No, the human brain is not Turing complete. In fact, computers aren't Turing complete either. Turing completeness is the ability to simulate any Turing machine,

No, the human brain is not Turing complete. In fact, computers aren't Turing complete either. Turing completeness is the ability to simulate any Turing machine, and Turing machines have infinite memory. The brain has only finite memory, therefore, it cannot simulate a general Turing machine. If you mean "Turing complete" in the sense of "able to run the operations of some Turing complete abstract computation system", the answer is yes. If you can comprehend the instructions of a standard programming language, then by definition you are able to "execute" them in your mind, so you can "run" programs as long as they don't exceed your memory limits – just like any physical computer. The "human brain interface technologies" required already exist: Books that teach you how programming languages work.