We propose a framework for designing algorithms for early-fault-tolerant quantum computers by trading between error correction overhead and residual logical noise, and apply it to quantum phase estimation (QPE).
We introduce a new multi-control QPE algorithm robust to depolarizing noise, and further develop the first scheme that extends mitigation of arbitrary noise models beyond expectation values.
We estimate the physical cost of our algorithm applied to the ground state problem of the two-dimensional Hubbard model and various molecular Hamiltonians, identifying the trade-off between physical qubits and computation time.