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arXiv:1910.03181 · Physical Review A

Feedback ansatz for adaptive-feedback quantum metrology training with machine learning

Yi Peng, Heng Fan

Published Feb 14, 2020• 19 citations
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Abstract

It is challenging to construct metrology schemes which harness quantum features such as entanglement and coherence to surpass the standard quantum limit. We propose an ansatz for devising an adaptive-feedback quantum metrology (AFQM) strategy which greatly reduces the searching space. Combined with the Markovian feedback assumption, the computational complexity for designing AFQM would be reduced from ${N}^{7}$ to ${N}^{4}$, for $N$ probing systems. The feedback scheme devising via machine learning such as particle-swarm optimization and differential evolution would thus require much less time and produce equally good imprecision scaling. We have thus devised an AFQM for the 207-partite system. The imprecision scaling would persist for $N>207$ in an admirable range when the parameter setting for the 207-partite system is employed without further training. Our ansatz indicates an built-in resilience of the feedback strategy against qubit loss. The feedback strategies designed for the noiseless scenarios have been tested against the qubit loss noise and the phase fluctuation noise. Our numerical result confirms great resilience of the feedback strategies against the two kinds of noise.

DOI
10.1103/physreva.101.022107

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It is challenging to construct metrology schemes which harness quantum features such as entanglement and coherence to surpass the standard quantum limit. We propose an ansatz for devising an adaptive-feedback quantum metrology (AFQM) strategy which greatly reduces the searching space. Combined with the Markovian feedback assumption, the computational complexity for designing AFQM would be reduced from N7{N}^{7}N7 to N4{N}^{4}N4, for NNN probing systems. The feedback scheme devising via machine learning such as particle-swarm optimization and differential evolution would thus require much less time and produce equally good imprecision scaling. We have thus devised an AFQM for the 207-partite system. The imprecision scaling would persist for N>207N>207N>207 in an admirable range when the parameter setting for the 207-partite system is employed without further training. Our ansatz indicates an built-in resilience of the feedback strategy against qubit loss. The feedback strategies designed for the noiseless scenarios have been tested against the qubit loss noise and the phase fluctuation noise. Our numerical result confirms great resilience of the feedback strategies against the two kinds of noise.
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We devise powerful algorithms based on differential evolution for adaptive many-particle quantum metrology. Our new approach delivers adaptive quantum metrology policies for feedback control that are orders-of-magnitude more efficient and surpass the few-dozen-particle limitation arising in methods based on particle-swarm optimization. We apply our method to the binary-decision-tree model for quantum-enhanced phase estimation as well as to a new problem: a decision tree for adaptive estimation of the unknown bias of a quantum coin in a quantum walk and show how this latter case can be realized experimentally.