Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation

Understand

We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to $0$ as the initial state approaches the target eigenstate.

• The total cost of the algorithm satisfies the Heisenberg-limited scaling $\widetilde{\mathcal{O}}(\epsilon^{-1})$.
• As a result, our algorithm may significantly reduce the circuit depth for performing phase estimation tasks on early fault-tolerant quantum computers.
• The key technique is a simple subroutine called quantum complex exponential least squares (QCELS).