[PDF] Top 20 Quantum algorithms and lower bounds for convex optimization
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Quantum algorithms and lower bounds for convex optimization
... the quantum Fourier transform to compute the gradient of a function using O(1) ˜ evaluation queries ([11, 15]) sug- gests the possibility of replacing the subgradient procedure with a faster quantum ... See full document
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Beyond the Regret Minimization Barrier: Optimal Algorithms for Stochastic Strongly-Convex Optimization
... Online convex optimization was introduced by Zinkevich ...Optimal lower bounds for the convex case, even in the stochastic setting, of Ω( √ T ) are simple and given in the book by ... See full document
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Convex optimization using quantum oracles
... continuous optimization paradigms is convex optimization, which optimizes a convex function over a convex set that is given explicitly (by a set of constraints) or implicitly (by an ... See full document
29
Polynomial Degree and Lower Bounds in Quantum Complexity: Collision and Element Distinctness with Small Range
... Quantum computing provides speedups for many search problems. The most famous example is Grover’s algorithm [14], which computes OR of N variables with O( √ N) queries. Other examples include counting [8], ... See full document
10
On Lower and Upper Bounds in Smooth and Strongly Convex Optimization
... address lower bounds (see Higham and Tisseur ...deriving lower bounds on the convergence rate of optimization algorithms which employed heavy machinery from the field of extremal ... See full document
51
Approximating the AND-OR Tree
... circuit lower bounds and oracle separations of complexity classes [27, 41, 5, 20, 21, ...tight lower bounds on quantum query complexity, ...are lower bounds in relevant ... See full document
11
Hierarchy of efficiently computable and faithful lower bounds to quantum discord
... a lower bound to the standard quantum ...a quantum state can be locally broad- cast, we generalize the surprisal of measurement recover- ability to obtain a hierarchy of numerically computable ... See full document
9
Analysis of Langevin Monte Carlo via Convex Optimization
... get bounds on the KL diver- gence from π to the iterates of ...strongly convex case and get tighter ...known bounds between π and ULA in Wasserstein distance and the total variation distance but with ... See full document
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Optimization Algorithms in Wireless and Quantum Communications
... of quality of the broadcast system at hand. The overall amount of the information which equals the summation of the amount of information transmitted to each user is often called the sum-rate. The sum-rate capacity is ... See full document
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Optimal Quantum Sample Complexity of Learning Algorithms
... that if a learner gets ε-close to the minimal error, then it will have to learn Ω(d) bits of information about the distribution (i.e., about a). Hence the first step of the argument remains the same. The second step of ... See full document
36
Applying Quantum Optimization Algorithms for Linear Programming
... In other words, linear programming is a technique used to optimize a linear objective function, subject to linear equality and linear inequality constraints. The feasible region is a convex polytope, defined as ... See full document
6
Quantum SDP-Solvers: Better upper and lower bounds
... a quantum algorithm for approximating Tr(Aρ) efficiently (see also Appendix A for a classical ...a quantum computer and on a classical computer (of course, resulting in different ...obtain quantum ... See full document
69
Interleave Variational Optimization with Monte Carlo Sampling: A Tale of Two Approximate Inference Paradigms
... variational bounds with importance sampling from the very beginning, and provides an instance-specific balance designed to give rapid anytime ...interleaves optimization of variational upper bounds ... See full document
8
Monotone Projection Lower Bounds from Extended Formulation Lower Bounds
... exponential lower bound on arbitrary extended formulations of several different ...their lower bound on the cut polytope ...such lower bounds on several other polytopes; we use his ... See full document
15
Optimal bounds for the Neuman Sándor mean in terms of the first Seiffert and quadratic means
... and lower bounds for the Neuman-Sándor mean M(a, b) in terms of the geometric convex combinations of the first Seiffert mean P(a, b) and the quadratic mean Q(a, ... See full document
13
The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean
... Wang, “The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means,” Abstract and Applied Analysis, vol.. Long, “Best possible inequali[r] ... See full document
7
Lower Bounds for Data Structures with Space Close to Maximum Imply Circuit Lower Bounds
... briefly lower bounds for dynamic data ...update) algorithms whose time is also taken into ...known lower bounds are Ω(log ...strong lower bound for such “half-dynamic” data ... See full document
9
Lower Bounds for Generalized Regulators
... This thesis demonstrates how a technique of Friedman and Skoruppa [8] can be generalized. Before proceeding to the generalization, we first review their paper. Friedman and Skoruppa proved lower bounds for ... See full document
86
The Optimal Convex Combination Bounds for Seiffert's Mean
... Wang, “The optimal upper and lower power mean bounds for a convex combination of the arithmetic and logarithmic means,” Abstract and Applied Analysis, vol.. Long, “Best possible inequali[r] ... See full document
9
Quantum-Walk Speedup of Backtracking Algorithms
... The algorithms which achieve the bounds of Theorems ...discrete-time quantum walk to find a marked vertex within the tree produced by the classical backtracking algorithm, corresponding to a partial ... See full document
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