Well, quantum computation is weaker than a nondeterministic Turing machine, so not the same thing I'm saying. Penrose correctly identifies the mind cannot be a deterministic Turing machine, but his invocation of quantum mechanics does not solve the problem he points out. A DTM can simulate an NTM and hence anything inbetween, so the inbetween of quantum computation does not solve anything.

The fundamental problem Penrose identifies boils down to the halting problem, which requires a halting oracle to be solved. Hence, a halting oracle is the best explanation for the human mind, and no form of computation, quantum or otherwise, suffices.

UPDATE:

Since I'm rate limited, here is my answer to the replier's comment:

A partial answer: the mind has access to the concept of infinity, and can identify new, consistent axioms. Other possibilities: future causality and ability to change the fundamental probability distribution.

But, it's also important to note that we don't have to answer the "how" question in order to identify halting oracles as a viable explanation. We often identify new phenomena and anomalies without being able to explain them, so the identification is a first step.