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This chapter presents a quantum computing-based approach to study and harnessneuronal correlates of mental activity for the development of Brain-ComputerInterface (BCI) systems. It introduces the notion of a logic of the mind, whereneurophysiological data are encoded as logical expressions representing mentalactivity. Effective logical expressions are likely to be extensive, involvingdozens of variables. Large expressions require considerable computational powerto be processed. This is problematic for BCI applications because they requirefast reaction times to execute sequences of commands. Quantum computers holdmuch promise in terms of processing speed for some problems, including thoseinvolving logical expressions. Hence, we propose to use quantum computers toprocess the logic of the mind. The chapter begins with an introduction to BCIand the electroencephalogram, which is the neurophysiological signal that isnormally used in BCI. Then, it briefly discusses how the EEG corresponds tomental states, followed by an introduction to the logic of the mind. Afterthat, there is an overview of quantum computing, focusing on the basics deemednecessary to understand how it processes logical expressions. An example of aBCI system is presented. In a nutshell, the system reads the EEG and buildslogical expressions, which are sent to a quantum computer to solve them. Inturn, the system converts the results into sounds by means of a bespokesynthesiser. Essentially, the BCI here is a musical instrument controlled bythe mind of the player. Our BCI is a proof-of-concept aimed at demonstratinghow quantum computing may support the development of sophisticated BCI systems.The remaining of the chapter is devoted to technical and practicalconsiderations on the limitations of current quantum computing hardwaretechnology and scalability of the system.

On Interfacing the Brain with Quantum Computers: An Approach to Listen to the Logic of the Mind