Related papers: Quantum Time-Space Tradeoffs for Matrix Problems

Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…

In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…

Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…

We develop an extension of recently developed methods for obtaining time-space tradeoff lower bounds for problems of learning from random test samples to handle the situation where the space of tests is signficantly smaller than the space…

Obeying constraints imposed by classical physics, we give optimal fine-grained algorithms for matrix multiplication and problems involving graphs and mazes, where all calculations are done in 3-dimensional space. We assume that whatever the…

We consider the problem of preprocessing an $n\times n$ matrix $\mathbf{M}$, and supporting queries that, for any vector $v$, returns the matrix-vector product $\mathbf{M} v$. This problem has been extensively studied in both theory and…

Since Harrow, Hassidim, and Lloyd (2009) showed that a system of linear equations with $N$ variables and condition number $\kappa$ can be solved on a quantum computer in $\operatorname{poly}(\log(N), \kappa)$ time, exponentially faster than…

Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…

In this work, we establish the first separation between computation with bounded and unbounded space, for problems with short outputs (i.e., working memory can be exponentially larger than output size), both in the classical and the quantum…

We describe two algorithms for multiplying n x n matrices using time and energy n^2 polylog(n) under basic models of classical physics. The first algorithm is for multiplying integer-valued matrices, and the second, quite different…

We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves…

This work explores fundamental modeling and algorithmic issues arising in the well-established MapReduce framework. First, we formally specify a computational model for MapReduce which captures the functional flavor of the paradigm by…

A tight lower bound for required I/O when computing an ordinary matrix-matrix multiplication on a processor with two layers of memory is established. Prior work obtained weaker lower bounds by reasoning about the number of segments needed…

Branching programs are quite popular for studying time-space lower bounds. Bera et al. recently introduced the model of generalized quantum branching program aka. GQBP that generalized two earlier models of quantum branching programs. In…

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…

For a decision problem from coding theory, we prove a quadratic expected time-space tradeoff of the form $\eT\eS=\Omega(\tfrac{n^2}{q})$ for $q$-way deterministic decision branching programs, where $q\geq 2$. Here $\eT$ is the expected…