Related papers: Testing Permanent Oracles -- Revisited
The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
We give a new quantum circuit approximation of quantum multiplexors based on the idea of complexity theory oracles. As an added bonus, our multiplexor approximation immediately gives a quantum circuit approximation of diagonal unitary…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
We propose a polynomial time $f$-algorithm (a deterministic algorithm which uses an oracle for factoring univariate polynomials over $\mathbb{F}_q$) for computing an isomorphism (if there is any) of a finite dimensional…
Much of reinforcement learning theory is built on top of oracles that are computationally hard to implement. Specifically for learning near-optimal policies in Partially Observable Markov Decision Processes (POMDPs), existing algorithms…
Grover's algorithm, orginally conceived as a means of searching an unordered database, can also be used to extract solutions from the result sets generated by quantum computations. The Grover algorithm exploits the concept of an oracle…
We study the complexity of approximating the permanent of a positive semidefinite matrix $A\in \mathbb{C}^{n\times n}$. 1. We design a new approximation algorithm for $\mathrm{per}(A)$ with approximation ratio $e^{(0.9999 + \gamma)n}$,…
In this paper we present a deterministic polynomial time algorithm for testing if a symbolic matrix in non-commuting variables over $\mathbb{Q}$ is invertible or not. The analogous question for commuting variables is the celebrated…
This dissertation investigates questions arising in the consistent histories formulation of the quantum mechanics of closed systems. Various criteria for approximate consistency are analysed. The connection between the Dowker-Halliwell…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
In this paper, we consider a quantum algorithm for solving the following problem: ``Suppose $f$ is a function given as a black box (that is also called an oracle) and $f$ is invariant under some AND-mask. Examine a property of $f$ by…
We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete/continuous-variable (qubit/qumode) hardware. To illustrate the oracle's representation-theoretic power and near-term…
This paper explores the problem of quantum measurement complexity. In computability theory, the complexity of a problem is determined by how long it takes an effective algorithm to solve it. This complexity may be compared to the difficulty…
The search for "a quantum needle in a quantum haystack" is a metaphor for the problem of finding out which one of a permissible set of unitary mappings---the oracles---is implemented by a given black box. Grover's algorithm solves this…