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arXiv · 2601.16474

Quantum phase estimation with optimal confidence interval using three control qubits

Kaur Kristjuhan·Dominic W. Berry
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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.

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Kaur Kristjuhan, Dominic W. Berry. 2026-01-23. Quantum phase estimation with optimal confidence interval using three control qubits. https://doi.org/10.22331/q-2026-08-19-2193

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