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Quantum Physics Letters
An International Journal


Volumes > Vol. 6 > No. 2


Separable Quantum States are Easier to Synthesise

PP: 111-116
Dhananjay P. Mehendale,
An important application of Groverís search algorithm [2] in the domain of experimental physics is its use in the synthesis of any selected superposition state [3]. This paper is about showing how one can speedup this synthesis when selected superposition state to be synthesised factorizes into smaller sized factors under the application of factorization algorithm [1]. When selected superposition state is factorable we first factorize this state and carry out the synthesis of its factors in parallel by applying the algorithm for synthesis [3] simultaneously to each factor. Main steps of our modified algorithm are as follows: By making use of the factors we construct the corresponding operators needed for the synthesis of these factors as per [3]. We then build the operator called synthesiser by taking tensor product of these operators constructed for the synthesis of the factors. We then build a suitable register A, say, whose all the qubits have been initialized to |0i. Note that this register A is prepared by taking tensor product of smaller sized registers of suitable lengths chosen from lengths of the computational basis states required to represent the corresponding factors and the first qubit of all these smaller sized registers is ancilla qubit. We then apply the synthesiser on register A and carry out the measurement of all the ancillae qubits. If the measurement finds all the ancillae qubits in state |0i then we have arrived at the desired selected superposition state. We see that the greater the number of factors to the state, the easier it is to synthesise and the task of synthesising an n-qubit state which is completely factorable into

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