimization problems belong to the non-deterministic polynomial time (NP)-hard complexity class, and their computational requirements scale exponentially with problem size. They can be mapped into the problem of finding the ground state of an Ising model, which describes a physical system with converging dynamics. Various platforms, including optical, electronic and quantum approaches, have been explored to accelerate the ground-state search, but improvements in energy efficiencies and computational abilities are still required. Here we report an Ising solver based on a network of electrically coupled phase-transition nano-oscillators (PTNOs) that form a continuous-time dynamical system (CTDS). The bi-stable phases of the injection-locked PTNOs act as artificial Ising spins and the stable points of the CTDS act as the ground-state solution of the problem. We experimentally show that a prototype with eight PTNOs can solve an NP-hard MaxCut problem with high probability of success (96% for 600 annealing cycles). We also show via numerical simulations that our Ising Hamiltonian solver can solve MaxCut problems of 100 nodes with energy efficiency of 1.3 × 107 solutions per second per watt, offering advantages over other approaches including memristor-based Hopfield networks, quantum annealers and photonic Ising solvers. An Ising solver that is based on a network of electrically coupled phase-transition nano-oscillators, which provides a continuous-time dynamical system, can be used to efficiently solve a non-deterministic polynomial time (NP)-hard MaxCut problem.

Entanglement and complexity of purification in ( 1 + 1 )-dimensional free conformal field theories

Abstract: Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using the most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theory and the corresponding behavior of the mutual information, as well as the Hilbert space structure under the Jordan-Wigner mapping in the spin chain model of the Ising conformal field theory.

PyQUBO: Python Library for QUBO Creation

Abstract: We present PyQUBO, an open-source, Python library for constructing quadratic unconstrained binary optimizations (QUBOs) from the objective functions and the constraints of optimization problems. PyQUBO enables users to prepare QUBOs or Ising models for various combinatorial optimization problems with ease thanks to the abstraction of expressions and the extensibility of the program. QUBOs and Ising models formulated using PyQUBO are solvable by Ising machines, including quantum annealing machines. We introduce the features of PyQUBO with applications in the number partitioning problem, knapsack problem, graph coloring problem, and integer factorization using a binary multiplier. Moreover, we demonstrate how PyQUBO can be applied to production-scale problems through integration with quantum annealing machines. Through its flexibility and ease of use, PyQUBO has the potential to make quantum annealing a more practical tool among researchers.

Quantum Rescaling, Domain Metastability, and Hybrid Domain‐Walls in 2D CrI 3 Magnets

Abstract: Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of low-dimensional magnetic compounds. Here, the recently discovered 2D van der Waals (vdW) CrI3 is identified as a quantum non-Heisenberg material with properties far beyond an Ising magnet as initially assumed. It is found that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI3 but quantum rescaling corrections are required to reproduce its thermal properties. The quantum nature of the heat bath represented by discrete electron-spin and phonon-spin scattering processes induces the formation of spin fluctuations in the low-temperature regime. These fluctuations induce the formation of metastable magnetic domains evolving into a single macroscopic magnetization or even a monodomain over surface areas of a few micrometers. Such domains display hybrid characteristics of Neel and Bloch types with a narrow domain wall width in the range of 3-5 nm. Similar behavior is expected for the majority of 2D vdW magnets where higher-order exchange interactions are appreciable.

Universality class of the motility-induced critical point in large scale off-lattice simulations of active particles

Abstract: We perform large-scale computer simulations of an off-lattice two-dimensional model of active particles undergoing a motility-induced phase separation (MIPS) to investigate the system's critical behaviour close to the critical point of the MIPS curve By sampling steady-state configurations for large system sizes and performing finite size scaling analysis we provide exhaustive evidence that the critical behaviour of this active system belongs to the Ising universality class In addition to the scaling observables that are also typical of passive systems, we study the critical behaviour of the kinetic temperature difference between the two active phases This quantity, which is always zero in equilibrium, displays instead a critical behavior in the active system which is well described by the same exponent of the order parameter in agreement with mean-field theory

Quantitative and interpretable order parameters for phase transitions from persistent homology

Abstract: We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define "persistence" critical exponents and study how they are related to those critical exponents usually considered.

Entanglement View of Dynamical Quantum Phase Transitions.

Abstract: The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of "precession" and "entanglement" DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.

Strangeness-neutral equation of state for QCD with a critical point

Abstract: We present a strangeness-neutral equation of state for QCD that exhibits critical behavior and matches lattice QCD results for the Taylor-expanded thermodynamic variables up to fourth order in $$\mu _B/T$$ . It is compatible with the SMASH hadronic transport approach and has a range of temperatures and baryonic chemical potentials relevant for phase II of the Beam Energy Scan at RHIC. We provide an updated version of the software BES-EoS, which produces an equation of state for QCD that includes a critical point in the 3D Ising model universality class. This new version also includes isentropic trajectories and the critical contribution to the correlation length. Since heavy-ion collisions have zero global net-strangeness density and a fixed ratio of electric charge to baryon number, the BES-EoS is more suitable to describe this system. Comparison with the previous version of the EoS is thoroughly discussed.

Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits

Abstract: We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the autoregressive network generates bitstring samples as input states to the quantum circuit. We devise an efficient variational algorithm to jointly optimize the classical neural network and the quantum circuit to solve quantum statistical mechanics problems. One can obtain thermal observables such as the variational free energy, entropy, and specific heat. As a byproduct, the algorithm also gives access to low energy excitation states. We demonstrate applications of the approach to thermal properties and excitation spectra of the quantum Ising model with resources that are feasible on near-term quantum computers.

On Mixing of Markov Chains: Coupling, Spectral Independence, and Entropy Factorization.

Abstract: For general spin systems, we prove that a contractive coupling for any local Markov chain implies optimal bounds on the mixing time and the modified log-Sobolev constant for a large class of Markov chains including the Glauber dynamics, arbitrary heat-bath block dynamics, and the Swendsen-Wang dynamics. This reveals a novel connection between probabilistic techniques for bounding the convergence to stationarity and analytic tools for analyzing the decay of relative entropy. As a corollary of our general results, we obtain $O(n\log{n})$ mixing time and $\Omega(1/n)$ modified log-Sobolev constant of the Glauber dynamics for sampling random $q$-colorings of an $n$-vertex graph with constant maximum degree $\Delta$ when $q > (11/6 - \epsilon_0)\Delta$ for some fixed $\epsilon_0>0$. We also obtain $O(\log{n})$ mixing time and $\Omega(1)$ modified log-Sobolev constant of the Swendsen-Wang dynamics for the ferromagnetic Ising model on an $n$-vertex graph of constant maximum degree when the parameters of the system lie in the tree uniqueness region. At the heart of our results are new techniques for establishing spectral independence of the spin system and block factorization of the relative entropy. On one hand we prove that a contractive coupling of a local Markov chain implies spectral independence of the Gibbs distribution. On the other hand we show that spectral independence implies factorization of entropy for arbitrary blocks, establishing optimal bounds on the modified log-Sobolev constant of the corresponding block dynamics.

Performance Comparison of Typical Binary-Integer Encodings in an Ising Machine

Abstract: The differences in performance among binary-integer encodings in an Ising machine, which can solve combinatorial optimization problems, are investigated. Many combinatorial optimization problems can be mapped to find the lowest-energy (ground) state of an Ising model or its equivalent model, the Quadratic Unconstrained Binary Optimization (QUBO). Since the Ising model and QUBO consist of binary variables, they often express integers as binary when using Ising machines. A typical example is the combinatorial optimization problem under inequality constraints. Here, the quadratic knapsack problem is adopted as a prototypical problem with an inequality constraint. It is solved using typical binary-integer encodings: one-hot encoding, binary encoding, and unary encoding. Unary encoding shows the best performance for large-sized problems.

Spectral Lyapunov exponents in chaotic and localized many-body quantum systems

Abstract: We consider the spectral statistics of the Floquet operator for disordered, periodically driven spin chains in their quantum chaotic and many-body localized phases (MBL). The spectral statistics are characterized by the traces of powers $t$ of the Floquet operator, and our approach hinges on the fact that, for integer $t$ in systems with local interactions, these traces can be re-expressed in terms of products of dual transfer matrices, each representing a spatial slice of the system. We focus on properties of the dual transfer matrix products as represented by a spectrum of Lyapunov exponents, which we call \textit{spectral Lyapunov exponents}. In particular, we examine the features of this spectrum that distinguish chaotic and MBL phases. The transfer matrices can be block-diagonalized using time-translation symmetry, and so the spectral Lyapunov exponents are classified according to a momentum in the time direction. For large $t$ we argue that the leading Lyapunov exponents in each momentum sector tend to zero in the chaotic phase, while they remain finite in the MBL phase. These conclusions are based on results from three complementary types of calculation. We find exact results for the chaotic phase by considering a Floquet random quantum circuit with on-site Hilbert space dimension $q$ in the large-$q$ limit. In the MBL phase, we show that the spectral Lyapunov exponents remain finite by systematically analyzing models of non-interacting systems, weakly coupled systems, and local integrals of motion. Numerically, we compute the Lyapunov exponents for a Floquet random quantum circuit and for the kicked Ising model in the two phases. As an additional result, we calculate exactly the higher point spectral form factors (hpSFF) in the large-$q$ limit, and show that the generalized Thouless time scales logarithmically in system size for all hpSFF in the large-$q$ chaotic phase.

Frozen 1-RSB structure of the symmetric Ising perceptron

Abstract: We prove, under an assumption on the critical points of a real-valued function, that the symmetric Ising perceptron exhibits the `frozen 1-RSB' structure conjectured by Krauth and Mezard in the physics literature; that is, typical solutions of the model lie in clusters of vanishing entropy density. Moreover, we prove this in a very strong form conjectured by Huang, Wong, and Kabashima: a typical solution of the model is isolated with high probability and the Hamming distance to all other solutions is linear in the dimension. The frozen 1-RSB scenario is part of a recent and intriguing explanation of the performance of learning algorithms by Baldassi, Ingrosso, Lucibello, Saglietti, and Zecchina. We prove this structural result by comparing the symmetric Ising perceptron model to a planted model and proving a comparison result between the two models. Our main technical tool towards this comparison is an inductive argument for the concentration of the logarithm of number of solutions in the model.

Logarithmic Entanglement Growth from Disorder-Free Localization in the Two-Leg Compass Ladder

Abstract: We explore the finite-temperature dynamics of the quasi-1D orbital compass and plaquette Ising models. We map these systems onto a model of free fermions coupled to strictly localized spin-1/2 degrees of freedom. At finite temperature, the localized degrees of freedom act as emergent disorder and localize the fermions. Although the model can be analyzed using free-fermion techniques, it has dynamical signatures in common with typical many-body localized systems: Starting from generic initial states, entanglement grows logarithmically; in addition, equilibrium dynamical correlation functions decay with an exponent that varies continuously with temperature and model parameters. These quasi-1D models offer an experimentally realizable setting in which natural dynamical probes show signatures of disorder-free many-body localization.

Evidence of Potts-Nematic Superfluidity in a Hexagonal s p 2 Optical Lattice

Abstract: As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry ${C}_{4}$ broken down to ${C}_{2}$. Here, we report an observation of a three-state (${\mathbb{Z}}_{3}$) quantum nematic order, dubbed ``Potts-nematicity'', in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an $s{p}^{2}$-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.

High-accuracy Ising machine using Kerr-nonlinear parametric oscillators with local four-body interactions

Abstract: A two-dimensional array of Kerr-nonlinear parametric oscillators (KPOs) with local four-body interactions is a promising candidate for realizing an Ising machine with all-to-all spin couplings, based on adiabatic quantum computation in the Lechner–Hauke–Zoller (LHZ) scheme. However, its performance has been evaluated only for a symmetric network of three KPOs, and thus it has been unclear whether such an Ising machine works in general cases with asymmetric networks. By numerically simulating an asymmetric network of more KPOs in the LHZ scheme, we find that the asymmetry in the four-body interactions causes inhomogeneity in photon numbers and hence degrades the performance. We then propose a method for reducing the inhomogeneity, where the discrepancies of the photon numbers are corrected by tuning the detunings of KPOs depending on their positions, without monitoring their states during adiabatic time evolution. Our simulation results show that the performance can be dramatically improved by this method. The proposed method, which is based on the understanding of the asymmetry, is expected to be useful for general networks of KPOs in the LHZ scheme and thus for their large-scale implementation.