Related papers: Quantum Algorithms for Connectivity and Related Pr…
We introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to…
Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity,…
Span program is a linear-algebraic model of computation which can be used to design quantum algorithms. For any Boolean function there exists a span program that leads to a quantum algorithm with optimal quantum query complexity. In…
We present quantum algorithms for various problems related to graph connectivity. We give simple and query-optimal algorithms for cycle detection and odd-length cycle detection (bipartiteness) using a reduction to st-connectivity.…
In this work, we unify several quantum algorithmic frameworks for boolean functions that are based on the quantum adversary bound. First, we show that the $st$-connectivity framework subsumes the (adaptive/extended) learning graph…
We give a new upper bound on the quantum query complexity of deciding $st$-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation…
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query…
Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity,…
Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and…
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced…
Besides the Hidden Subgroup Problem, the second large class of quantum speed-ups is for functions with constant-sized 1-certificates. This includes the OR function, solvable by the Grover algorithm, the distinctness, the triangle and other…
We introduce a new quantum algorithm for computing the Betti numbers of a simplicial complex. In contrast to previous quantum algorithms that work by estimating the eigenvalues of the combinatorial Laplacian, our algorithm is an instance of…
We present a quantum algorithm for sampling an edge on a path between two nodes s and t in an undirected graph given as an adjacency matrix, and show that this can be done in query complexity that is asymptotically the same, up to log…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
Quantum span program algorithms for function evaluation commonly have reduced query complexity when promised that the input has a certain structure. We design a modified span program algorithm to show these speed-ups persist even without…
Span program is a linear-algebraic model of computation originally proposed for studying the complexity theory. Recently, it has become a useful tool for designing quantum algorithms. In this paper, we present a time-efficient…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device with limited connectivity, and the other is a…