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We introduce the Hidden Polynomial Function Graph Problem as a natural generalization of an abelian Hidden Subgroup Problem (HSP) where the subgroups and their cosets correspond to graphs of linear functions over the finite field F_p. For…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic…
We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…
In \cite{simon2023algorithms} we introduced four algorithms for the training of neural support vector machines (NSVMs) and demonstrated their feasibility. In this note we introduce neural quantum support vector machines, that is, NSVMs with…
Constraint-solving-based program invariant synthesis takes a parametric invariant template and encodes the (inductive) invariant conditions into constraints. The problem of characterizing the set of all valid parameter assignments is…
A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of…
In complexity theory, there exists a famous unsolved problem whether NP can be P or not. In this paper, we discuss this aspect in SAT (satisfiability) problem, and it is shown that the SAT can be solved in plynomial time by means of quantum…
Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
The hidden subgroup problem ($\mathsf{HSP}$) has been attracting much attention in quantum computing, since several well-known quantum algorithms including Shor algorithm can be described in a uniform framework as quantum methods to address…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
We develop a polynomial time $\Omega\left ( \frac 1R \log R \right)$ approximate algorithm for Max 2CSP-$R$, the problem where we are given a collection of constraints, each involving two variables, where each variable ranges over a set of…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…
While quantum computing has strong potential in data-driven fields, the privacy issue of sensitive or valuable information involved in the quantum algorithm should be considered. Differential privacy (DP), which is a fundamental privacy…
We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we…
This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…