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Since the early days of quantum mechanics, it has been clear that there is a fundamental difficulty in studying many-body quantum systems: the configuration space, or Hilbert space, of a [...], The original motivation to build a quantum computer came from Feynman (1), who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd (2), who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm (3), a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.

Cross-disciplinary collaborations have initiated translational studies in an effort to harness naturally occurring diseases in companion animals to accelerate the development of new treatment modalities, drugs, and device inventions. These synergistic collaborations can identify clinically relevant models that offer the opportunity to conduct rigorous translational investigations. However, the relationship between craniomaxillofacial diseases in companion animals and humans has been widely overlooked. We report here an innovative and visionary 2-d symposium that was organized to gather professionals working on craniomaxillofacial disorders and solutions in humans and/or animals from multiple disciplines, including veterinary physicians, basic scientists, biomedical engineers, physicians, and dentists. The symposium provided a platform for junior and senior investigators and basic science and clinical researchers to network, collaborate, and develop a new clinical and translational framework for accelerated therapy development. [ABSTRACT FROM AUTHOR]

Background There are several reports of incisor tooth resorption and hypercementosis in horses but, to date, studies have been limited in case numbers and to advanced lesions. Tooth resorption in other species is a radiographic diagnosis of types of resorption that are often identified before clinical signs. Our goal was to evaluate radiographically incisor tooth resorption in a large population of horses, utilising interpretation criteria from canine and human dentistry. Objective To document and classify incisor tooth resorption and hypercementosis. Study design Retrospective descriptive case series. Methods Horses presented for routine dental care >5 years old were included only if owners were unaware of incisor pathology. Radiographs (three views) were obtained of the incisor teeth and incisor teeth resorption was classified according to the radiographic criteria described for man and dogs. Hypercementosis and its location were recorded. Results Tooth resorption was detected in 149 of 169 (88.2%) horses and 951 of 1952 (48.7%) of incisor teeth. The classification system used was applicable in 926 (97.2%) of 951 affected teeth. Hypercementosis was detected in 34 (20.1%) horses and 148 (7.6%) teeth. As horses increased in age, resorption and hypercementosis was more frequent; no significant differences were found among sex or breed categories. All horses with hypercementosis had resorption, but only 23.4% of horses with resorption had hypercementosis. Advanced (stage ≥3) resorption was detected in 159 (8.1%) teeth and 54 (32.0%) horses in an otherwise clinically healthy population. Main limitations Certain horses' anatomy precluded isolation of the mandibular third incisor teeth from the canine teeth due to superimposition. Conclusions Incisor tooth resorption, in particular external replacement resorption and external inflammatory resorption, is common in horses. Hypercementosis is consistently associated with resorption, but the inverse association is inconsistent. [ABSTRACT FROM AUTHOR]

Reasons for performing study Local anaesthesia is often required to facilitate invasive procedures in equine dental patients under standing sedation. Objectives To show that an intraoral approach can be used to desensitise the inferior alveolar nerve in horses and report complications seen with this technique. Methods The distance of the mandibular foramen from the distal (caudal) edge of the mandibular third molar tooth, rostral edge of the mandibular ramus and ventral margin of the mandible were measured in 26 adult equine skulls of various ages and breeds. Computed tomography ( CT) was used to verify the placement of the local anaesthetic with a custom-made device on 4 equine cadaver heads. The technique was applied in 43 clinical cases having procedures performed on the mandibular quadrants using the delivery device. Results Computed tomography demonstrated that the intraoral approach provided deposition of the local anaesthetic at the mandibular foramen and anatomical localisation of mandibular foramen indicated that anaesthetic solution could be delivered with a 38 mm needle. Clinical patients to lerated invasive dental procedures following the inferior alveolar nerve block with a 5 ml dose of local anaesthetic, without evidence of self-inflicted lingual trauma. Conclusions The inferior alveolar nerve was successfully desensitised with the intraoral approach with minimal complications. The reduced volume of local anaesthetic and ability to deposit the local anaesthetic in close proximity to the nerve compared with an extraoral technique may decrease the complication of self-inflicted lingual trauma. [ABSTRACT FROM AUTHOR]

We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D3, where g(D,ξ/N) is a nontrivial function. For ξ⪡N, this scaling reduces to D3, independent of the system size N, making our method N times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system. [ABSTRACT FROM AUTHOR]

We introduce quantum versions of the χ2-divergence, provide a detailed analysis of their properties, and apply them in the investigation of mixing times of quantum Markov processes. An approach similar to the one presented in the literature for classical Markov chains is taken to bound the trace-distance from the steady state of a quantum processes. A strict spectral bound to the convergence rate can be given for time-discrete as well as for time-continuous quantum Markov processes. Furthermore, the contractive behavior of the χ2-divergence under the action of a completely positive map is investigated and contrasted to the contraction of the trace norm. In this context we analyze different versions of quantum detailed balance and, finally, give a geometric conductance bound to the convergence rate for unital quantum Markov processes. [ABSTRACT FROM AUTHOR]

We show how to construct relevant families of matrix product operators (MPOs) in one and higher dimensions. These form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In particular, we construct translationally invariant MPOs suitable for time evolution, and show how such descriptions are possible for Hamiltonians with long-range interactions. We show how these tools can be exploited for constructing new algorithms for simulating quantum spin systems. [ABSTRACT FROM AUTHOR]

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states. [ABSTRACT FROM AUTHOR]

Abstract This report describes a 16-month-old female, otherwise seemingly healthy, Siberian husky dog with severe oral papillomatosis that did not regress spontaneously and was refractory to surgical treatment over a 6-month period. Regression of the papillomas was achieved by administering a series of experimental vaccinations starting at the time of the last surgery. The vaccine consisted of systemically administered canine oral papillomavirus major coat protein L1 that has been shown to self-assemble into virus-like particles. They cause a humoral response that has been shown to prevent the onset and development of papillomas. In this case, however, following unsuccessful surgical treatment, the vaccine acted therapeutically, causing the papillomas that had regrown to shrink. No side-effects were noted. [ABSTRACT FROM AUTHOR]

Thirty-two client-owned dogs treated for periodontal disease were divided in group 1 if no periodontitis, group 2 if ≤25%, and group 3 if >25% of the teeth present were affected with periodontitis. Blood was tested before and 2 weeks after periodontal therapy for nitrosyl hemoglobin (HbNO), plasma nitrite/ nitrate (NOx) and 3-nitrotyrosine (NT) levels. No HbNO was detected in any of the animals tested. There was no significant difference in the NOx plasma levels within each group or across the groups before and after the treatment, but a noticeable increase in NOx plasma levels was observed in group 3 after the treatment. Plasma NT was detected in only one third of the animals. NO levels varied greatly across individual dogs. The data are suggestive of an overall increase in systemic NO response 2 weeks after periodontal treatment in dogs with advanced periodontal disease, but the response is greatly individually-dependent. [ABSTRACT FROM AUTHOR]

Summary Over a 10-month period, 24 randomly selected riding horses were fed various amounts of biotin. Statistically significant improvements in growth rates and hardness of hooves were produced by biotin supplementation. Greater growth rates and hardness were achieved at a daily dose of 15 mg than at 7.5 mg. Increased hoof hardness was greatest in the hoof quarters and toe. No ring formation occurred in hooves of horses fed biotin intermittently. [ABSTRACT FROM AUTHOR]

The algebraic Bethe ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard, in general, to extract properties from the states, for example, correlation functions. In our work, we apply the tools of tensor-network states to describe the eigenstates approximately as matrix product states. From the matrix product state expression, we then obtain observables like the structure factor, dimer-dimer correlation functions, chiral correlation functions, and one-particle Green function directly. [ABSTRACT FROM AUTHOR]

We study a matrix product state algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of Ôstlund and Rommer [see S. Ôstlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995);S. RommerandS. Ôstlund, Phys. Rev. B 55, 2164 (1997)], we separate the Hilbert space of the system into subspaces with different momentum. This gives rise to a direct sum of effective Hamiltonians, each one corresponding to a different momentum, and we determine their spectrum by solving a generalized eigenvalue equation. Surprisingly, many branches of the dispersion relation are approximated to a very good precision. We benchmark the accuracy of the algorithm by comparison with the exact solutions and previous numerical results for the quantum Ising, the antiferromagnetic Heisenberg spin-1/2, and the bilinear-biquadratic spin-1 models. [ABSTRACT FROM AUTHOR]

We consider a model of strongly correlated electrons in ID called the t-J model, which was solved by the graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a matrix product state. As a proof of principle, we calculate observables of ground states and excited states of finite lattices up to 18 lattice sites. [ABSTRACT FROM AUTHOR]

We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the spin chain and D is the dimension of the MPS matrices. In the first regime, MPS can be used to perform finite size scaling (FSS). In the complementary regime, the MPS simulations show instead the clear signature of finite entanglement scaling (FES). In the thermodynamic limit (or large N limit), only MPS in the FSS regime maintain a finite overlap with the exact ground state. This observation has implications on how to correctly perform FSS with MPS as well as on the performance of recent MPS algorithms for systems with PBC. It also gives clear evidence that critical models can actually be simulated very well with MPS by using the right scaling relations; in the appendixes, we give an alternative derivation of the result of Pollmann et al. [Phys. Rev. Lett. 102, 255701 (2009)] relating the bond dimension of the MPS to an effective correlation length. [ABSTRACT FROM AUTHOR]

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation. [ABSTRACT FROM AUTHOR]

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015); S. Yang, Z.-C. Gu, and X.-G. Wen, Phys. Rev. Lett. 118, 110504 (2017)], we obtain approximate fixed point tensor networks at criticality. Our formalism, however, preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model. [ABSTRACT FROM AUTHOR]

The truncation or compression of the spectrum of Schmidt values is inherent to the matrix product state (MPS) approximation of one-dimensional quantum ground states. We provide a renormalization group picture by interpreting this compression as an application of Wilson's numerical renormalization group along the imaginary time direction appearing in the path integral representation of the state. The location of the physical index is considered as an impurity in the transfer matrix and static MPS correlation functions are reinterpreted as dynamical impurity correlations. Coarse-graining the transfer matrix is performed using a hybrid variational ansatz based on matrix product operators, combining ideas of MPS and the multiscale entanglement renormalization ansatz. Through numerical comparison with conventional MPS algorithms, we explicitly verify the impurity interpretation of MPS compression, as put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015)] for the transverse-field Ising model. Additionally, we motivate the conceptual usefulness of endowing MPS with an internal layered structure by studying restricted variational subspaces to describe elementary excitations on top of the ground state, which serves to elucidate a transparent renormalization group structure ingrained in MPS descriptions of ground states. [ABSTRACT FROM AUTHOR]

We analyze the low energy excitations of spin lattice systems in two dimensions at zero temperature within the framework of projected entangled pair state models. Perturbations in the bulk give rise to physical excitations located at the edge. We identify the corresponding degrees of freedom, give a procedure to derive the edge Hamiltonian, and illustrate that it can exhibit a rich phase diagram. For topological models, the edge Hamiltonian is constrained by the topological order in the bulk, which gives rise to one-dimensional edge models with unconventional properties; for instance, a topologically ordered bulk can protect a ferromagnetic Ising chain at the edge against spontaneous symmetry breaking. [ABSTRACT FROM AUTHOR]

The use of finite entanglement scaling with matrix product states (MPS) has become a crucial tool for studying one-dimensional critical lattice theories, especially those with emergent conformal symmetry. We argue that finite entanglement introduces a relevant deformation in the critical theory. As a result, the bipartite entanglement Hamiltonian defined from the MPS can be understood as a boundary conformal field theory with a physical and an entanglement boundary. We are able to exploit the symmetry properties of the MPS to engineer the physical conformal boundary condition. The entanglement boundary, on the other hand, is related to the concrete lattice model and remains invariant under this relevant perturbation. Using critical lattice models described by the Ising, Potts, and free compact boson conformal field theories, we illustrate the influence of the symmetry and the relevant deformation on the conformal boundaries in the entanglement spectrum.

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e., the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical SU(2) Heisenberg chains with half-integer spin S>1/2 with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions.

Tensor-network methods are used to perform a comparative study of the two-dimensional classical Heisenberg and RP^{2} models. We demonstrate that uniform matrix product states (MPSs) with explicit SO(3) symmetry can probe correlation lengths up to O(10^{3}) sites accurately, and we study the scaling of entanglement entropy and universal features of MPS entanglement spectra. For the Heisenberg model, we find no signs of a finite-temperature phase transition, supporting the scenario of asymptotic freedom. For the RP^{2} model we observe an abrupt onset of scaling behavior, consistent with hints of a finite-temperature phase transition reported in previous studies. A careful analysis of the softening of the correlation length divergence, the scaling of the entanglement entropy, and the MPS entanglement spectra shows that our results are inconsistent with true criticality, but are rather in agreement with the scenario of a crossover to a pseudocritical region which exhibits strong signatures of nematic quasi-long-range order at length scales below the true correlation length. Our results reveal a fundamental difference in scaling behavior between the Heisenberg and RP^{2} models: Whereas the emergence of scaling in the former shifts to zero temperature if the bond dimension is increased, it occurs at a finite bond-dimension independent crossover temperature in the latter.

We demonstrate that projected entangled-pair states are able to represent ground states of critical, fermionic systems exhibiting both 1d and 0d Fermi surfaces on a 2D lattice with an efficient scaling of the bond dimension. Extrapolating finite size results for the Gaussian restriction of fermionic projected entangled-pair states to the thermodynamic limit, the energy precision as a function of the bond dimension is found to improve as a power law, illustrating that an arbitrary precision can be obtained by increasing the bond dimension in a controlled manner. In this process, boundary conditions and system sizes have to be chosen carefully so that nonanalyticities of the Ansatz, rooted in its nontrivial topology, are avoided.

We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions D. The key ingredient consists of using the effective correlation length ξ for inducing a collapse of data points, f(D,χ)=f(ξ(D,χ)), for arbitrary values of D and the environment bond dimension χ. As such we circumvent the need for extrapolations in χ and can use many distinct data points for a fixed value of D. Here, we need that the PEPSs have been optimized using a fixed-χ gradient method, which can be achieved using a novel tensor-network algorithm for finding fixed points of 2D transfer matrices, or by using the formalism of backwards differentiation. We test our hypothesis on the critical 3D dimer model, the 3D classical Ising model, and the 2D quantum Heisenberg model.

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category H_{3} as input data. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge c=2. Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix, and the conformal towers are separated in the spectra through their identification with the topological sectors. It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input Z(H_{3}), which is the simplest modular tensor category that does not admit an algebraic construction. This provides a counterexample for the conjecture that all rational CFT can be constructed from standard methods.

Just as matrix product states represent ground states of one-dimensional quantum spin systems faithfully, continuous matrix product states (cMPS) provide faithful representations of the vacuum of interacting field theories in one spatial dimension. Unlike the quantum spin case, however, for which the density matrix renormalization group and related matrix product state algorithms provide robust algorithms for optimizing the variational states, the optimization of cMPS for systems with inhomogeneous external potentials has been problematic. We resolve this problem by constructing a piecewise linear parameterization of the underlying matrix-valued functions, which enables the calculation of the exact reduced density matrices everywhere in the system by high-order Taylor expansions. This turns the variational cMPS problem into a variational algorithm from which both the energy and its backwards derivative can be calculated exactly and at a cost that scales as the cube of the bond dimension. We illustrate this by finding ground states of interacting bosons in external potentials and by calculating boundary or Casimir energy corrections of continuous many-body systems with open boundary conditions.