An alternative formulation of the quantum phase estimation using projection-based tensor decompositions

In this paper, an alternative version of the quantum phase estimation is proposed, in which the Hadamard gates at the beginning are substituted by a quantum Fourier transform. This new circuit coincides with the original one, when the ancilla is initialized with \(\left| {0}\right\rangle \) $\left|0\right.〉$ . With the help of a projection-based tensor decomposition and closed-form expressions of its exponential, this new method can be interpreted as a multiplier coupled to the Hamiltonian of the corresponding target unitary operator. Based on this observation, a recursive decomposition is derived.