Related papers: Quantum Speedup Based on Classical Decision Trees
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
We study quantum property testing for directed graphs with maximum in-degree and out-degree bounded by some universal constant $d$. For a proximity parameter $\varepsilon$, we show that any property that can be tested with…
The query model offers a concrete setting where quantum algorithms are provably superior to randomized algorithms. Beautiful results by Bernstein-Vazirani, Simon, Aaronson, and others presented partial Boolean functions that can be computed…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
We will show that if there exists a quantum query algorithm that exactly computes some total Boolean function f by making T queries, then there is a classical deterministic algorithm A that exactly computes f making O(T^3) queries. The best…
We present a bounded-error quantum algorithm for evaluating Min-Max trees. For a tree of size N our algorithm makes N^{1/2+o(1)} comparison queries, which is close to the optimal complexity for this problem.
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
We introduce a notion of the quantum query complexity of a certificate structure. This is a formalisation of a well-known observation that many quantum query algorithms only require the knowledge of the disposition of possible certificates…
Let $A$ be an $s$-sparse Hermitian matrix, $f(x)$ be a univariate function, and $i, j$ be two indices. In this work, we investigate the query complexity of approximating $\bra{i} f(A) \ket{j}$. We show that for any continuous function…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
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…
Quantum computing is a popular topic in computer science, which has recently attracted many studies in various areas such as machine learning and network. However, the topic of quantum data structures seems neglected. There is an open…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…