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arXiv:1608.06238 · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Single-shot adaptive measurement for quantum-enhanced metrology

Pantita Palittapongarnpim, Peter Wittek, Barry C. Sanders

Published Sep 13, 2016• 5 citations
arXivHTMLPDF

Abstract

Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and formalism for the adaptive case are quite different from the usual non-adaptive quantum metrology approach due to the causal relationship between measurements and outcomes. We construct a formal framework for AQEM by modeling the procedure as a decision-making process, and we derive the imprecision and the Cram´er- Rao lower bound with explicit dependence on the feedback policy. We also explain the reinforcement learning approach for generating quantum control policies, which is adopted due to the optimal policy being non-trivial to devise. Applying a learning algorithm based on differential evolution enables us to attain imprecision for adaptive interferometric phase estimation, which turns out to be SQL when non-entangled particles are used in the scheme.

DOI
10.1117/12.2237355

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Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and formalism for the adaptive case are quite different from the usual non-adaptive quantum metrology approach due to the causal relationship between measurements and outcomes. We construct a formal framework for AQEM by modeling the procedure as a decision-making process, and we derive the imprecision and the Cram´er- Rao lower bound with explicit dependence on the feedback policy. We also explain the reinforcement learning approach for generating quantum control policies, which is adopted due to the optimal policy being non-trivial to devise. Applying a learning algorithm based on differential evolution enables us to attain imprecision for adaptive interferometric phase estimation, which turns out to be SQL when non-entangled particles are used in the scheme.
Reinforcement learning algorithms have been shown to generate procedures for executing quantum control tasks to desired performances. Although reinforcement learning has been effective, its robustness in generating quantum control procedures under general noise condition needs to be tested. Here we consider adaptive quantum-enhanced interferometric phase estimation as a case study in quantum feedback control. The algorithm is determined to deliver a robust quantum-metrological procedure under various phase-noise models when the imprecision surpasses the standard quantum limit. The robustness against unknown environmental variations positions the reinforcement learning as a practical approach for devising quantum control procedures.
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.
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.
We aim to construct tests for evaluating whether policies for adaptive quantum-enhanced metrology are robust against unknown phase noise and are tractable to construct and to execute. Specifically, one of our tests determines scaling of phase-estimate precision with respect to photon number; the other two tests concern resource complexity with respect to the training time required to construct the policy and the execution time for the policy so constructed. The robustness test is performed on quantum-enhanced adaptive phase estimation by simulating the scheme under four phase-noise models corresponding to normal-distribution noise, random-telegraph noise, skew-normal-distribution noise, and log-normal-distribution noise. Control policies are devised either by an evolutionary algorithm under the same noisy conditions, albeit ignorant of its properties, or a Bayesian-based feedback method that assumes no noise. We have introduced an approach to evaluating quantum-control policies for metrology that relies on testing against unusual phase-noise models and accepting that the policies are robust only if scaling of phase-estimate precision beats the standard quantum limit and policy-design resource complexity, in the presence of phase noise, is polynomial in the number of photons.
Quantum-enhanced metrology infers an unknown quantity with accuracy beyond the standard quantum limit (SQL). Feedback-based metrological techniques are promising for beating the SQL but devising the feedback procedures is difficult and inefficient. Here we introduce an efficient self-learning swarm-intelligence algorithm for devising feedback-based quantum metrological procedures. Our algorithm can be trained with simulated or real-world trials and accommodates experimental imperfections, losses, and decoherence.
Abstract Quantum phase estimation is a paradigmatic problem in quantum sensing and metrology. Here we show that adaptive methods based on classical machine learning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ramsey-fringe visibility due to decoherence. We discuss their robustness against noise in connection with real experimental setups such as Mach–Zehnder interferometry with optical photons and Ramsey interferometry in trapped ions, superconducting qubits and nitrogen-vacancy (NV) centers in diamond.