A polynomial-time classical algorithm for noisy random circuit sampling

We give a polynomial time classical algorithm for sampling from the output distribution of a noisy random quantum circuit in the regime of anti-concentration to within inverse polynomial total variation distance. This gives strong evidence that, in the presence of a constant rate of noise per gate, random circuit sampling (RCS) cannot be the basis of a scalable experimental violation of the extended Church-Turing thesis. Our algorithm is not practical in its current form, and does not address finite-size RCS based quantum supremacy experiments.Comment: 27 pages, 2 figure

Braiding higher-order Majorana corner states through their spin degree of freedom

In this work, we study the spin texture of a class of higher-order topological superconductors (HOTSC) and show how it can be used to detect and braid Majorana corner modes (MCMs). This class of HOTSC is composed of two-dimensional topological insulators with s-wave superconductivity and in-plane magnetic fields, which offers advantages in experimental implementation. The spin polarization of the MCMs in this class is perpendicular with the applied magnetic field direction and is opposite on intrinsic orbitals, resulting in an overall ferrimagnetic spin texture. As a result, we find that the spin-selective Andreev reflection can be observed in a transverse instead of parallel direction to the applied magnetic field. Meanwhile, this spin texture leads to the gate-tunable $4\pi$ periodic $\phi_0$ Josephson current that performs qualitatively different behavior from the topologically trivial $\phi_0$-junction under rotating the in-plane magnetic field. Meanwhile, the existence of the MCMs in this class does not depend on the in-plane magnetic field direction. This gives rise to great advantage in constructing all electronically controlled Majorana network for braiding, which is confirmed through our numerical simulation. We thus provide a comprehensive scheme for probing non-Abelian statistics in this class of HOTSCs.Comment: 6 pages, 4 figure

A quantitative study of financing efficiency of low?carbon companies: A three?stage data envelopment analysis

This study set out to evaluate the financing efficiency of low?carbon companies. Applying a three?stage data envelopment analysis with the data from 85 listed companies in China's low?carbon industries over the period 2011 to 2017, this study has found that the overall financing efficiency of low?carbon companies was relatively high, and the pure technical efficiency was quite steady over the period. The overall financing efficiency of these low?carbon companies on average tended to change with the scale efficiency. This study has also shown that the scale efficiency was the main constraint influencing the financing efficiency of low?carbon companies in China over the period. Our results are robust and have significant implications for policy makers and corporate managers

Modification of Transition-Metal Redox by Interstitial Water in Hexacyanometalate Electrodes for Sodium-Ion Batteries.

A sodium-ion battery (SIB) solution is attractive for grid-scale electrical energy storage. Low-cost hexacyanometalate is a promising electrode material for SIBs because of its easy synthesis and open framework. Most hexacyanometalate-based SIBs work with aqueous electrolyte, and interstitial water in the material has been found to strongly affect the electrochemical profile, but the mechanism remains elusive. Here we provide a comparative study of the transition-metal redox in hexacyanometalate electrodes with and without interstitial water based on soft X-ray absorption spectroscopy and theoretical calculations. We found distinct transition-metal redox sequences in hydrated and anhydrated NaxMnFe(CN)6·zH2O. The Fe and Mn redox in hydrated electrodes are separated and are at different potentials, leading to two voltage plateaus. On the contrary, mixed Fe and Mn redox in the same potential range is found in the anhydrated system. This work reveals for the first time how transition-metal redox in batteries is strongly affected by interstitial molecules that are seemingly spectators. The results suggest a fundamental mechanism based on three competing factors that determine the transition-metal redox potentials. Because most hexacyanometalate electrodes contain water, this work directly reveals the mechanism of how interstitial molecules could define the electrochemical profile, especially for electrodes based on transition-metal redox with well-defined spin states

PatchGT: Transformer over Non-trainable Clusters for Learning Graph Representations

Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision transformer, which applies to image patches, we propose a new Transformer-based graph neural network: Patch Graph Transformer (PatchGT). Unlike previous transformer-based models for learning graph representations, PatchGT learns from non-trainable graph patches, not from nodes directly. It can help save computation and improve the model performance. The key idea is to segment a graph into patches based on spectral clustering without any trainable parameters, with which the model can first use GNN layers to learn patch-level representations and then use Transformer to obtain graph-level representations. The architecture leverages the spectral information of graphs and combines the strengths of GNNs and Transformers. Further, we show the limitations of previous hierarchical trainable clusters theoretically and empirically. We also prove the proposed non-trainable spectral clustering method is permutation invariant and can help address the information bottlenecks in the graph. PatchGT achieves higher expressiveness than 1-WL-type GNNs, and the empirical study shows that PatchGT achieves competitive performances on benchmark datasets and provides interpretability to its predictions. The implementation of our algorithm is released at our Github repo: https://github.com/tufts-ml/PatchGT.Comment: 25 pages, 10 figure

Computing solution space properties of combinatorial optimization problems via generic tensor networks

We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given size, and enumeration and sampling of solutions of a given size. Using the independent set problem as an example, we show how all these solution space properties can be computed in the unified approach of generic tensor networks. We demonstrate the versatility of this computational tool by applying it to several examples, including computing the entropy constant for hardcore lattice gases, studying the overlap gap properties, and analyzing the performance of quantum and classical algorithms for finding maximum independent sets.Comment: Github repo: https://github.com/QuEraComputing/GenericTensorNetworks.j

CD44ICD promotes breast cancer stemness via PFKFB4-mediated glucose metabolism.

CD44 is a single-pass cell surface glycoprotein that is distinguished as the first molecule used to identify cancer stem cells in solid tumors based on its expression. In this regard, the CD44high cell population demonstrates not only the ability to regenerate a heterogeneous tumor, but also the ability to self-regenerate when transplanted into immune-deficient mice. However, the exact role of CD44 in cancer stem cells remains unclear in part because CD44 exists in various isoforms due to alternative splicing. Methods: Gain- and loss-of-function methods in different models were used to investigate the effects of CD44 on breast cancer stemness. Cancer stemness was analyzed by detecting SOX2, OCT4 and NANOG expression, ALDH activity, side population (SP) and sphere formation. Glucose consumption, lactate secretion and reactive oxygen species (ROS) levels were detected to assess glycolysis. Western blot, immunohistochemical staining, ELISA and TCGA dataset analysis were performed to determine the association of CD44ICD and PFKFB4 with clinical cases. A PFKFB4 inhibitor, 5MPN, was used in a xenograft model to inhibit breast cancer development. Results: In this report, we found that the shortest CD44 isoform (CD44s) inhibits breast cancer stemness, whereas the cleaved product of CD44 (CD44ICD) promotes breast cancer stemness. Furthermore, CD44ICD interacts with CREB and binds to the promoter region of PFKFB4, thereby regulating PFKFB4 transcription and expression. The resultant PFKFB4 expression facilitates the glycolysis pathway (vis-à-vis oxidative phosphorylation) and promotes stemness of breast cancer. In addition, we found that CD44ICD and PFKFB4 expressions are generally up-regulated in the tumor portion of breast cancer patient samples. Most importantly, we found that 5MPN (a selective inhibitor of PFKFB4) suppresses CD44ICD-induced tumor development. Conclusion: CD44ICD promotes breast cancer stemness via PFKFB4-mediated glycolysis, and therapies that target PFKFB4 (e.g., 5MPN therapy) may lead to improved outcomes for cancer patients

Reversible resistance switching properties in Ti-doped polycrystalline Ta2O5 thin films

Unipolar reversible resistance switching effects were found in 5 at% Ti-doped polycrystalline Ta 2O 5 films with the device structure of Pt/Ti-Ta 2O 5/Pt. Results suggest that the recovery/rupture of the conductive filaments which are involved in the participation of oxygen vacancies and electrons leads to the resistance switching process. Tidoped Ta 2O 5 thin films possess higher resistance whether in low-resistance state or high-resistance state and higher resistance switching ratio than Ta 2O 5 thin films, where Ti addition plays an important role in the resistance switching process by suppressing the migration of oxygen vacancies via forming an electrically inactive Ti/O-vacancy complex. Excellent retention properties of the high and low resistances under constant stress of applied voltage were obtained

SnarkFold: Efficient SNARK Proof Aggregation from Split Incrementally Verifiable Computation

The succinct non-interactive argument of knowledge (SNARK) technique is widely used in blockchain systems to replace the costly on-chain computation with the verification of a succinct proof. However, when dealing with multiple proofs, most existing applications require each proof to be independently verified, resulting in a heavy load on nodes and high transaction fees for users. To improve the efficiency of verifying multiple proofs, we introduce SnarkFold, a universal SNARK-proof aggregation scheme based on incrementally verifiable computation (IVC). Unlike previous proof aggregation approaches based on inner product arguments, which have a logarithmic proof size and verification cost, SnarkFold achieves constant verification time and proof size. One core technical advance in SnarkFold, of independent interest, is the ``split IVC\u27\u27: rather than using one running instance to fold/accumulate the computation, we employ two (or more) running instances of different types in the recursive circuit to avoid transferring into the same structure. This distinguishing feature is particularly well-suited for proof aggregation scenarios, as constructing arithmetic circuits for pairings can be expensive. We further demonstrate how to fold Groth16 proofs with our SnarkFold. With some further optimizations, SnarkFold achieves the highest efficiency among all approaches