相关论文: A New Algorithm for Computing $\alpha$-Capacity

In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power…

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $\alpha = m/n$ stays finite. Using exact but non-rigorous methods…

While time complexity and space complexity of an algorithm helps to determine its efficiency when time or space needs to be optimized respectively, they fail to determine the more efficient algorithm when time and space both need to be…

This paper characterizes the capacity region of Gaussian MIMO broadcast channels (BCs) with per-antenna power constraint (PAPC). While the capacity region of MIMO BCs with a sum power constraint (SPC) was extensively studied, that under…

We consider the classical problem of sequential resource allocation where a decision maker must repeatedly divide a budget between several resources, each with diminishing returns. This can be recast as a specific stochastic optimization…

We propose an iterative method for approximately computing the capacity of discrete memoryless channels, possibly under additional constraints on the input distribution. Based on duality of convex programming, we derive explicit upper and…

The capacity of a channel can usually be characterized as a maximization of certain entropic quantities. From a practical point of view it is of primary interest to not only compute the capacity value, but also to find the corresponding…

Consider a polynomial optimisation problem, whose instances vary continuously over time. We propose to use a coordinate-descent algorithm for solving such time-varying optimisation problems. In particular, we focus on relaxations of…

This paper proposes two low-complexity iterative algorithms to compute the capacity of a single-user multiple-input multiple-output channel with per-antenna power constraint. The first method results from manipulating the optimality…

Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…

By considering quantum computation as a communication process, we relate its efficiency to a communication capacity. This formalism allows us to rederive lower bounds on the complexity of search algorithms. It also enables us to link the…

We present an optimized implementation of the Blahut-Arimoto algorithm via GPU parallelization, which we use to obtain improved upper bounds on the capacity of the binary deletion channel. In particular, our results imply that the capacity…

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…

Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…

Compressed Counting (CC) was recently proposed for very efficiently computing the (approximate) $\alpha$th frequency moments of data streams, where $0<\alpha <= 2$. Several estimators were reported including the geometric mean estimator,…

Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…

In many applications one wants to identify identical subtrees of a program syntax tree. This identification should ideally be robust to alpha-renaming of the program, but no existing technique has been shown to achieve this with good…

We present a general framework for determining the power-efficiency trade-off relations across arbitrary thermal machines, addressing the lack of unified optimization results stemming from their diverse functionalities (e.g., heat engines,…

We give an explicit algorithm and source code for computing optimal weights for combining a large number N of alphas. This algorithm does not cost O(N^3) or even O(N^2) operations but is much cheaper, in fact, the number of required…

An algorithm for image processing is proposed. The proposed algorithm, which can be viewed as a quantum-classical hybrid algorithm, can transform a low-resolution bitonal image of a character from the set of alphanumeric characters (A-Z,…