Quantum programming
As we know, old computers work according to the rules of Boolean logic and classical set theory . On the other hand there is a discussion about quantum computers nowadays. If we accept that (the hardware of ) these computers work according to the rules of quantum mechanics (QM), is it plausible that their software must obey the rules of quantum logic and mathematical description of QM (like c*-algebras)? It is wellknown that the distributive law of intersection over union fails in QM though there are some rules in lattice theory which are true in both Boolean and quantum logics.
Do we need to rethink about computer programming or at least in the ways we interact with quantum machines of future?
Can we say that the future programmers or software developers of such machines need some basic skills in mathematical theory of QM like c-*algebras? What would be the role of such mathematics in quantum computers?
The "quantum" part in "quantum computing" refers mostly to the hardware used to implement the computations (quantum systems that can exist in a superposition of basic states). Quantum mechanics is a linear theory (these states are elements of a linear space, endowed with a Hermitean structure), so in the end you will be dealing basically with linear algebra (although at an advanced level). All the known quantum algorithms are reducible to linear algebra along with a little bit of group and Lie algebra theory (reflecting the importance of symmetries in Quantum Physics. In fact, one of the basic problems in Quantum Computing is called the "Hidden subgroup problem"). You can find good examples of that point of view in the books "Quantum algorithms via Linear Algebra", by Lipton and Regan, and "Quantum Computing", by Rieffel and Polack (both published by the MIT Press).
I think Set Theory, Graph Theory, Algebra, Calculus, ODE, PDE and mathematical statistics are sufficient for data analysis.
The "quantum" part in "quantum computing" refers mostly to the hardware used to implement the computations (quantum systems that can exist in a superposition of basic states). Quantum mechanics is a linear theory (these states are elements of a linear space, endowed with a Hermitean structure), so in the end you will be dealing basically with linear algebra (although at an advanced level). All the known quantum algorithms are reducible to linear algebra along with a little bit of group and Lie algebra theory (reflecting the importance of symmetries in Quantum Physics. In fact, one of the basic problems in Quantum Computing is called the "Hidden subgroup problem"). You can find good examples of that point of view in the books "Quantum algorithms via Linear Algebra", by Lipton and Regan, and "Quantum Computing", by Rieffel and Polack (both published by the MIT Press).
Linear Algebra :
Matrices multiplication , Inner Products, Tensor Products, etc.
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