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The quantum speed limit bounds establish an upper bound at which computation can be performed. Computational machinery is constructed out of physical matter that follows quantum mechanics, and each operation, if it is to be unambiguous, must be a transition of the system from one state to an orthogonal state.
The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons.. Shor's algorithm for factoring and for finding discrete logarithms (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite abelian groups.
In quantum information theory, the classical capacity of a quantum channel is the maximum rate at which classical data can be sent over it error-free in the limit of many uses of the channel. Holevo , Schumacher, and Westmoreland proved the following least upper bound on the classical capacity of any quantum channel N {\displaystyle {\mathcal ...
Their theorem based in control theory states that for a finite-dimensional, closed-quantum system, the system is completely controllable, i.e. an arbitrary unitary transformation of the system can be realized by an appropriate application of the controls [20] if the control operators and the unperturbed Hamiltonian generate the Lie algebra of ...
Download as PDF; Printable version ... 12 references as further reading (out of "the 10 10 5000 quantum algorithm tutorials ... " and "Hacking at Quantum Speed with ...
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
Since quantum computations are reversible, at each 'step' the number of lines must be the same number of input lines. Also, each input combination must be mapped to a single combination at each 'step'. This means that each intermediate combination in a quantum circuit is a bijective function of the input. [6]
The DiVincenzo criteria are conditions necessary for constructing a quantum computer, conditions proposed in 1996 by the theoretical physicist David P. DiVincenzo, [1] as being those necessary to construct such a computer—a computer first proposed by mathematician Yuri Manin, in 1980, [2] and physicist Richard Feynman, in 1982 [3] —as a means to efficiently simulate quantum systems, such ...