As I wrote:
Nanog News wrote:
Latest from ICANN: Quantum Computers are "Interesting"… But Don't Lose your Head
Uselessness of quantum logic gate style quantum computers will be discussed in a separate mail.
Quantum logic gate style quantum computers use qubits, which have two orthogonal quantum state |0> and |1> (which may be a horizontally and vertically polarized photon, correspondingly, which is familiar for us, communication engineers) used as bit values of 0 and 1. As they are orthogonal, we can consider |0>+|1>, (which may be a diagonally polarized photon, easy to understand classically). But such addition is improperly called quantum superposition. Two qubit states are represented as |00>, |11> and |00>+|11>. Then, if we can construct a linear circuit to compute f, a 3 input and 3 output bits function, f(a, b, c)=(d, e, f) as f(|abc>)=|def>. Then, we can compute f(|000>)+f(|001>>+...+f(|111>) as f(|000>+|001>+...+|111>), that is evaluating f not 8 times but only once, which is quantum parallelism. It can be extended for N qubit cases for 2**N parallelism by 2**N terms. However, though an N qubit state, like an N bit string, can naturally distinguish 2**N cases, 2**N term quantum superpositioned states require distinguishing 2**(2**N) cases, which is obviously impossible because of noise/error (theory of Shannon). So, QEC (Quantum Error Correction) was invented, which was expected to reduce noise/error. QEC certainly work for single term states. Small non linear error on single term states is no different from linear error. The problem, however, is that, QEC is non-linear, which means not applicable to 2**N term superpositioned states. But, it is implicitly and wrongly assumed that all the 2**N terms will suffer from identical error, in which case, QEC become linear. That is single, so called, bit flip error on the first qubit of: |000>+|111> occurs as: |100>+|111> or: |000>+|011> not (unless strong correlation exists, which is an improper assumption): |100>+|011> which is the reason why quantum logic gate quantum computer with practical number of qubits is impossible. A complication is that it is possible to construct complex QEC scheme applicable for 2 term states. So called Shor code is such QEC. But Shor code itself use states with more than 2 terms. Anyway, once QEC scheme is fixed, it is not applicable to 2**N term states for large N. It should also be noted that though non-linear error on two or more term states imply errors caused by interactions of multiple terms, they are ignored. Masataka Ohta