Rodney Van Meter wrote:
Other sources include John Preskill's lecture notes (which are freely available) at http://www.theory.caltech.edu/~preskill/ph219/ph219_2018-19
Nice reference. As is stated in http://www.theory.caltech.edu/~preskill/ph229/notes/chap1.pdf that As we have noted, the essential property of quantum information that a quantum computer exploits is the existence of nonlocal correlations among the di fferent parts of a physical system. "nonlocal correlations among the different parts of a physical system" generates nonlocal, that is, globally affecting all qubits, noises, which can not be corrected (when probability that more than half of qubits (including those used for error correction) are erroneous is not negligible, error correction is impossible) which is overlooked by Shor. He improperly assumed that environment states around qubits are same between terms consisting entangled states, whereas, entanglement means the states can be different term by term. Even though qubits are thermally isolated, if they are entangled, nonlocal correlations occur between not-really-QEC circuits, which can not be corrected locally within the circuits. A complication, as is explained in my draft, is that Shor's model on noise covers slightly entangled, that is, slightly nonlocal, cases, but, is not useful against a fact that input qubits to QEC circuits in quantum computers running quantum algorithms are aggressively entangled with other qubits outside of the circuit but still within the computer (seemingly, Gil Kalai thought about interaction with qubits (or whaterver) totally outside of the computer, entanglement with which can be arbitrary small if the computer is thermally isolated from outside environment). Masataka Ohta
