Tensor network methods for extracting conformal field theory data from fixed-point tensors and defect coarse graining.

We present a comprehensive study on extracting conformal field theory data using tensor network methods, especially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the classical two-dimensional Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator product expansion coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of pointlike defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from the lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with pointlike defects, including graph-independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tensor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.

A universal variational quantum eigensolver for non-Hermitian systems.

Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices-Inspired by Schur's triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver-With additional [Formula: see text] quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm's feasibility. We also undertake a comprehensive parametric study to validate VQUE's scalability, generality, and performance in realistic applications.

Demonstrating the Affleck-Kennedy-Lieb-Tasaki Spectral Gap on 2D Degree-3 Lattices.

We report results on solving a long outstanding problem-whether the two-dimensional spin-3/2 antiferromagnetic valence-bond model of Affleck, Kennedy, Lieb, and Tasaki (AKLT) possesses a nonzero gap above its ground state. We exploit a relation between the anticommutator and sum of two projectors and apply it to ground-space projectors on regions of the honeycomb lattice. After analytically reducing the complexity of the resultant problem, we are able to use a standard Lanczos method to establish the existence of a nonzero gap. This approach is also successfully applied to spin-3/2 AKLT models on other degree-3 semiregular tilings, namely, the square-octagon, star, and cross lattices, where the complexity is low enough that exact diagonalization can be used instead. In addition, we close the previously open cases of hybrid AKLT models on the singly decorated honeycomb and singly decorated square lattices.

Machine learning of phase transitions in the percolation and XY models.

In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two-dimensional lattices, whose transitions involve nonlocal or topological properties, including site and bond percolations, the XY model, and the generalized XY model. We find that using just one hidden layer in a fully connected neural network, the percolation transition can be learned and the data collapse by using the average output layer gives correct estimate of the critical exponent ν. We also study the Berezinskii-Kosterlitz-Thouless transition, which involves binding and unbinding of topological defects, vortices and antivortices, in the classical XY model. The generalized XY model contains richer phases, such as the nematic phase, the paramagnetic and the quasi-long-range ferromagnetic phases, and we also apply machine learning method to it. We obtain a consistent phase diagram from the network trained with only data along the temperature axis at two particular parameter Δ values, where Δ is the relative weight of pure XY coupling. Aside from using the spin configurations (either angles or spin components) as the input information in a convolutional neural network, we devise a feature engineering approach using the histograms of the spin orientations in order to train the network to learn the three phases in the generalized XY model and demonstrate that it indeed works. The trained network by using system size L×L can be used to the phase diagram for other sizes (L^{'}×L^{'}, where L^{'}≠L) without any further training.

Computational Power of Symmetry-Protected Topological Phases.

We consider ground states of quantum spin chains with symmetry-protected topological (SPT) order as resources for measurement-based quantum computation (MBQC). We show that, for a wide range of SPT phases, the computational power of ground states is uniform throughout each phase. This computational power, defined as the Lie group of executable gates in MBQC, is determined by the same algebraic information that labels the SPT phase itself. We prove that these Lie groups always contain a full set of single-qubit gates, thereby affirming the long-standing conjecture that general SPT phases can serve as computationally useful phases of matter.

Superdense teleportation using hyperentangled photons.

Transmitting quantum information between two remote parties is a requirement for many quantum applications; however, direct transmission of states is often impossible because of noise and loss in the communication channel. Entanglement-enhanced state communication can be used to avoid this issue, but current techniques require extensive experimental resources to transmit large quantum states deterministically. To reduce these resource requirements, we use photon pairs hyperentangled in polarization and orbital angular momentum to implement superdense teleportation, which can communicate a specific class of single-photon ququarts. We achieve an average fidelity of 87.0(1)%, almost twice the classical limit of 44% with reduced experimental resources than traditional techniques. We conclude by discussing the information content of this constrained set of states and demonstrate that this set has an exponentially larger state space volume than the lower-dimensional general states with the same number of state parameters.

Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization.

Topological order in two-dimensional (2D) quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here, we show how topological phase transitions in 2D systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on projected entangled pair states to compute this quantity for a torus partitioned into cylinders and then use this method to find sharp evidence of topological phase transitions in 2D systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, additionally, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows us to extract the critical exponent of the correlation length and shows that there is no continuous entanglement loss along renormalization group flows in topological phases.

Thermal states as universal resources for quantum computation with always-on interactions.

Measurement-based quantum computation utilizes an initial entangled resource state and proceeds with subsequent single-qubit measurements. It is implicitly assumed that the interactions between qubits can be switched off so that the dynamics of the measured qubits do not affect the computation. By proposing a model spin Hamiltonian, we demonstrate that measurement-based quantum computation can be achieved on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault tolerantly if the temperature is below a threshold value.

Experimental quantum simulation of entanglement in many-body systems.

We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.

Expression of Crip2, a LIM-domain-only protein, in the mouse cardiovascular system under physiological and pathological conditions.

LIM domain-containing proteins mediate protein-protein interactions and play regulatory roles in various physiopathological processes. The mRNA of Crip2, a LIM-only gene, has been detected abundantly in developing and adult hearts but its cell-type specific expression profile has not been well characterized. In this study, we showed that Crip2 is highly expressed in the myocardium, moderately expressed in the endocardium and absent from the epicardium of the developing mouse heart. Interestingly, Crip2 expression is present in the endocardial cells that line both endocardial cushions, whereas it is markedly reduced in the cushion mesenchymes during valve leaflet formation. In the developing vascular system, Crip2 is detected in the endothelial cells of both blood and lymphatic vessels. Consistent with the expression pattern observed in embryos, Crip2 is also highly expressed in the myocardium, endocardium and coronary vascular endothelial cells of the adult heart. In the cardiomyocytes, Crip2 is colocalized with cardiac troponin T in the thin-filaments of sarcomeres. Nonetheless, experimental studies revealed that the expression level of Crip2 is not altered in the isoproterenol (ISO) induced hypertrophic heart. Moreover, Crip2 is detected in endothelial cells of the neovasculature during wound healing and tumor growth. The persistence of Crip2 expression in cardiovascular tissues implies that Crip2 might exert an important impact on the cardiovascular development, maintenance and homeostasis.

Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal quantum computational resource.

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation.

Tunable Luttinger liquid physics in biased bilayer graphene.

Electronically gated bilayer graphene behaves as a tunable gap semiconductor under a uniform interlayer bias V(g). Imposing a spatially varying bias, which changes polarity from -V(g) to +V(g), leads to one dimensional (1D) chiral modes localized along the domain wall of the bias. Because of the broad transverse spread of their low-energy wave functions, we find that the dominant interaction between these 1D electrons is the forward scattering part of the Coulomb repulsion. Incorporating these interactions and the gate voltage dependence of the dispersion and wave functions, we find that these 1D modes behave as a strongly interacting Tomonaga-Luttinger liquid with three distinct mode velocities and a bias dependent Luttinger parameter, and discuss its experimental signatures.

Remote preparation of single-photon "hybrid" entangled and vector-polarization States.

Quantum teleportation faces increasingly demanding requirements for transmitting large or even entangled systems. However, knowledge of the state to be transmitted eases its reconstruction, resulting in a protocol known as remote state preparation. A number of experimental demonstrations to date have been restricted to single-qubit systems. We report the remote preparation of two-qubit "hybrid" entangled states, including a family of vector-polarization beams. Our single-photon states are encoded in the photon spin and orbital angular momentum. We reconstruct the states by spin-orbit state tomography and transverse polarization tomography. The high fidelities achieved for the vector-polarization states opens the door to optimal coupling of down-converted photons to other physical systems, such as an atom, as required for scalable quantum networks, or plasmons in photonic nanostructures.

Interacting boson problems can be QMA hard.

Computing the ground-state energy of interacting electron problems has recently been shown to be hard for quantum Merlin Arthur (QMA), a quantum analogue of the complexity class NP. Fermionic problems are usually hard, a phenomenon widely attributed to the so-called sign problem. The corresponding bosonic problems are, according to conventional wisdom, tractable. Here, we demonstrate that the complexity of interacting boson problems is also QMA hard. Moreover, the bosonic version of N-representability problem is QMA complete. Consequently, these problems are unlikely to have efficient quantum algorithms.

Remote state preparation: arbitrary remote control of photon polarization.

We experimentally demonstrate the first remote state preparation of arbitrary single-qubit states, encoded in the polarization of photons generated by spontaneous parametric down-conversion. Utilizing degenerate and nondegenerate wavelength entangled sources, we remotely prepare arbitrary states at two wavelengths. Further, we derive theoretical bounds on the states that may be remotely prepared for given two-qubit resources.

h/e magnetic flux modulation of the energy gap in nanotube quantum dots.

We report experiments on quantum dot single-electron-tunneling (SET) transistors made from short multiwall nanotubes and threaded by magnetic flux. Such systems allow us to probe the electronic energy spectrum of the nanotube and its dependence on the magnetic field. Evidence is provided for the interconversion between gapped (semiconducting) and ungapped (metallic) states. Our tubes exhibit h/e-period magnetic flux dependence, in agreement with simple tight-binding calculations.

Maximally entangled mixed states: creation and concentration.

Using correlated photons from parametric down-conversion, we extend the boundaries of experimentally accessible two-qubit Hilbert space. Specifically, we have created and characterized maximally entangled mixed states that lie above the Werner boundary in the linear entropy-tangle plane. In addition, we demonstrate that such states can be efficiently concentrated, simultaneously increasing both the purity and the degree of entanglement. We investigate a previously unsuspected sensitivity imbalance in common state measures, i.e., the tangle, linear entropy, and fidelity.