Related papers: Average-Case Quantum Query Complexity
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
We consider the scenario where Alice wants to send a secret (classical) $n$-bit message to Bob using a classical key, and where only one-way transmission from Alice to Bob is possible. In this case, quantum communication cannot help to…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
Given a classical query algorithm as a decision tree, when does there exist a quantum query algorithm with a speed-up over the classical one? We provide a general construction based on the structure of the underlying decision tree, and…
A quantum algorithm to solve the parity problem is better than its most efficient classical counter- part with a separation that is polynomial in the number of queries. This was shown by E. Bernstein and U. Vazirani and was one of the…
Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a…
It is shown that a quantum computer can test the convexity and monotonicity of a given function exponentially more efficiently than a classical computer. This establishes another prominent example that showcases the potential of quantum…
The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size $n$ into smaller subproblems (say, $a$ copies of size $n/b$ each), along with some auxiliary work of cost…
Although classical computing has excelled in a wide range of applications, there remain problems that push the limits of its capabilities, especially in fields like cryptography, optimization, and materials science. Quantum computing…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the…
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm.…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
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.
An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various…
We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…
Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the…