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Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time ..."
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Cited by 7 (7 self)
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this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) "hypothetic" physical devices can compute NPhard problems faster than in exponential time
unknown title
, 2001
"... In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities in the set may be represented linearly via coefficients of ..."
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In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities in the set may be represented linearly via coefficients of density matrix and it is very similar with description using mixed states, but also may give some alternative view on specific properties of quantum circuits due to possibility of direct comparison with classical statistical paradigm. 1
HOW TO PLAY MACROSCOPIC QUANTUM GAME
, 811
"... Quantum games are usually considered as games with strategies defined not by the standard Kolmogorovian probabilistic measure but by the probability amplitude used in quantum physics. The reason for the use of the probability amplitude or ”quantum probabilistic measure ” is the nondistributive latti ..."
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Quantum games are usually considered as games with strategies defined not by the standard Kolmogorovian probabilistic measure but by the probability amplitude used in quantum physics. The reason for the use of the probability amplitude or ”quantum probabilistic measure ” is the nondistributive lattice occurring in physical situations with quantum microparticles. In our paper we give examples of getting nondistributive orthomodular lattices in some special macroscopic situations without use of quantum microparticles. Mathematical structure of these examples is the same as that for the spin one half quantum microparticle with two noncommuting observables being measured. So we consider the so called SternGerlach quantum games. In quantum physics it corresponds to the situation when two partners called Alice and Bob do experiments with two beams of particles independently measuring the spin projections of particles on two different directions In case of coincidences defined by the payoff matrix Bob pays Alice some sum of money. Alice and Bob can prepare particles in the beam in certain independent states defined by the probability amplitude so that probabilities of different outcomes are known. Nash equilibrium for such a game can be defined and it is called the quantum Nash equilibrium. The same lattice occurs in the example of the firefly flying in a box observed through two windows one at the bottom another at the right hand side of the box with a line in the middle of each window. This means that two such boxes with fireflies inside them imitate two beams in the SternGerlach quantum game. However there is a difference due to the fact that in microscopic case Alice and Bob freely choose the representation of the lattice in terms of noncommuting projectors in some Hilbert space. In our macroscopic imitation there is a problem of the choice of this representation(of the
mlq header will be provided by the publisher Fast Quantum Algorithms for Handling Probabilistic and Interval Uncertainty
, 2003
"... In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn). Measurements are never 100 % ac ..."
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In many reallife situations, we are interested in the value of a physical quantity y that is difficult or impossible to measure directly. To estimate y, we find some easiertomeasure quantities x1,..., xn which are related to y by a known relation y = f(x1,..., xn). Measurements are never 100 % accurate; hence, the measured values ˜xi are different from xi, and the resulting estimate ˜y = f(˜x1,..., ˜xn) is different from the desired value y = f(x1,..., xn). How different can it be? Traditional engineering approach to error estimation in data processing assumes that we know the probabildef ities of different measurement errors ∆xi = ˜xi − xi. In many practical situations, we only know the upper bound ∆i for this error; hence, after the measurement, the only information that we have about xi is that it def belongs to the interval xi = [˜xi − ∆i, ˜xi + ∆i]. In this case, it is important to find the range y of all possible values of y = f(x1,..., xn) when xi ∈ xi. We start the paper with a brief overview of the computational complexity of the corresponding interval computation problems. Most of the related problems turn out to be, in general, at least NPhard. In this paper, we show how the use of quantum computing can speed up some computations related to interval and probabilistic uncertainty. We end the paper with speculations on whether (and how) “hypothetic ” physical devices can compute NPhard problems faster than in exponential time. Most of the paper’s results were first presented at NAFIPS’2003 [30]. Copyright line will be provided by the publisher 1 Introduction: Data Processing