An Alternative Formulation of the Quantum Phase Estimation Using Projection-Based Tensor Decompositions

• URL: http://arxiv.org/abs/2303.05894v2
• Date: Tue, 01 Oct 2024 18:46:09 GMT
• Title: An Alternative Formulation of the Quantum Phase Estimation Using Projection-Based Tensor Decompositions
• Authors: Marian Stengl,
• Abstract summary: 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 with $ket0$. 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.
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• Abstract: 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 $\ket{0}$. 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.

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