Related papers: Translation-Invariant Quantum Algorithms for Order…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
Quantum algorithms can be analyzed in a query model to compute Boolean functions. Function input is provided in a black box, and the aim is to compute the function value using as few queries to the black box as possible. A repetition code…
Quantum algorithms and circuits can, in principle, outperform the best non-quantum (classical) techniques for some hard computational problems. However, this does not necessarily lead to useful applications. To gauge the practical…
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root.…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
In the field of quantum information, classical optimizers play an important role. From experimentalists optimizing their physical devices to theorists exploring variational quantum algorithms, many aspects of quantum information require the…
A quantum computer has a clear advantage over a classical computer for exhaustive search. The quantum mechanical algorithm for exhaustive search was originally derived by using subtle properties of a particular quantum mechanical operation…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Quantum search is among the most important algorithms in quantum computing. At its core is quantum amplitude amplification, a technique that achieves a quadratic speedup over classical search by combining two global reflections: the oracle,…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
This paper shows that, if we could examine the entire history of a hidden variable, then we could efficiently solve problems that are believed to be intractable even for quantum computers. In particular, under any hidden-variable theory…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…