Quantum phase estimation with optimal confidence interval using three control qubits

Abstract:Quantum phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state, controlled by an auxiliary state prepared on a control register. In many applications the goal is to provide a confidence interval for the phase estimate, and optimal performance is provided by a discrete prolate spheroidal sequence. We show how to prepare the corresponding state in a far more efficient way than prior work. We find that a matrix product state representation with a bond dimension of 4 is sufficient to give a highly accurate approximation for all dimensions tested, up to $2^{24}$. This matrix product state can be efficiently prepared using a sequence of simple three-qubit operations. When the dimension is a power of 2, the phase estimation can be performed with only three qubits for the control register, making it suitable for early-generation fault-tolerant quantum computers with a limited number of logical qubits.

arXiv:2601.16474 [quant-ph]

(or arXiv:2601.16474v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2601.16474 Focus to learn more arXiv-issued DOI via DataCite

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