Long-Term Memory, Simulated Qubits, Physical Qubits - Brain Theory from a Circuits and Systems Perspective - page 72

Fig. 4.14 Probability-phase
sphere applied to neuro-
multivibrators

are possible, each with a certain probability. Prior to sampling, the vectors that
represent these outcomes are known in the abstract as probability space.
The author places 0 as being a lower frequency on the bottom of a sphere, since
low usually means closer to bottom (usually in quantum physics, 0

j > is at the top).

Physical Qubits

Analogy to Physical Qubits

A physical qubit is an entity in a quantum system with appropriate quantum
properties, for instance, a rotating electron with two quantum states, spin up and
spin down. These may be thought of as rotation counterclockwise and clockwise.
Spin up and spin down defines two basis states 0 >

j , 1 > j which may be expressed

as vectors:

;

1
0

0
1

j 0 > ¼ j 1 > ¼ (4.7)

0 0

(the prime denotes a
transpose and is a way to express a vertical vector on a horizontal line). Qubit
vectors may combine linearly. A general expression for a single qubit state vector is
a mathematically linear combination of the two possible states:

These can be written as 0 > ¼½ 10 and 1 > ¼½ 01

jψ> ¼ α j 0 > þβ j 1 >: (4.8)

This implies the surprising situation that a qubit can be in two logical states at
once. In general | 2 α and β are complex numbers. According to the quantummodel | α