Creating Very True Quantum Algorithms for Quantum Energy Based Computing
An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f ( x ) := s . x = s 1 x 1 + s 2 x 2 + ⋯ +...
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Published in | International journal of theoretical physics Vol. 57; no. 4; pp. 973 - 980 |
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Main Authors | , , , , , , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.04.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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Summary: | An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function
f
(
x
) :=
s
.
x
=
s
1
x
1
+
s
2
x
2
+ ⋯ +
s
N
x
N
is proposed. Here
x
= (
x
1
, … ,
x
N
),
x
j
∈
R
and the coefficients
s
= (
s
1
, … ,
s
N
),
s
j
∈
N
. Given the interpolation values
(
f
(
1
)
,
f
(
2
)
,
...
,
f
(
N
)
)
=
y
→
, the unknown coefficients
s
=
(
s
1
(
y
→
)
,
…
,
s
N
(
y
→
)
)
of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of
N
. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using
M
parallel quantum systems,
M
homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of
M
homogeneous linear functions is shown to outperform the classical case by a factor of
N
×
M
. |
---|---|
ISSN: | 0020-7748 1572-9575 |
DOI: | 10.1007/s10773-017-3630-1 |