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Harnessing the full power of nascent quantum processors requires the efficient management of a limited number of quantum bits with finite lifetime. Hybrid algorithms leveraging classical resources have demonstrated promising initial results…
The rapid expansion of biomolecular datasets presents significant challenges for computational biology. Quantum computing emerges as a promising solution to address these complexities. This study introduces a novel quantum framework for…
Signature-based algorithms is a popular kind of algorithms for computing Gr\"obner bases, and many related papers have been published recently. In this paper, no new signature-based algorithms and no new proofs are presented. Instead, a…
An overview on current developments in post quantum cryptography
Studying sequential measurements is of the utmost importance to both the foundational aspects of quantum theory and the practical implementations of quantum technologies, with both of these applications being abstractly described by the…
We propose a novel variational method for solving the sub-graph isomorphism problem on a gate-based quantum computer. The method relies (1) on a new representation of the adjacency matrices of the underlying graphs, which requires a number…
The present paper is concerned with the concept of the one-way quantum computer, beyond binary-systems, and its relation to the concept of stabilizer quantum codes. This relation is exploited to analyze a particular class of quantum…
Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features…
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
Based on the numerical solution of the quantum lattice Boltzmann method in curved space, we predict the onset of a quantized alternating current on curved graphene sheets. Such numerical prediction is verified analytically via a set of…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…
This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…
Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is: how might we use imperfect near-term quantum computers to solve problems of practical value? We…
BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is…
A new basis adaptive algorithm for hybrid quantum-classical platforms is introduced to efficiently find the ground-state (gs) properties of quantum many-body systems. The method addresses limitations of many algorithms, such as Variational…
In 2004, Aaronson introduced the complexity class $\mathsf{PostBQP}$ ($\mathsf{BQP}$ with postselection) and showed that it is equal to $\mathsf{PP}$. Following their line of work, we introduce two new complexity classes. The first,…
Quantum computing is evolving so rapidly that it forces us to revisit, rewrite, and update the foundations of the theory. \emph{Basic Quantum Algorithms} revisits the earliest quantum algorithms. The journey began in 1985 with Deutsch…
We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We…
Despite the practicality of quantile regression (QR), simultaneous estimation of multiple QR curves continues to be challenging. We address this problem by proposing a Bayesian nonparametric framework that generalizes the quantile pyramid…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…