Related papers: An explanation of the quantum speed up
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future…
We explain the mechanism of the quantum speed-up - quantum algorithms requiring fewer computation steps than their classical equivalent - for a family of algorithms. Bob chooses a function and gives to Alice the black box that computes it.…
In classical problem solving, there is of course correlation between the selection of the problem on the part of Bob (the problem setter) and that of the solution on the part of Alice (the problem solver). In quantum problem solving, this…
The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii)…
Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…
We investigate the reason for the quantum speedup -- quantum algorithms requiring fewer computation steps than their classical counterparts. We extend their representation to the process of setting the problem. The initial measurement…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum…
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…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…