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The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in…
This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of…
A classical analogue of Deutsch and Jozsa's algorithm is given and its implications on quantum computing is discussed
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
We consider online algorithms with respect to the competitive ratio. Here, we investigate quantum and classical one-way automata with non-constant size of memory (streaming algorithms) as a model for online algorithms. We construct problems…
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
We show that a separation between the class of all problems that can efficiently be solved on a quantum computer and those solvable using probabilistic classical algorithms in polynomial time implies the generalized contextuality of quantum…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
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…
We study a longstanding question of Aaronson and Kuperberg on whether there exists a classical oracle separating $\mathsf{QMA}$ from $\mathsf{QCMA}$. Settling this question in either direction would yield insight into the power of quantum…
We investigate how much quantum distributed algorithms can outperform classical distributed algorithms with respect to the message complexity (the overall amount of communication used by the algorithm). Recently, Dufoulon, Magniez and…
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,…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
We study computation of the mean of sequences with values in finite dimensional normed spaces and compare the computational power of classical randomized with that of quantum algorithms for this problem. It turns out that in contrast to the…
Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…