Related papers: Upper bounds on quantum query complexity inspired …
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 present general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Our results are based on the adversary method of Ambainis.
We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…
Harry Buhrman et al gave an Omega(sqrt n) lower bound for monotone graph properties in the adjacency matrix query model. Their proof is based on the polynomial method. However for some properties stronger lower bounds exist. We give an…
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this…
Quantum computing has shown promise for solving complex optimization problems in databases, such as join ordering and index selection. Prior work often submits formulated problems directly to black-box quantum or quantum-inspired solvers…
The complex systems with edge computing require a huge amount of multi-feature data to extract appropriate insights for their decision making, so it is important to find a feasible feature selection method to improve the computational…
We examine the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}^N in the black-box model. We show that, in the black-box model, the exponential quantum speed-up obtained for partial functions…
Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we say that x_i is an \epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
The standard model of quantum circuits assumes operations are applied in a fixed sequential "causal" order. In recent years, the possibility of relaxing this constraint to obtain causally indefinite computations has received significant…
The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
In the $k$-junta testing problem, a tester has to efficiently decide whether a given function $f:\{0,1\}^n\rightarrow \{0,1\}$ is a $k$-junta (i.e., depends on at most $k$ of its input bits) or is $\epsilon$-far from any $k$-junta. Our main…
Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory…
The textbook adversary bound for function evaluation states that to evaluate a function $f\colon D\to C$ with success probability $\frac{1}{2}+\delta$ in the quantum query model, one needs at least $\left( 2\delta -\sqrt{1-4\delta^2}…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
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…