Approximating local observables on projected entangled pair states

Tensor network states are for good reasons believed to capture ground states of gapped local Hamiltonians arising in the condensed matter context, states which are in turn expected to satisfy an entanglement area law. However, the computational hardness of contracting projected entangled pair states in two and higher dimensional systems is often seen as a significant obstacle when devising higher-dimensional variants of the density-matrix renormalisation group method. In this work, we show that for those projected entangled pair states that are expected to provide good approximations of such ground states of local Hamiltonians, one can compute local expectation values in quasi-polynomial time. We therefore provide a complexity-theoretic justification of why state-of-the-art numerical tools work so well in practice. We comment on how the transfer operators of such projected entangled pair states have a gap and discuss notions of local topological quantum order. We finally turn to the computation of local expectation values on quantum computers, providing a meaningful application for a small-scale quantum computer.Comment: 7 pages, 1 figure, minor changes in v

Active elastic dimers: Cells moving on rigid tracks

Experiments suggest that the migration of some cells in the three-dimensional extra cellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell made of two beads and an active spring moving along a rigid track. The active spring models the stress fibers with their myosin-driven contractility and alpha-actinin-driven extendability, while the friction coefficients of the two beads describe the catch/slip bond behavior of the integrins in focal adhesions. In the absence of active noise, net motion arises from an interplay between active contractility (and passive extendability) of the stress fibers and an asymmetry between the front and back of the cell due to catch bond behavior of integrins at the front of the cell and slip bond behavior of integrins at the back. We obtain reasonable cell speeds with independently estimated parameters. We also study the effects of hysteresis in the active spring, due to catch bond behavior and the dynamics of cross-linking, and the addition of active noise on the motion of the cell. Our model highlights the role of alpha-actinin in three-dimensional cell motility and does not require Arp2/3 actin filament nucleation for net motion.Comment: 13 pages, 9 figure

A framework to combine low- and high-resolution spectroscopy for the atmospheres of transiting exoplanets

Current observations of the atmospheres of close-in exoplanets are predominantly obtained with two techniques: low-resolution spectroscopy with space telescopes and high-resolution spectroscopy from the ground. Although the observables delivered by the two methods are in principle highly complementary, no attempt has ever been made to combine them, perhaps due to the different modeling approaches that are typically used in their interpretation. Here we present the first combined analysis of previously-published dayside spectra of the exoplanet HD 209458b obtained at low resolution with HST/WFC3 and Spitzer/IRAC, and at high resolution with VLT/CRIRES. By utilizing a novel retrieval algorithm capable of computing the joint probability distribution of low- and high-resolution spectra, we obtain tight constraints on the chemical composition of the planet's atmosphere. In contrast to the WFC3 data, we do not confidently detect H2O at high spectral resolution. The retrieved water abundance from the combined analysis deviates by 1.9 sigma from the expectations for a solar-composition atmosphere in chemical equilibrium. Measured relative molecular abundances of CO and H2O strongly favor an oxygen-rich atmosphere (C/O<1 at 3.5 sigma) for the planet when compared to equilibrium calculations including O rainout. From the abundances of the seven molecular species included in this study we constrain the planet metallicity to 0.1-1.0x the stellar value (1 sigma). This study opens the way to coordinated exoplanet surveys between the flagship ground- and space-based facilities, which ultimately will be crucial for characterizing potentially-habitable planets.Comment: 7 pages, 5 figures, accepted for publication in ApJL. Section 4 largely updated from previous version, Figure 2 updated to contain information on the T-p profil

Direct certification of a class of quantum simulations

One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which one cannot classically calculate local expectation values of state preparations efficiently. In this work, we develop weak-membership formulations of the certification of ground state preparations. We provide a non-interactive protocol for certifying ground states of frustration-free Hamiltonians based on simple energy measurements of local Hamiltonian terms. This certification protocol can be applied to classically intractable analog quantum simulations: For example, using Feynman-Kitaev Hamiltonians, one can encode universal quantum computation in such ground states. Moreover, our certification protocol is applicable to ground states encodings of IQP circuits demonstration of quantum supremacy. These can be certified efficiently when the error is polynomially bounded.Comment: 10 pages, corrected a small error in Eqs. (2) and (5

Weak Scale Superstrings

Recent developments in string duality suggest that the string scale may not be irrevocably tied to the Planck scale. Two explicit but unrealistic examples are described where the ratio of the string scale to the Planck scale is arbitrarily small. Solutions which are more realistic may exist in the intermediate coupling or ``truly strong coupling'' region of the heterotic string. Weak scale superstrings have dramatic experimental consequences for both collider physics and cosmology.Comment: harvmac, 14 pages. References added, 3 typos fixed, Comments added at beginning of section 4 emphasizing flaws of the toy example