## Separable Quantum States Are Easier to Synthesize

**Authors:** Dhananjay P. Mehendale

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 the utility of factorisation using [1] 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

**Download:** **PDF**

### Submission history

[v1] 2017-05-09 06:25:08

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