Quantum neural networks
Abstract
Quantum computing is becoming a reality, at least on a small scale. However, designing
a good quantum algorithm is still a challenging task. This has been a huge major
bottleneck in quantum computation for years. In this work, we will show that it is possible to
take a detour from the conventional programming approach by incorporating machine learning
techniques, speci cally neural networks, to train a quantum system such that the desired
algorithm is \learned," thus obviating the program design obstacle. Our work here merges
quantum computing and neural networks to form what we call \Quantum Neural Networks"
(QNNs). Another serious issue one needs to overcome when doing anything quantum is
the problem of \noise and decoherence". A well-known technique to overcome this issue is
using error correcting code. However, error correction schemes require an enormous amount
of additional ancilla qubits, which is not feasible for the current state-of-the-art quantum
computing devices or any near-term devices for that matter. We show in this work that
QNNs are robust to noise and decoherence, provide error suppression quantum algorithms.
Furthermore, not only are our QNN models robust to noise and decoherehce, we show that
they also possess an inherent speed-up, in term of being able to learned a task much faster,
over various classical neural networks, at least on the set of problems we benchmarked them
on. Afterward, we show that although our QNN model is designed to run on a fundamental
level of a quantum system, we can also decompose it into a sequence of gates and implement
it on current quantum hardware devices. We did this for a non-trivial problem known as
the \entanglement witness" calculation. We then propose a couple of di erent hybrid quantum
neural network architectures, networks with both quantum and classical information
processing. We hope that this might increase the capability over previous QNN models in
terms of the complexity of the problems it might be able to solve.
Description
Thesis (Ph.D.)-- Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics