Related papers: Origin of the quantum speed-up
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…
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…
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…
The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the…
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…
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…
Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a…
Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between…
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.…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary…
Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible…
Consider two agents, Alice and Bob, each of whom takes a quantum input, operates on a shared quantum system $K$, and produces a quantum output. Alice and Bob's operations may commute, in the sense that the joint input-output behaviour is…
Quantum physics exhibits remarkable distinguishing characteristics. For example, it gives only probabilistic predictions (non-determinism) and does not allow copying of unknown state (no-cloning). Quantum correlations may be stronger than…
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…
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…
We present a formalism that captures the process of proving quantum superiority to skeptics as an interactive game between two agents, supervised by a referee. Bob, is sampling from a classical distribution on a quantum device that is…
An open quantum system leaks information into its environment. In some circumstances it is possible for an observer, say Alice, to recover that information, as a classical measurement record, in a variety of different ways, using different…