Can the human brain be simulated by a computer?
To my knowledge (I hold an advanced degree in the field), there is no widely-accepted research that documents that the brain cannot be simulated using a classical computer.
Our current understanding of the human brain is that the primary functional mechanisms consist of neurons that transmit data via chemical and electrical connections.
That said, we have no comprehensive, finite, and accurate definition of &quot;consciousness&quot;, and therefore we cannot prove or disprove consciousness of a computer simulation.  For that matter, as much as we have tried, it is questionable if we can truly prove or disprove consciousness in human beings, although that is the topic of much debate.  It largely depends on how one defines the term &quot;consciousness&quot;.
Outside of consciousness and several other more abstract and philosophical matters (such as feelings and emotions), we know of no limits to our cognitive simulations.