Related papers: Super-exponential query complexity reduction via n…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Quantum computers promise a great computational advantage over classical computers, yet currently available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
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…
We discuss the quantum search algorithm using complex queries that has recently been published by Grover (quant-ph/9706005). We recall the algorithm adding some details showing which complex query has to be evaluated. Based on this version…
Suppose, we are given a set of $n$ elements to be clustered into $k$ (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements $u$ and $v$ belong to the same cluster?".…
Finding the minimum value in an unordered database is a common and fundamental task in computer science. However, the optimal classical deterministic algorithm can find the minimum value with a time complexity that grows linearly with the…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled…
In this article, we discuss the implementation of a quantum recommendation system that uses a quantum variant of the k-nearest neighbours algorithm and the Grover algorithm to search for a specific element in unstructured database. In…
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…
We show that any quantum algorithm searching an ordered list of n elements needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries are both necessary and sufficient. This shows that quantum algorithms can achieve only…
Classical verification of quantum learning allows classical clients to reliably leverage quantum computing advantages by interacting with untrusted quantum servers. Yet, current quantum devices available in practice suffers from a variety…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
The paper considers the problem of finding a given substring in a text. It is known that the complexity of a classical search query in an unordered database is linear in the length of the text and a given substring. At the same time,…
We demonstrate that the ability to estimate the relative sign of an arbitrary $n$-qubit quantum state (with real amplitudes), given only $k$ copies of that state, would yield a $kn$-query algorithm for unstructured search. Thus the quantum…
In this paper, we extend a previously presented Grover-based heuristic to tackle general combinatorial optimization problems with linear constraints. We further describe the introduced method as a framework that enables performance…