Related papers: Exact quantum query complexity of $\rm{EXACT}_{k,l…
Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…
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…
The $k$'th frequency moment of a sequence of integers is defined as $F_k = \sum_j n_j^k$, where $n_j$ is the number of times that $j$ occurs in the sequence. Here we study the quantum complexity of approximately computing the frequency…
Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in…
We describe a quantum black-box network computing the majority of N bits with zero-sided error eps using only 2N/3 + O(sqrt{N (log log N + log 1/eps)}) queries: the algorithm returns the correct answer with probability at least 1 - eps, and…
The quantum hybrid algorithm has become a very promising and speedily method today for solving the larger-scale optimization in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
We identify "proper quantum computation" with computational processes that cannot be efficiently simulated on a classical computer. For optical quantum computation, we establish "no-go" theorems for classes of quantum optical experiments…
Approximate Counting refers to the problem where we are given query access to a function $f : [N] \to \{0,1\}$, and we wish to estimate $K = #\{x : f(x) = 1\}$ to within a factor of $1+\epsilon$ (with high probability), while minimizing the…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
In this note we investigate the relationship between worst-case quantum query complexity and average-case classical query complexity. Specifically, we show that if a quantum computer can evaluate a total Boolean function f with bounded…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
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…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
The question of answering queries over ML predictions has been gaining attention in the database community. This question is challenging because the cost of finding high quality answers corresponds to invoking an oracle such as a human…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…