Related papers: Time and Query Optimal Quantum Algorithms Based on…
A recent breakthrough by Ambainis, Balodis, Iraids, Kokainis, Pr\=usis and Vihrovs (SODA'19) showed how to construct faster quantum algorithms for the Traveling Salesman Problem and a few other NP-hard problems by combining in a novel way…
The generalized egg dropping problem is a classic challenge in sequential decision-making. Standard dynamic programming evaluates the minimax minimum number of tests in $\mathcal{O}(K \cdot N^2)$ time. A known approach formulates the…
We consider a classical k-center problem in trees. Let T be a tree of n vertices and every vertex has a nonnegative weight. The problem is to find k centers on the edges of T such that the maximum weighted distance from all vertices to…
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…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
It's the key research topic of signal processing that recognizing genuine targets real time from the disturbed signal which has giant amount of data. A quantum algorithm for pattern recognition of classical signal which has time complexity…
We study the fundamental problem of guessing cryptographic keys, drawn from some non-uniform probability distribution $D$, as e.g. in LPN, LWE or for passwords. The optimal classical algorithm enumerates keys in decreasing order of…
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…
While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a…
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
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,…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
We observe that any $T(n)$ time algorithm (quantum or classical) for several central linear algebraic problems, such as computing $\det(A)$, $tr(A^3)$, or $tr(A^{-1})$ for an $n \times n$ integer matrix $A$, yields a $O(T(n)) + \tilde…
Given the success of deep learning in classical machine learning, quantum algorithms for traditional neural network architectures may provide one of the most promising settings for quantum machine learning. Considering a fully-connected…
We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such…
While the quantum query complexity of $k$-distinctness is known to be $O\left(n^{3/4-1/4(2^k-1)}\right)$ for any constant $k \geq 4$, the best previous upper bound on the time complexity was $\widetilde{O}\left(n^{1-1/k}\right)$. We give a…