Implementation of quantum gate operations using neural networks
Abstract
All quantum circuits are designed using different quantum gates, which can be
decomposed into elementary gates. The number of elementary gates in a quantum circuit is
called the gate count. Typically, there is a direct correspondence between the gate count and the
complexity of a quantum circuit. Quantum systems are generally very fragile, and a quantum bit
(qubit) can lose its super-position state very easily. This process is called decoherence. As such,
when implementing a quantum operation, it becomes necessary to minimize the gate count as
much as possible.
This thesis focuses on two important applications where reducing the gate count is very
significant. The first is quantum error correction (QEC). In a quantum error correction code
(QECC), one information qubit is encoded with two or more auxiliary qubits to form a
logical/encoded qubit. Oftentimes, when performing gate operations on logical qubits, decoding
is required, which opens the system to decoherence. The aim here is to design encoded quantum
gates in such a way that the decoding process is no longer needed for implementing gate
operations on QEC circuits. The second focus is a controlled-NOT (CNOT) gate operation
between uncoupled (remote) qubits. In order to implement a gate operation in a linear nearest
neighbor (LNN) architecture, the qubits that are not neighbors need to be brought adjacent to
each other before a gate operation can be performed between them. The LNN architecture is
significant because most physical implementations of a practical quantum computer use this
layout. Here, the aim is to implement a CNOT gate between remote qubits in an LNN
architecture without bringing the qubits adjacent to each other, thereby tremendously reducing
the gate count. This research employed a neural network approach based on gradient descent
technique to reduce the gate count.
Description
Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Electrical Engineering and Computer Science