Related papers: An Improved Quantum Scheduling Algorithm
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. For example, edit distance of two strings of length $n$ can be solved in $O(n^2/w)$ time. In a reasonable…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
The problem of scheduling in quantum networks amounts to choosing which entanglement swapping operations to perform to better serve user demand. The choice can be carried out following a variety of criteria (e.g. ensuring all users are…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on $n$ bits for which…
We revisit two well-known algorithmic problems on strings: computing a shortest unique substring (SUS) and a shortest absent substring (SAS) of a string $S$ of length $n$. Both problems admit folklore $\mathcal{O}(n)$-time solutions using…
We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(\log n) qubits for…
Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training…
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…
We consider online algorithms for the $k$-server problem on trees. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, a naive implementation of their algorithm has…
Withdrawn by the author due to irreparable errors. We present a quantum algorithm that in the black-box model performs a search in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a success probability of at least…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
This paper explores Quantum Search on the two dimensional spatial grid. Recent exploration into the topic has devised a solution that runs in O(sqrt(n*ln(n))). This paper explores a new algorithm that gives promise for the O(sqrt(n)) result…
A degenerate string is a sequence of sets of characters. A generalized degenerate (GD) string extends this notion to the sequence of sets of strings, where strings of the same set are of equal length. Finding an exact match for a pattern…
Building quantum devices using fixed operators is a must to simplify the hardware construction. Quantum search engine is not an exception. In this paper, a fixed phase quantum search algorithm that searches for M matches in an unstructured…
How to uses shared entanglement and forward classical communication to remotely prepare an arbitrary (mixed or pure) state has been fascinating quantum information scientists. A constructive scheme has been given by Berry for remotely…
Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the Carmichael function for any integer $N$ with a…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that…