Bayesian deep learning on a quantum computer

Abstract

Bayesian methods in machine learning, such as Gaussian processes, have great advantages compared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected deep feedforward neural networks with Gaussian processes, allowing training without backpropagation. This connection enables us to leverage a quantum algorithm designed for Gaussian processes and develop a new algorithm for Bayesian deep learning on quantum computers. The properties of the kernel matrix in the Gaussian process ensure the efficient execution of the core component of the protocol, quantum matrix inversion, providing an at least polynomial speedup over classical algorithms. Furthermore, we demonstrate the execution of the algorithm on contemporary quantum computers and analyze its robustness with respect to realistic noise models.

Fast variational quantum algorithms for training neural networks and solving convex optimizations

“…Thus, g t,n /L returns an L -approximate of g i (w(n)). By setting = L, we can get an -approximate of g i (w(n)) in time (14).…”

“…Note that when closing to the end of the training, the gradient can be very small. To obtain a good approximate of the gradient, one idea is to increase the precision , which in turn increases the complexity (14) of Algorithm 1. Another idea is that we set a threshold about the gradient.…”

“…And we can stop the training now. The complexity has a similar form to (14), except that is changed into .…”

“…A simple modification at the parameters gives the quantum circuit to calculate the derivative of U ( θ ). Many works have been recently reported about variational algorithms, such as combinatorial optimization problems [8,9], variational quantum eigensolvers [10,11], quantum neural network [12][13][14], quantum classifier [15][16][17], etc. This paper can be viewed as another important application in this direction.…”

Demonstration of the no-hiding theorem on the 5-Qubit IBM quantum computer in a category-theoretic framework

“…Using this web interface researchers have run a variety of quantum computing and quantum information experiments and demonstrations. These include experiments/demonstrations in the field of quantum information [2,3], condensed matter physics [4,5], quantum artificial intelligence [6], quantum gravity [7], quantum simulation [8,9], quantum cryptography [10,11], quantum error correction [12,13,14,15], quantum entanglement based protocols [16,17,18,19,20] and quantum cloud computing [21,22] to name a few.…”