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The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{\epsilon^2})$ to $O(\frac{1}{\epsilon^2})$ for a system of $N$ qubits and accuracy $\epsilon$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{\epsilon^2})$ to $O(\frac{N^3}{\epsilon^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem.

Our primary objective is to conduct a brief survey of various classical and quantum neural net sequence models, which includes self-attention and recurrent neural networks, with a focus on recent quantum approaches proposed to work with near-term quantum devices, while exploring some basic enhancements for these quantum models. We re-implement a key representative set of these existing methods, adapting an image classification approach using quantum self-attention to create a quantum hybrid transformer that works for text and image classification, and applying quantum self-attention and quantum recurrent neural networks to natural language processing tasks. We also explore different encoding techniques and introduce positional encoding into quantum self-attention neural networks leading to improved accuracy and faster convergence in text and image classification experiments. This paper also performs a comparative analysis of classical self-attention models and their quantum counterparts, helping shed light on the differences in these models and their performance., Comment: 6 pages, 10 figures, accepted as a COMSNETS paper

A complete accounting of nearby objects -- from the highest-mass white dwarf progenitors down to low-mass brown dwarfs -- is now possible, thanks to an almost complete set of trigonometric parallax determinations from Gaia, ground-based surveys, and Spitzer follow-up. We create a census of objects within a Sun-centered sphere of 20-pc radius and check published literature to decompose each binary or higher-order system into its separate components. The result is a volume-limited census of $\sim$3,600 individual star formation products useful in measuring the initial mass function across the stellar ($<8 M_\odot$) and substellar ($\gtrsim 5 M_{Jup}$) regimes. Comparing our resulting initial mass function to previous measurements shows good agreement above 0.8$M_\odot$ and a divergence at lower masses. Our 20-pc space densities are best fit with a quadripartite power law, $\xi(M) = dN/dM \propto M^{-\alpha}$ with long-established values of $\alpha = 2.3$ at high masses ($0.55 < M < 8.00 M_\odot$) and $\alpha = 1.3$ at intermediate masses ($0.22 < M < 0.55 M_\odot$), but at lower masses we find $\alpha = 0.25$ for $0.05 < M <0.22 M_\odot$ and $\alpha = 0.6$ for $0.01 < M < 0.05 M_\odot$. This implies that the rate of production as a function of decreasing mass diminishes in the low-mass star/high-mass brown dwarf regime before increasing again in the low-mass brown dwarf regime. Correcting for completeness, we find a star to brown dwarf number ratio of, currently, 4:1, and an average mass per object of 0.41 $M_\odot$., Comment: Accepted for publication in The Astrophysical Journal Supplement Series. 123 pages with four ancillary files

H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over direct mapping and allows quantum simulation of the HMO model for systems with up to 2^N conjugated centers in N qubits. The transformation of the H\"uckel Hamiltonian to qubit space is achieved by two different strategies: a machine-learning-assisted transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated {\pi}-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. The higher excited states of large systems, however, are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C_{60} fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are system-agnostic and hence are easily adaptable to similar problems of different complexity in other fields of research.

Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space provides us with a series of Pauli strings and the energy calculation involves the evaluation of the expectation values of all these individual strings. This introduces a major bottleneck for applications of VQEs in quantum chemistry. Unlike the fermionic Hamiltonian, the terms in a qubit Hamiltonian are additive and the present paper exploits this property to describe a new approach for extracting information from the partial qubit Hamiltonian of simple molecules to design more efficient variational quantum eigensolvers. In the partial (qubit) Hamiltonian approach (PHA), the qubit Hamiltonian is studied term-by-term to understand their relative contributions to the overall energy and a partial Hamiltonian is constructed with fewer Pauli strings that can resolve the entire Hamiltonian. With PHA, we can simulate molecules at a much lower computational cost with a truncated Hamiltonian. Additionally, the outcomes of the measurements with PHA quench the error due to noise introduced by the quantum circuits. We have also demonstrated the application of PHA as an initialization technique, where the simple partial Hamiltonian can be used to find a suitable initial state for a more complex system. The results of this study have the potential to demonstrate the potential advancement in the field of quantum computing and its implementation in quantum chemistry.

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms. In literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as Hydrogen, Lithium Hydride, Beryllium Hydride, water, and Hydrogen Fluoride. The errors in the ground-state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster (UCC) ansatz for simulations, and the number of qubits varied from two, starting from the Hydrogen molecule to ten qubits, in Hydrogen Fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno bound (L_BFGS)B), and sequential least squares programming (SLSQP) optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and POWELL perform most efficiently among the gradient-free methods. However, in noisy quantum circuit conditions, Simultaneous Perturbation Stochastic Approximation (SPSA), POWELL, and COBYLA are among the best-performing optimizers.

In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. In particular, we introduce a new class of MDS double-twisted Reed-Solomon codes $\mathcal{C}_{\bm \alpha, \bm t, \bm h, \bm \eta}$ with twists $\bm t = (1, 2)$ and hooks $\bm h = (0, 1)$ over the finite field $\mathbb{F}_q$, providing a non-trivial example over $\mathbb{F}_{16}$ and enumeration over the finite fields of size up to 17. Moreover, we obtain necessary conditions for the existence of multi-twisted Reed-Solomon codes with small dimensional hull. Consequently, we derive conditions for the existence of MDS multi-twisted Reed-Solomon codes with small dimensional hull., Comment: 19 pages

In order to design a more potent and effective chemical entity, it is essential to identify molecular structures with the desired chemical properties. Recent advances in generative models using neural networks and machine learning are being widely used by many emerging startups and researchers in this domain to design virtual libraries of drug-like compounds. Although these models can help a scientist to produce novel molecular structures rapidly, the challenge still exists in the intelligent exploration of the latent spaces of generative models, thereby reducing the randomness in the generative procedure. In this work we present a manifold traversal with heuristic search to explore the latent chemical space. Different heuristics and scores such as the Tanimoto coefficient, synthetic accessibility, binding activity, and QED drug-likeness can be incorporated to increase the validity and proximity for desired molecular properties of the generated molecules. For evaluating the manifold traversal exploration, we produce the latent chemical space using various generative models such as grammar variational autoencoders (with and without attention) as they deal with the randomized generation and validity of compounds. With this novel traversal method, we are able to find more unseen compounds and more specific regions to mine in the latent space. Finally, these components are brought together in a simple platform allowing users to perform search, visualization and selection of novel generated compounds., Comment: 5 pages, 2 figures, Presented in First workshop on Applied Deep Generative Networks - ECAI 2020 ("link for the workshop: https://sites.google.com/view/adgn-20/home")

Wikipedia's contents are based on reliable and published sources. To this date, relatively little is known about what sources Wikipedia relies on, in part because extracting citations and identifying cited sources is challenging. To close this gap, we release Wikipedia Citations, a comprehensive dataset of citations extracted from Wikipedia. A total of 29.3M citations were extracted from 6.1M English Wikipedia articles as of May 2020, and classified as being to books, journal articles or Web contents. We were thus able to extract 4.0M citations to scholarly publications with known identifiers -- including DOI, PMC, PMID, and ISBN -- and further equip an extra 261K citations with DOIs from Crossref. As a result, we find that 6.7% of Wikipedia articles cite at least one journal article with an associated DOI, and that Wikipedia cites just 2% of all articles with a DOI currently indexed in the Web of Science. We release our code to allow the community to extend upon our work and update the dataset in the future.

This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying code-based cryptography. Here, we briefly describe the first scheme of code based public key cryptosystems given by R. J. McEliece in 1978 and its improved version given by H. Niederreiter in 1986. We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD). Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix. This report elaborates a key encapsulation mechanism (KEM), namely Classic McEliece, based on algebraic coding theory to establish a symmetric key for two users., Comment: 45 pages, 2 figures

Let $\mathbb{F}_{q}$ denote the finite field of order $q,$ let $m_1,m_2,\cdots,m_{\ell}$ be positive integers satisfying $\gcd(m_i,q)=1$ for $1 \leq i \leq \ell,$ and let $n=m_1+m_2+\cdots+m_{\ell}.$ Let $\Lambda=(\lambda_1,\lambda_2,\cdots,\lambda_{\ell})$ be fixed, where $\lambda_1,\lambda_2,\cdots,\lambda_{\ell}$ are non-zero elements of $\mathbb{F}_{q}.$ In this paper, we study the algebraic structure of $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ and their dual codes with respect to the standard inner product on $\mathbb{F}_{q}^n.$ We provide necessary and sufficient conditions for the existence of a self-dual $\Lambda$-multi-twisted code of length $n$ over $\mathbb{F}_{q},$ and obtain enumeration formulae for all self-dual and self-orthogonal $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}.$ We also derive some sufficient conditions under which a $\Lambda$-multi-twisted code is LCD. We determine the parity-check polynomial of all $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ from the generating sets of the codes. Besides this, we provide a trace description for all $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ by viewing these codes as direct sums of certain concatenated codes, which leads to a method to construct these codes. We also obtain a lower bound on their minimum Hamming distances using their multilevel concatenated structure.