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Linear real-valued computations over distributed datasets are common in many applications, most notably as part of machine learning inference. In particular, linear computations that are quantized, i.e., where the coefficients are…
A new ensemble of structured codes is introduced. These codes are called Quasi Linear Codes (QLC). The QLC's are constructed by taking subsets of linear codes. They have a looser structure compared to linear codes and are not closed under…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
Complex queries for massive data analysis jobs have become increasingly commonplace. Many such queries contain com- mon subexpressions, either within a single query or among multiple queries submitted as a batch. Conventional query…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
The quantum approximate optimization algorithm (QAOA) has rapidly become a cornerstone of contemporary quantum algorithm development. Despite a growing range of applications, only a few results have been developed towards understanding the…
Computational constraints permeate the controller design process, and yet are rarely treated as explicit design constraints. Towards addressing this gap, we propose a quantitative framework that captures the effects of common design…
Two of the major obstacles to achieve quantum computing (QC) are (i) scalability to many qubits and (ii) controlled connectivity between any selected qubits. Using Josephson charge qubits, here we propose an experimentally realizable method…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…
The hopes for scalable quantum computing rely on the "threshold theorem": once the error per qubit per gate is below a certain value, the methods of quantum error correction allow indefinitely long quantum computations. The proof is based…