Channeling Quantum Criticality.

We analyze the effect of decoherence, modeled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g function" in conformal field theory, allowing us to define a notion of renormalization group (RG) flow (or "phase transitions") between quantum channels. We also find that the entropy of a subsystem in the decohered state has a subleading logarithmic scaling with subsystem size, and we relate it to correlation functions of boundary condition changing operators in the conformal field theory. Finally, we find that the subsystem entanglement negativity, a measure of quantum correlations within mixed states, can exhibit log scaling or area law based on the RG flow. When the channel corresponds to a marginal perturbation, the coefficient of the log scaling can change continuously with decoherence strength. We illustrate all these possibilities for the critical ground state of the transverse-field Ising model, in which we identify four RG fixed points of dephasing channels and verify the RG flow numerically. Our results are relevant to quantum critical states realized on noisy quantum simulators, in which our predicted entanglement scaling can be probed via shadow tomography methods.

Cross Entropy Benchmark for Measurement-Induced Phase Transitions.

We investigate prospects of employing the linear cross entropy to experimentally access measurement-induced phase transitions without requiring any postselection of quantum trajectories. For two random circuits that are identical in the bulk but with different initial states, the linear cross entropy χ between the bulk measurement outcome distributions in the two circuits acts as an order parameter, and can be used to distinguish the volume law from area law phases. In the volume law phase (and in the thermodynamic limit) the bulk measurements cannot distinguish between the two different initial states, and χ=1. In the area law phase χ<1. For circuits with Clifford gates, we provide numerical evidence that χ can be sampled to accuracy ϵ from O(1/ϵ^{2}) trajectories, by running the first circuit on a quantum simulator without postselection, aided by a classical simulation of the second. We also find that for weak depolarizing noise the signature of the measurement-induced phase transitions is still present for intermediate system sizes. In our protocol we have the freedom of choosing initial states such that the "classical" side can be simulated efficiently, while simulating the "quantum" side is still classically hard.

Development and validation of a risk prediction model for diabetic retinopathy in type 2 diabetic patients.

To establish a risk prediction model and make individualized assessment for the susceptible diabetic retinopathy (DR) population in type 2 diabetic mellitus (T2DM) patients. According to the retrieval strategy, inclusion and exclusion criteria, the relevant meta-analyses on DR risk factors were searched and evaluated. The pooled odds ratio (OR) or relative risk (RR) of each risk factor was obtained and calculated for ß coefficients using logistic regression (LR) model. Besides, an electronic patient-reported outcome questionnaire was developed and 60 cases of DR and non-DR T2DM patients were investigated to validate the developed model. Receiver operating characteristic curve (ROC) was drawn to verify the prediction accuracy of the model. After retrieving, eight meta-analyses with a total of 15,654 cases and 12 risk factors associated with the onset of DR in T2DM, including weight loss surgery, myopia, lipid-lowing drugs, intensive glucose control, course of T2DM, glycated hemoglobin (HbA1c), fasting plasma glucose, hypertension, gender, insulin treatment, residence, and smoking were included for LR modeling. These factors, followed by the respective ß coefficient was bariatric surgery (- 0.942), myopia (- 0.357), lipid-lowering drug follow-up < 3y (- 0.994), lipid-lowering drug follow-up > 3y (- 0.223), course of T2DM (0.174), HbA1c (0.372), fasting plasma glucose (0.223), insulin therapy (0.688), rural residence (0.199), smoking (- 0.083), hypertension (0.405), male (0.548), intensive glycemic control (- 0.400) with constant term α (- 0.949) in the constructed model. The area under receiver operating characteristic curve (AUC) of the model in the external validation was 0.912. An application was presented as an example of use. In conclusion, the risk prediction model of DR is developed, which makes individualized assessment for the susceptible DR population feasible and needs to be further verified with large sample size application.

Modular Commutators in Conformal Field Theory.

The modular commutator is a recently discovered entanglement quantity that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field theories in 1+1 dimensions and discuss its salient features. We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We test this formula for a gapped (2+1)-dimensional system with a chiral edge, i.e., the quantum Hall state, and observe excellent agreement with numerical simulations. Furthermore, we propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence. For these states, we argue that the modular commutator can be obtained from a set of crossing angles between intersecting Ryu-Takayanagi surfaces.

Universal Tripartite Entanglement in One-Dimensional Many-Body Systems.

Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.

Conformal Fields and Operator Product Expansion in Critical Quantum Spin Chains.

At a quantum critical point, the low-energy physics of a quantum spin chain is described by conformal field theory (CFT). Given the Hamiltonian of a critical spin chain, we propose a variational method to build an approximate lattice representation ϕ_{α} of the corresponding primary CFT operators ϕ_{α}^{CFT}. We then show how to numerically compute the operator product expansion coefficients C_{αßγ}^{CFT} governing the fusion of two primary fields. In this way, we complete the implementation of Cardy's program, outlined in the 1980s, which aims to extract the universality class of a phase transition, as encoded in the so-called conformal data of the underlying CFT, starting from a microscopic description. Our approach, demonstrated here for the critical quantum Ising model, only requires a generic (i.e., in general, nonintegrable) critical lattice Hamiltonian as its input.

Conformal Data and Renormalization Group Flow in Critical Quantum Spin Chains Using Periodic Uniform Matrix Product States.

We establish that a Bloch-state ansatz based on periodic uniform matrix product states (PUMPS), originally designed to capture single-quasiparticle excitations in gapped systems, is in fact capable of accurately approximating all low-energy eigenstates of critical quantum spin chains on the circle. When combined with the methods of [Milsted and Vidal, Phys. Rev. B 96, 245105PRBMDO2469-995010.1103/PhysRevB.96.245105] based on the Koo-Saleur formula, PUMPS Bloch states can then be used to identify each low-energy eigenstate of a chain made of up to hundreds of spins with its corresponding scaling operator in the emergent conformal field theory (CFT). This enables the following two tasks that we demonstrate using the quantum Ising model and a recently proposed generalization thereof due to O'Brien and Fendley [Phys. Rev. Lett. 120, 206403]. (i) From the spectrum of low energies and momenta we extract conformal data (specifying the emergent CFT) with unprecedented numerical accuracy. (ii) By changing the lattice size, we investigate nonperturbatively the renormalization group flow of the low-energy spectrum between two CFTs. In our example, where the flow is from the tricritical Ising CFT to the Ising CFT, we obtain excellent agreement with an analytical result [Klassen and Melzer, Nucl. Phys. B370, 51110.1016/0550-3213(92)90422-8] conjectured to describe the flow of the first spectral gap directly in the continuum.