Related papers: Grover search and the no-signaling principle
Grover search is a well-known quantum algorithm that outperforms any classical search algorithm. It is known that quantum correlations such as entanglement are necessary for the power of quantum computation. But entanglement is not the only…
Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the…
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
We consider the problem of deriving the no-signaling condition from the assumption that, as seen from a complexity theoretic perspective, the universe is not an exponential place. A fact that disallows such a derivation is the existence of…
Entanglement lies at the heart of quantum mechanics and has no classical analogue. It is central to the speed up achieved by quantum algorithms over their classical counterparts. The Grover's search algorithm is one such algorithm which…
A quantum computer encodes information in quantum states and runs quantum algorithms to surpass the classical counterparts by exploiting quantum superposition and quantum correlation. Grover's quantum search algorithm is a typical quantum…
Grover's quantum search algorithm can be formulated as a quantum particle randomly walking on the (highly symmetric) complete graph, with one vertex marked by a nonzero potential. From an initial equal superposition, the state evolves in a…
Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key…
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…
We provide a general framework of utilizing the no-signaling principle in derivation of the guessing probability in the minimum-error quantum state discrimination. We show that, remarkably, the guessing probability can be determined by the…
Although strongly regular graphs and the hypercube are not complete, they are "sufficiently complete" such that a randomly walking quantum particle asymptotically searches on them in the same $\Theta(\sqrt{N})$ time as on the complete…
What ultimately fixes the sample cost of quantum learning -- algorithmic ingenuity or physical law? We study this question in an arena where computation, learning, and causality collide. A twist on Grover's search that reflects about an a…
Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence,…
The execution of Grover's quantum search algorithm needs rather limited resources without much fine tuning. Consequently, the algorithm can be implemented in a variety of physical set-ups, which involve wave dynamics but may not need other…
The hybrid quantum-classical learning scheme provides a prominent way to achieve quantum advantages on near-term quantum devices. A concrete example towards this goal is the quantum neural network (QNN), which has been developed to…
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…
Grover's algorithm is one of the most famous algorithms which explicitly demonstrates how the quantum nature can be utilized to accelerate the searching process. In this work, Grover's quantum search problem is mapped to a time-optimal…
Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude…
Grover's algorithm for quantum searching is generalized to deal with arbitrary initial complex amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the marked and unmarked…
We analyze the structure of the so called non-signaling theories respecting relativistic causality but allowing correlations violating bounds imposed by quantum mechanics such as CHSH inequality. We discuss relations among such theories,…