Authors: Dhananjay P. Mehendale
An important application of Grover's search algorithm  in the domain of experimental physics is its use in the synthesis of any selected superposition state . This paper is about showing the utility of factorisation using  of the quantum state to be synthesised. We first factorise the given quantum state to be synthesised when it is factorable. We then make use of these factors and construct the corresponding operators useful for synthesis of those factors. We then build the operator called synthesizer by taking tensor product of these operators constructed using factors and useful for synthesis of those factors. We then apply the synthesizer made up of the tensor product of the operators that we built using the corresponding factors on the suitable register whose all the qubits have been initialised to |0>: Further, this register is also made up of tensor product of registers of suitable lengths and the first qubit of all these registers is ancilla qubit initialised to |0>: We show that we can achieve the speeding up of the process of synthesising the desired quantum state with our modified algorithm when the state is factorable and has at least two factors. It is shown here that the greater the number of factors of the quantum state, the easier it is to synthesise. We will see that in fact the task of synthesising an n-qubit quantum state which is completely factorable into n single qubit factors is exponentially easier than the task of synthesising an n-qubit completely entangled quantum state having no factors.
Comments: 11 pages
[v1] 2017-05-09 06:25:08
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