Quantum machine learning with adaptive linear optics

We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine – either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements. We then challenge these quantum algorithms by deriving classical simulation algorithms for the tasks of output probability estimation and overlap estimation. We obtain different classical simulability regimes for these two computational tasks in terms of the number of adaptive measurements and input photons. In both cases, our results set explicit limits to the range of parameters for which a quantum advantage can be envisaged with adaptive linear optics compared to classical machine learning algorithms: we show that the number of input photons and the number of adaptive measurements cannot be simultaneously small compared to the number of modes. Interestingly, our analysis leaves open the possibility of a near-term quantum advantage with a single adaptive measurement.

Efficient qubit phase estimation using adaptive measurements

Estimating correctly the quantum phase of a physical system is a central problem in quantum parameter estimation theory due to its wide range of applications from quantum metrology to cryptography. Ideally, the optimal quantum estimator is given by the so-called quantum Cramér-Rao bound, so any measurement strategy aims to obtain estimations as close as possible to it. However, more often than not, the current state-of-the-art methods to estimate quantum phases fail to reach this bound as they rely on maximum likelihood estimators of non-identifiable likelihood functions. In this work we thoroughly review various schemes for estimating the phase of a qubit, identifying the underlying problem which prohibits these methods to reach the quantum Cramér-Rao bound, and propose a new adaptive scheme based on covariant measurements to circumvent this problem. Our findings are carefully checked by Monte Carlo simulations, showing that the method we propose is both mathematically and experimentally more realistic and more efficient than the methods currently available.

Evaluation of Italian Simplified Matrix Test for Speech-Recognition Measurements in Noise

This study aimed at the evaluation of a simplified Italian matrix test (SiIMax) for speech-recognition measurements in noise for adults and children. Speech-recognition measurements with adults and children were conducted to examine the training effect and to establish reference speech-recognition thresholds of 50% (SRT50) and 80% (SRT80) correct responses. Test-list equivalency was evaluated only with adults. Twenty adults and 96 children—aged between 5 and 10 years—participated. Evaluation measurements with the adults confirmed the equivalence of the test lists, with a mean SRT50 of −8.0 dB and a standard deviation of 0.2 dB across the test lists. The test-specific slope (the average of the list-specific slopes) was 11.3%/dB, with a standard deviation of 0.6%/dB. For both adults and children, only one test list of 14 phrases needs to be presented to account for the training effect. For the adults, adaptive measurements of the SRT50 and SRT80 showed mean values of −7.0 ± 0.6 and −4.5 ± 1.1 dB, respectively. For children, a slight influence of age on the SRT was observed. The mean SRT50s were −5.6 ± 1.2, −5.8 ± 1.2 and −6.6 ± 1.3 dB for the children aged 5–6, 7–8 and 9–10 years, respectively. The corresponding SRT80s were −1.5 ± 2.7, −3.0 ± 1.7 and −3.7 ± 1.4 dB. High test–retest reliabilities of 1.0 and 1.1 dB for the SRT80 were obtained for the adults and children, respectively. This makes the test suitable for accurate and reliable speech-recognition measurements.

Optbayesexpt: Sequential Bayesian Experiment Design for Adaptive Measurements

Optbayesexpt is a public domain, open-source python package that provides adaptive algorithms for efficient estimation/measurement of parameters in a model function. Parameter estimation is the type of measurement one would conventionally tackle with a sequence of data acquisition steps followed by fitting. The software is designed to provide data-based control of experiments, effectively learning from incoming measurement results and using that information to select future measurement settings live and online as measurements progress. The settings are chosen to have the best chances of improving the measurement results. With these methods optbayesexpt is designed to increase the efficiency of a sequence of measurements, yielding better results and/or lower cost. In a recent experiment, optbayesexpt yielded an order of magnitude increase in speed for measurement of a few narrow peaks in a broad spectral range.