Related papers: Span-program-based quantum algorithms for graph bi…
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…
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…
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…
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 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,…
Recently, span programs have been shown to be equivalent to quantum query algorithms. It is an open problem whether this equivalence can be utilized in order to come up with new quantum algorithms. We address this problem by providing span…
The formula-evaluation problem is defined recursively. A formula's evaluation is the evaluation of a gate, the inputs of which are themselves independent formulas. Despite this pure recursive structure, the problem is combinatorially…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
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…
Span programs are an important model of quantum computation due to their tight correspondence with quantum query complexity. For any decision problem $f$, the minimum complexity of a span program for $f$ is equal, up to a constant factor,…
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.…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
An important family of span programs, st-connectivity span programs, have been used to design quantum algorithms in various contexts, including a number of graph problems and formula evaluation problems. The complexity of the resulting…
Span programs characterize the quantum query complexity of binary functions $f:\{0,\ldots,\ell\}^n \to \{0,1\}$ up to a constant factor. In this paper we generalize the notion of span programs for functions with non-binary input/output…
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…
We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion,…
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…
We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow…
Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…