Latest from ICANN: Quantum Computers + N85 Peering Forum
Masataka Ohta
mohta at necom830.hpcl.titech.ac.jp
Sun Mar 20 08:53:43 UTC 2022
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
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