  This chapter presents a quantum computing-based approach to study and harness
neuronal correlates of mental activity for the development of Brain-Computer
Interface (BCI) systems. It introduces the notion of a logic of the mind, where
neurophysiological data are encoded as logical expressions representing mental
activity. Effective logical expressions are likely to be extensive, involving
dozens of variables. Large expressions require considerable computational power
to be processed. This is problematic for BCI applications because they require
fast reaction times to execute sequences of commands. Quantum computers hold
much promise in terms of processing speed for some problems, including those
involving logical expressions. Hence, we propose to use quantum computers to
process the logic of the mind. The chapter begins with an introduction to BCI
and the electroencephalogram, which is the neurophysiological signal that is
normally used in BCI. Then, it briefly discusses how the EEG corresponds to
mental states, followed by an introduction to the logic of the mind. After
that, there is an overview of quantum computing, focusing on the basics deemed
necessary to understand how it processes logical expressions. An example of a
BCI system is presented. In a nutshell, the system reads the EEG and builds
logical expressions, which are sent to a quantum computer to solve them. In
turn, the system converts the results into sounds by means of a bespoke
synthesiser. Essentially, the BCI here is a musical instrument controlled by
the mind of the player. Our BCI is a proof-of-concept aimed at demonstrating
how quantum computing may support the development of sophisticated BCI systems.
The remaining of the chapter is devoted to technical and practical
considerations on the limitations of current quantum computing hardware
technology and scalability of the system.
