




Separable Quantum States are Easier to Synthesise 

PP: 111116 

doi:10.18576/qpl/060206


Author(s) 

Dhananjay P. Mehendale,


Abstract 

An important application of Grover’s 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 nqubit state
which is completely factorable into 




