Achieving Heisenberg-limited sensitivity with scrambling dynamics

Quantum-enhanced metrology leverages entanglement to improve sensitivity to an external signal. It is often assumed that achieving beyond-classical sensitivities requires preparing finely tuned entangled states, such as the GHZ state or a spin-squeezed state. Here, we demonstrate instead that the fundamental limit on quantum sensing -- the celebrated Heisenberg limit -- can be achieved with a much broader class of entangled states, and we introduce an explicit protocol for preparing such states and reading out an accumulated phase. Crucially, our protocol requires only the ability to evolve forward and backward in time under generic interacting quantum dynamics and is thus compatible with a wide variety of analog quantum simulators; alternatively, it can be employed in the context of digital quantum devices to suppress the effects of coherent errors. We analyze the sensitivity of our protocol for time-evolution corresponding to (i) Haar-random unitary evolution, (ii) one-dimensional spin chains and (iii) a trapped-ion quantum computer subject to control errors. Our protocol provides a witness for many-body entanglement and thus significantly relaxes the requirements for demonstrating large-scale entanglement on near-term quantum devices.