TY - JOUR

T1 - Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks

AU - Kaubruegger, Raphael

AU - Vasilyev, Denis V.

AU - Schulte, Marius

AU - Hammerer, Klemens

AU - Zoller, Peter

N1 - Funding Information: We thank R. Blatt, T. Feldker, A. Kaufman, D. Leibrandt, K. Macieszczak, C. Marciniak, T. Monz, I. Pogorelov, P. Schmidt, P. Silvi, and Jun Ye for discussions and valuable comments on the manuscript. Computational results were based on the LEO HPC infrastructure of the University of Innsbruck. Research in Innsbruck is supported by the U.S. Air Force Office of Scientific Research (AFOSR) via IOE Grant No. FA9550-19-1-7044 LASCEM, the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 817482 (PASQuanS) and No. 731473 (QuantERA via QTFLAG), the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440 P. Z.), and by the Institut für Quanteninformation. Innsbruck theory is a member of the NSF Quantum Leap Challenge Institute Q-Sense. M. S. and K. H. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967 and CRC 1227 “DQ-mat” project A06.

PY - 2021/12/6

Y1 - 2021/12/6

N2 - We discuss quantum variational optimization of Ramsey interferometry with ensembles of \(N\) entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean square error of the estimated phase for a given prior distribution, i.e. we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.

AB - We discuss quantum variational optimization of Ramsey interferometry with ensembles of \(N\) entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Bayesian mean square error of the estimated phase for a given prior distribution, i.e. we optimize for a finite dynamic range of the interferometer. In analogous variational optimizations of optical atomic clocks, we use the Allan deviation for a given Ramsey interrogation time as the relevant cost function for the long-term instability. Remarkably, even low-depth quantum circuits yield excellent results that closely approach the fundamental quantum limits for optimal Ramsey interferometry and atomic clocks. The quantum metrological schemes identified here are readily applicable to atomic clocks based on optical lattices, tweezer arrays, or trapped ions.

KW - quant-ph

KW - physics.atom-ph

UR - http://www.scopus.com/inward/record.url?scp=85122528025&partnerID=8YFLogxK

U2 - 10.1103/PhysRevX.11.041045

DO - 10.1103/PhysRevX.11.041045

M3 - Article

VL - 11

JO - Physical Review X

JF - Physical Review X

SN - 2160-3308

IS - 4

M1 - 041045

ER -