Heisenberg-Limited Bayesian Interferometry with Low-Depth Digital Quantum Circuits

Optimal phase estimation protocols require global squeezing operations and complex readout schemes, generically unavailable or unscalable in many quantum platforms. Working in a Bayesian context, we develop and analyze a scheme that achieves an almost optimal precision, using simple digital quantum circuits with at most logarithmic-depth, and local measurements. We find that for any prior phase distribution, the optimal initial state can be approximated with a suitable combination of GHZ states with varying numbers of qubits. Using local, adaptive measurements optimized for the prior distribution and the initial state, we show that Heisenberg scaling is achievable. We compare our scheme to the fundamental quantum limits and discuss the impact of noise and imperfect gates. Lastly, we analyze an application of the scheme for atomic clocks.