Quantum phase estimation with optimal confidence interval using three control qubits

TL;DR

This paper presents an efficient method for quantum phase estimation using only three control qubits, leveraging matrix product states for optimal confidence intervals, suitable for early quantum computers.

Contribution

It introduces a novel, efficient state preparation technique for phase estimation that reduces control qubits to three and employs matrix product states for high accuracy.

Findings

Matrix product state with bond dimension 4 suffices for high accuracy

Phase estimation with three control qubits is feasible for dimensions up to 2^24

Efficient preparation using simple three-qubit operations

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.