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The Theory Of The Quantum Computation Model

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Living in a world where computers have solved some of the world’s biggest problems and revolutionised the way science and technology function in our day to day lives there still exists a number of problems that even classical computers cannot solve or take an incredibly large amount to do so. For example RSA encryption works on the basis that factoring large numbers takes incredible amounts of time even the most sophisticated classical factoring algorithms take unrealistic amounts to factor large numbers such as the ones used in RSA cryptography. The theory of the quantum computation model takes advantage of quantum mechanics to solve problems that normal computers cannot solve and solve problems much faster in reasonable amounts of time. …show more content…

However if we were to multiply the vector |ψ> by e^iϕ, puts the vector psi in a state that we cannot define. A system with an “N” number of qubits is described by a unit vector C^2⊗C^2⊗…⊗C^2 repeated “N” number of times each C^2 is the space of one single qubit with the basis |0> and |1> the space is denoted by B^(⊗n) the basis state for the space are all products of the form |X_1>⊗|X_2>⊗…⊗|X_n> while X is an element of a real number of zero or one. Having these basis states the N-qubit system can be represented in the form ∑_(〖xϵ{0,1}〗^n)▒〖a_x |x>.〗
Example 1: We have a quantum system composed of 2 qubits we can then write the vector including all the possible states like this |ψ> = α_00 |00> + a_01 |01> + α_10 |10> +α_11 |11>.

H|x> = ∑_(zϵ{0,1})▒〖(-1)〗^xz/√2
W|x,y> =|x,y⊕f(x)> ⊕means addition modulo 2. Let’s do a simple quantum algorithm say we have a function f: (0,1) is f one-one meaning the does the function return the same value when two different inputs are given, generally we would solve this by inputting 0 and then inputting 1 if both outputs are the same then f is one-one. However, we could also solve this problem with only one input. We do this by creating a

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