Exploring Measurement and Feedforward-Assisted Quantum Metrology

A multitude of recent studies have proposed and demonstrated the use of mid-circuit measurements and feedforward to efficiently prepare entangled states on digital quantum platforms. Here, we examine the possible role of mid-circuit measurements and feedforward in a quantum metrology context. We consider the classic phase shift estimation problem, which is standard quantum limited on single qubits but enjoys Heisenberg scaling on GHZ states with collective measurements. It is known that unitary GHZ state preparation requires linear circuit depth on a linear nearest-neighbour qubit connectivity topology, but this complexity can be reduced to constant depth with measurements and feedforward. More broadly, we investigate circuit structures that interpolate between the unitary and measurement-based extremes, on both the pre- and post-processing portions of the experiment circuits. We show in a simplified setting that different families of such circuits are preferable for quantum metrology depending on noise characteristics. We investigate the applicability of measurement-assisted circuits for metrology on present-day quantum devices.