Showing papers on "Ising model published in 2020"

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator.

Abstract: Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

Exact dynamics in dual-unitary quantum circuits

Abstract: We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs.

Hilbert-Space Fragmentation from Strict Confinement.

Abstract: We study one-dimensional spin-$1/2$ models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of ${\mathbb{Z}}_{2}$ gauge theory coupled to fermionic matter, leading to a hierarchy of timescales for motion of the fermions. This model can be realized experimentally in two complementary settings.

Benchmarking the quantum approximate optimization algorithm

Abstract: The performance of the quantum approximate optimization algorithm is evaluated by using three different measures: the probability of finding the ground state, the energy expectation value, and a ratio closely related to the approximation ratio. The set of problem instances studied consists of weighted MaxCut problems and 2-satisfiability problems. The Ising model representations of the latter possess unique ground states and highly degenerate first excited states. The quantum approximate optimization algorithm is executed on quantum computer simulators and on the IBM Q Experience. Additionally, data obtained from the D-Wave 2000Q quantum annealer are used for comparison, and it is found that the D-Wave machine outperforms the quantum approximate optimization algorithm executed on a simulator. The overall performance of the quantum approximate optimization algorithm is found to strongly depend on the problem instance.

Measurement Protected Quantum Phases

Abstract: We introduce a class of hybrid quantum circuits, with random unitaries and projective measurements, which host long-range order in the area law entanglement phase of the steady state. Our primary example is circuits with unitaries respecting a global Ising symmetry and two competing types of measurements. The phase diagram has an area law phase with spin glass order, which undergoes a direct transition to a paramagnetic phase with volume law entanglement, as well as a critical regime. Using mutual information diagnostics, we find that such entanglement transitions preserving a global symmetry are in new universality classes. We analyze generalizations of such hybrid circuits to higher dimensions, which allow for coexistence of order and volume law entanglement, as well as topological order without any symmetry restrictions.

A Conformal Dispersion Relation: Correlations from Absorption

Abstract: We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.

Accelerating recurrent Ising machines in photonic integrated circuits

Abstract: Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks such as the Ising problem, which requires finding the ground state spin configuration of an arbitrary Ising graph. Physical Ising machines have recently been developed as an alternative to conventional exact and heuristic solvers; however, these machines typically suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS), using a hybrid scheme combining electronics and silicon-on-insulator photonics, that is capable of converging to the ground state of various four-spin graphs with high probability. The INPRIS results indicate that noise may be used as a resource to speed up the ground state search and to explore larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem and therefore compatible with optoelectronic architectures that support GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), this work suggests the potential for future systems that could achieve orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.

Entanglement transition in the projective transverse field Ising model

Abstract: Random quantum circuits have emerged as useful toy models for entanglement transitions in quantum many-body systems Here, the authors study a projective version of the transverse-field Ising model without unitary dynamics where the competition between two noncommuting measurements drives an entanglement transition The authors identify a nonlocal classical process that captures the entanglement dynamics and relate the model to bond percolation in space-time This leads to a conformal field theory description of the system at criticality which they verify numerically for large systems

Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas

Abstract: We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Forster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.

Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group

Abstract: We compute the critical exponents ν, η and ω of O(N) models for various values of N by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted O(∂^{4})]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter, typically between 1/9 and 1/4, compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field-theoretical techniques. We also reach a better precision than Monte Carlo simulations in some physically relevant situations. In the O(2) case, where there is a long-standing controversy between Monte Carlo estimates and experiments for the specific heat exponent α, our results are compatible with those of Monte Carlo but clearly exclude experimental values.

Generation of thermofield double states and critical ground states with a quantum computer.

Abstract: Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the quantum approximate optimization algorithm (QAOA), we generate nontrivial thermal quantum states of the transverse-field Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum–classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest-depth QAOA circuits provide the best results.

Analytic functional bootstrap for CFTs in d > 1

Abstract: We introduce analytic functionals which act on the crossing equation for CFTs in arbitrary spacetime dimension. The functionals fully probe the constraints of crossing symmetry on the first sheet, and are in particular sensitive to the OPE, (double) lightcone and Regge limits. Compatibility with the crossing equation imposes constraints on the functional kernels which we study in detail. We then introduce two simple classes of functionals. The first class has a simple action on generalized free fields and their deformations and can be used to bootstrap AdS contact interactions in general dimension. The second class is obtained by tensoring holomorphic and antiholomorphic copies of d = 1 functionals which have been considered recently. They are dual to simple solutions to crossing in d = 2 which include the energy correlator of the Ising model. We show how these functionals lead to optimal bounds on the OPE density of d = 2 CFTs and argue that they provide an equivalent rewriting of the d = 2 crossing equation which is better suited for numeric computations than current approaches.

Slow Quantum Thermalization and Many-Body Revivals from Mixed Phase Space

Abstract: The relaxation of few-body quantum systems can strongly depend on the initial state when the system’s semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of “quantum many-body scars,” i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems.

Digital-analog quantum computation

Abstract: Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and $M$-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

Quantum optimization with a novel Gibbs objective function and ansatz architecture search

Abstract: This work proposes modifications on two key components of the Quantum Approximate Optimization Algorithm (QAOA): a Gibbs objective function and an ansatz architecture search algorithm. The authors explore how these propositions improve upon ordinary QAOA when finding low-energy states by using numerical experiments on grid and complete graph Ising models.

Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling

Abstract: We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number C=1. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing us to control topological phase transitions. We also propose, using density functional theory, a material platform—graphene on Ising antiferromagnet MnPSe3—to realize staggered exchange (pseudospin Zeeman) coupling.

Quasilocalized dynamics from confinement of quantum excitations

Abstract: Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signaled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long-time scales by effective Hamiltonians exhibiting Stark localization of excitations and weak growth of the entanglement entropy for arbitrary coupling strength. This analysis explains the phenomenology of real-time string dynamics investigated in a number of lattice gauge theories, as well as the anomalous dynamics observed in quantum Ising chains after quenches. Our findings establish confinement as a robust mechanism for hindering the approach to equilibrium in translationally invariant quantum statistical systems with local interactions.

Confinement and Lack of Thermalization after Quenches in the Bosonic Schwinger Model.

Abstract: We excite the vacuum of a relativistic theory of bosons coupled to a U(1) gauge field in 1+1 dimensions (bosonic Schwinger model) out of equilibrium by creating a spatially separated particle-antiparticle pair connected by a string of electric field. During the evolution, we observe a strong confinement of bosons witnessed by the bending of their light cone, reminiscent of what has been observed for the Ising model [Nat. Phys. 13, 246 (2017)NPAHAX1745-247310.1038/nphys3934]. As a consequence, for the timescales we are able to simulate, the system evades thermalization and generates exotic asymptotic states. These states are made of two disjoint regions, an external deconfined region that seems to thermalize, and an inner core that reveals an area-law saturation of the entanglement entropy.

Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4.

Abstract: Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations—of both equilibrium and dynamical properties—for a frustrated rare-earth magnet TmMgGaO4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz–Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex–antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties. TmMgGaO4 is one of a number of recently-synthesized quantum magnets that are proposed to realize important theoretical models. Here the authors demonstrate the agreement between detailed experimental measurements and state-of-the-art predictions based on the 2D transverse-field triangular lattice Ising model.

Asymptotically unbiased estimation of physical observables with neural samplers.

Abstract: We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the two-dimensional Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.

A quantum magnetic analogue to the critical point of water

Abstract: At the familiar liquid-gas phase transition in water, the density jumps discontinuously at atmospheric pressure, but the line of these first-order transitions defined by increasing pressures terminates at the critical point, a concept ubiquitous in statistical thermodynamics. In correlated quantum materials, a critical point was predicted and measured terminating the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge density. In quantum spin systems, continuous quantum phase transitions (QPTs) have been investigated extensively, but discontinuous QPTs have received less attention. The frustrated quantum antiferromagnet SrCu$_2$(BO$_3$)$_2$ constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model and displays exotic phenomena including magnetization plateaux, anomalous thermodynamics and discontinuous QPTs. We demonstrate by high-precision specific-heat measurements under pressure and applied magnetic field that, like water, the pressure-temperature phase diagram of SrCu$_2$(BO$_3$)$_2$ has an Ising critical point terminating a first-order transition line, which separates phases with different densities of magnetic particles (triplets). We achieve a quantitative explanation of our data by detailed numerical calculations using newly-developed finite-temperature tensor-network methods. These results open a new dimension in understanding the thermodynamics of quantum magnetic materials, where the anisotropic spin interactions producing topological properties for spintronic applications drive an increasing focus on first-order QPTs.

Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device

Abstract: We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on $L\ifmmode\times\else\texttimes\fi{}L$ lattices with $L\ensuremath{\le}32$. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal $L$ dependent annealing rate $v$ for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of $v$ and $L$-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when $v$ is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.

Symmetry resolved entanglement in integrable field theories via form factor bootstrap

Abstract: We consider the form factor bootstrap approach of integrable field theories to derive matrix elements of composite branch-point twist fields associated with symmetry resolved entanglement entropies. The bootstrap equations are determined in an intuitive way and their solution is presented for the massive Ising field theory and for the genuinely interacting sinh-Gordon model, both possessing a ℤ2 symmetry. The solutions are carefully cross-checked by performing various limits and by the application of the ∆-theorem. The issue of symmetry resolution for discrete symmetries is also discussed. We show that entanglement equipartition is generically expected and we identify the first subleading term (in the UV cutoff) breaking it. We also present the complete computation of the symmetry resolved von Neumann entropy for an interval in the ground state of the paramagnetic phase of the Ising model. In particular, we compute the universal functions entering in the charged and symmetry resolved entanglement.

Dualities and non-Abelian mechanics.

Abstract: Dualities are mathematical mappings that reveal links between apparently unrelated systems in virtually every branch of physics1–8. Systems mapped onto themselves by a duality transformation are called self-dual and exhibit remarkable properties, as exemplified by the scale invariance of an Ising magnet at the critical point. Here we show how dualities can enhance the symmetries of a dynamical matrix (or Hamiltonian), enabling the design of metamaterials with emergent properties that escape a standard group theory analysis. As an illustration, we consider twisted kagome lattices9–15, reconfigurable mechanical structures that change shape by means of a collapse mechanism9. We observe that pairs of distinct configurations along the mechanism exhibit the same vibrational spectrum and related elastic moduli. We show that these puzzling properties arise from a duality between pairs of configurations on either side of a mechanical critical point. The critical point corresponds to a self-dual structure with isotropic elasticity even in the absence of spatial symmetries and a twofold-degenerate spectrum over the entire Brillouin zone. The spectral degeneracy originates from a version of Kramers’ theorem16,17 in which fermionic time-reversal invariance is replaced by a hidden symmetry emerging at the self-dual point. The normal modes of the self-dual systems exhibit non-Abelian geometric phases18,19 that affect the semiclassical propagation of wavepackets20, leading to non-commuting mechanical responses. Our results hold promise for holonomic computation21 and mechanical spintronics by allowing on-the-fly manipulation of synthetic spins carried by phonons. Dualities—mathematical mappings between different systems—can act as hidden symmetries that enable materials design beyond that suggested by crystallographic space groups.

Type-II Ising Superconductivity and Anomalous Metallic State in Macro-Size Ambient-Stable Ultrathin Crystalline Films

Abstract: Recent emergence of two-dimensional (2D) crystalline superconductors has provided a promising platform to investigate novel quantum physics and potential applications. To reveal essential quantum p...

Anisotropic tensor renormalization group

Abstract: We propose a different tensor renormalization group algorithm, anisotropic tensor renormalization group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the higher-order tensor renormalization group (HOTRG) algorithm, i.e., it preserves the lattice topology after the renormalization. In comparison with HOTRG, both the computation cost and the memory footprint of our method are drastically reduced, especially in higher dimensions, by renormalizing tensors in an anisotropic way after the singular value decomposition. We demonstrate the ability of ATRG for the square lattice and the simple cubic lattice Ising models. Although the accuracy of the present method degrades when compared with HOTRG of the same bond dimension, the accuracy with fixed computation time is improved greatly due to the drastic reduction of the computation cost.

Rapid Mixing of Glauber Dynamics up to Uniqueness via Contraction

Abstract: For general antiferromagnetic 2-spin systems, including the hardcore model and the antiferromagnetic Ising model, there is an $\mathsf{FPTAS}$ for the partition function on graphs of maximum degree $\Delta$ when the infinite regular tree lies in the uniqueness region by Li et al. (2013). Moreover, in the tree non-uniqueness region, Sly (2010) showed that there is no $\mathsf{FPRAS}$ to estimate the partition function unless $\mathsf{NP}=\mathsf{RP}$. The algorithmic results follow from the correlation decay approach due to Weitz (2006) or the polynomial interpolation approach developed by Barvinok (2016). However the running time is only polynomial for constant $\Delta$. For the hardcore model, recent work of Anari et al. (2020) establishes rapid mixing of the simple single-site Markov chain known as the Glauber dynamics in the tree uniqueness region. Our work simplifies their analysis of the Glauber dynamics by considering the total pairwise influence of a fixed vertex $v$ on other vertices, as opposed to the total influence on $v$, thereby extending their work to all 2-spin models and improving the mixing time. More importantly our proof ties together the three disparate algorithmic approaches: we show that contraction of the tree recursions with a suitable potential function, which is the primary technique for establishing efficiency of Weitz's correlation decay approach and Barvinok's polynomial interpolation approach, also establishes rapid mixing of the Glauber dynamics. We emphasize that this connection holds for all 2-spin models (both antiferromagnetic and ferromagnetic), and existing proofs for correlation decay or polynomial interpolation immediately imply rapid mixing of Glauber dynamics. Our proof utilizes that the graph partition function divides that of Weitz's self-avoiding walk trees, leading to new tools for analyzing influence of vertices.

Steered quantum coherence as a signature of quantum phase transitions in spin chains

Abstract: We propose to use the steered quantum coherence (SQC) as a signature of quantum phase transitions (QPTs). By considering various spin chain models, including the transverse-field Ising model, $\mathit{XY}$ model, and $\mathit{XX}$ model with three-spin interaction, we showed that the SQC and its first-order derivative succeed in signaling different critical points of QPTs. In particular, the SQC method is effective for any spin pair chosen from the chain, and the strength of SQC, in contrast to entanglement and quantum discord, is insensitive to the distance (provided it is not very short) of the tested spins, which makes it convenient for practical use as there is no need for careful choice of two spins in the chain.

Adiabatic evolution on a spatial-photonic Ising machine

Abstract: Combinatorial optimization problems are crucial for widespread applications but remain difficult to solve on a large scale with conventional hardware. Novel optical platforms, known as coherent or photonic Ising machines, are attracting considerable attention as accelerators on optimization tasks formulable as Ising models. Annealing is a well-known technique based on adiabatic evolution for finding optimal solutions in classical and quantum systems made by atoms, electrons, or photons. Although various Ising machines employ annealing in some form, adiabatic computing on optical settings has been only partially investigated. Here, we realize the adiabatic evolution of frustrated Ising models with 100 spins programmed by spatial light modulation. We use holographic and optical control to change the spin couplings adiabatically, and exploit experimental noise to explore the energy landscape. Annealing enhances the convergence to the Ising ground state and allows to find the problem solution with probability close to unity. Our results demonstrate a photonic scheme for combinatorial optimization in analogy with adiabatic quantum algorithms and classical annealing methods but enforced by optical vector-matrix multiplications and scalable photonic technology.

Quasiparticle origin of dynamical quantum phase transitions

Abstract: Considering nonintegrable quantum Ising chains with exponentially decaying interactions, we present matrix product state results that establish a connection between low-energy quasiparticle excitations and the kind of nonanalyticities in the Loschmidt return rate. When domain walls in the spectrum of the quench Hamiltonian are energetically favored to be bound rather than freely propagating, anomalous cusps appear in the return rate regardless of the initial state. In the nearest-neighbor limit, domain walls are always freely propagating and anomalous cusps never appear. As a consequence, our work illustrates that models in the same equilibrium universality class can still exhibit fundamentally distinct out-of-equilibrium criticality. Our results are accessible to current ultracold-atom and ion-trap experiments.