Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms; leading algorithms use a near-term quantum computer to solve the ground state properties of molecules, simulate dynamics of different quantum systems, and so on. In the literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular and efficacious 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 finally 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 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, limited-memory Broyden—Fletcher—Goldfarb—Shanno bound, and sequential least squares programming optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and Powell's conjugate direction algorithm for unconstrained optimization (POWELL) perform most efficiently among the gradient-free methods, in noisy quantum circuit conditions, simultaneous perturbation stochastic approximation, POWELL, and COBYLA are among the best-performing optimizers.
Let Fq denote the finite field of order q, let m1, m2, · · · , m ℓ be positive integers satisfying gcd(mi, q) = 1 for 1 ≤ i ≤ ℓ, and let n = m1 + m2 + · · · + m ℓ . Let Λ = (λ1, λ2, · · · , λ ℓ ) be fixed, where λ1, λ2, · · · , λ ℓ are non-zero elements of Fq. In this paper, we study the algebraic structure of Λ-multi-twisted codes of length n over Fq and their dual codes with respect to the standard inner product on F n q . We provide necessary and sufficient conditions for the existence of a self-dual Λ-multi-twisted code of length n over Fq, and obtain enumeration formulae for all self-dual and self-orthogonal Λ-multi-twisted codes of length n over Fq. We also derive some sufficient conditions under which a Λ-multi-twisted code is LCD. We determine the parity-check polynomial of all Λ-multi-twisted codes of length n over Fq and obtain a BCH type bound on their minimum Hamming distances. We also determine generating sets of dual codes of some Λ-multi-twisted codes of length n over Fq from the generating sets of the codes. Besides this, we provide a trace description for all Λ-multi-twisted codes of length n over Fq 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.Theorem and the results derived in Ling and Solé [12]. They also obtained an improved lower bound on their minimum Hamming distances. Güneri et al. [6] decomposed GQC codes as direct sums of concatenated codes, which leads to a trace formula and a minimum distance bound for GQC codes. Jia [9] decomposed quasi-twisted (QT) codes and their dual codes over finite fields to a direct sum of linear codes over rings, and provided a method to construct quasi-twisted codes by using generalized discrete Fourier transform. Saleh and Esmaeili [16] gave some sufficient conditions under which a quasi-twisted code is LCD. In a recent work, Aydin and Halilovic [1] introduced multi-twisted (MT) codes as generalization of quasi-twisted codes. They studied basic properties of 1-generator multi-twisted codes and provided a lower bound on their minimum Hamming distances. The family of multi-twisted codes is much broader as compared to quasi-twisted and constacyclic codes.Throughout this paper, let F q denote the finite field of order q, and let Λ = (λ 1 , λ 2 , · · · , λ ℓ ) be fixed, where λ 1 , λ 2 , · · · , λ ℓ are non-zero elements of F q . Let n = m 1 + m 2 + · · ·+ m ℓ , where m 1 , m 2 , · · · , m ℓ are positive integers coprime to q. The main aim of this paper is to study the algebraic structure of Λ-multi-twisted codes of length n over F q and their dual codes with respect to the standard inner product on F n q . Enumeration formulae for their two interesting subclasses, viz. self-dual and self-orthogonal codes, are also obtained. These enumeration formulae are useful in the determination of complete lists of inequivalent self-dual and self-orthogonal Λ-multitwisted codes [7, Section 9.6...
In this paper, we find a necessary and sufficient condition for multi-twisted Reed-Solomon codes to be MDS. Further, we obtain necessary conditions for the existence of multi-twisted RS codes with zero and one-dimensional hulls.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.