Quantum Bayesian Networks

May 9, 2018

BBVI in quantum computing, classical vs quantum supervised learning (classical vs quantum ELBO)

Filed under: Uncategorized — rrtucci @ 2:18 am

Version 1 of the computer program “Quantum Edward” that I released a few days ago uses the BBVI (Black Box Variational Inference, see Ref. 1 below) to train a qc by maximizing with respect to a parameter lambda, a “classical ELBO” (an ELBO defined in terms of classical probability distributions). I call that “classical supervised learning” by a qc (quantum computer).

But one can easily come up with a BBVI that trains a qc by maximizing with respect to a parameter lambda, a “quantum ELBO” (one defined by replacing the classical probability distributions of the classical ELBO by density matrices and sums by traces). I call this second strategy “quantum supervised learning” by a qc.

One more distinction. In Version 1 of Quantum Edward, we do C. Supervised Learning by a simulated (on a classical computer, analytical) qc. More generally, one could do (C. or Q.) Supervised Learning by a (real or simulated) qc

C. or Q. Supervised Learning by a simulated qc is immune to the quantum noise that plagues current qc’s which have almost no quantum error correction. So we definitely should explore that type of learning today.

It will be interesting to compare classification performance for various models (for either layered or DAG models with varying amounts of entanglement) for

  1. C. supervised learning by a classical computer (e.g., for Classical Neural Net layered models or for Bayesian network DAG models)
  2. (C. or Q.) supervised learning by (simulated or real) qc (e.g., for Quantum Neural Network models or for Quantum Bayesian Network models)

Nerd Nirvana will only be achieved once we can do Q. Supervised Learning by an error corrected real qc. 🙂

References:
1. R. Ranganath, S. Gerrish, D. M. Blei, “Black Box Variational
Inference”, https://arxiv.org/abs/1401.0118

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1 Comment »

  1. We gave two boolean variables for QNN models
    1. C or Q supervised learning
    2. real or analytical qc
    A third one is
    3. C or Q input

    Comment by rrtucci — June 21, 2018 @ 2:36 am


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