Abstract
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.
Highlights
Quantum computers promise dramatic advantages over their classical counterparts [1, 2], but a fault-tolerant universal quantum computer is still far from being available [3]
We study Boson Sampling architectures [4], supplemented with a given number of adaptive measurements—that is, some of the modes are measured throughout the computation and the rest of the computation can depend on their outcome—which we refer to as adaptive linear optics
We have given a roadmap for performing quantum variational classification and quantum kernel estimation using adaptive linear optical interferometers
Summary
Quantum computers promise dramatic advantages over their classical counterparts [1, 2], but a fault-tolerant universal quantum computer is still far from being available [3]. Recent proposals have been driven by subuniversal models such as Gaussian Boson Sampling [25, 26] or IQP circuits [5, 19] In the latter, the authors considered supervised learning algorithms in which some computational subroutines are executed in a quantum way, namely the estimation of the output probabilities of quantum circuits, or the estimation of the overlap of the output states of quantum circuits. We give classical simulation algorithms whose runtimes are explicitly dependent on: (i) the number of modes m, (ii) the number of adaptive measurements k, (iii) the number of input photons n and (iv) the number of photons r detected during the adaptive measurements This effectively sets a limit on the range of parameters for which adaptive linear optics may provide an advantage for machine learning over classical computers using our methods, identifying the regimes where a quantum advantage can be envisaged.
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