Related papers: Oracles with Costs
Let a Boolean function be available as a black-box (oracle) and one likes to devise an algorithm to test whether it has certain property or it is $\epsilon$-far from having that property. The efficiency of the algorithm is judged by the…
I improve the tight bound on quantum searching by Boyer et al. (quant-ph/9605034) to a matching bound, thus showing that for any probability of success Grovers quantum searching algorithm is optimal. E.g. for near certain success we have to…
The classical algorithms for online learning and decision-making have the benefit of achieving the optimal performance guarantees, but suffer from computational complexity limitations when implemented at scale. More recent sophisticated…
We want to find a marked element out of a black box containing N elements. When the number of marked elements is known this can be done elegantly with Grover's algorithm, a variant of which even gives a correct result with certainty. On the…
We investigate the generalisation of quantum search of unstructured and totally ordered sets to search of partially ordered sets (posets). Two models for poset search are considered. In both models, we show that quantum algorithms can…
Selecting a set of basis states is a common task in quantum computing, in order to increase and/or evaluate their probabilities. This is similar to designing WHERE clauses in classical database queries. Even though one can find heuristic…
Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of…
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 introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition…
We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…
Variational quantum algorithms are a leading candidate for early applications on noisy intermediate-scale quantum computers. These algorithms depend on a classical optimization outer-loop that minimizes some function of a parameterized…
The Grover search algorithm performs an unstructured search of a marked item in a database quadratically faster than classical algorithms and is shown to be optimal. Here, we show that if the search space is divided into two blocks with the…
Quantum Amplitude Amplification (QAA), the generalization of Grover's algorithm, is capable of yielding optimal solutions to combinatorial optimization problems with high probabilities. In this work we extend the conventional 2-dimensional…
The optimal runtime of a quantum computer searching a database is typically cited as the square root of the number of items in the database, which is famously achieved by Grover's algorithm. With parallel oracles, however, it is possible to…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
Grover's algorithm provides a quadratic speedup over classical algorithms for searching unstructured databases and is known to be strictly optimal in oracle query complexity, with tight bounds on its success probability. Although the…