Journal of Quantum Information Science
Vol.4 No.3(2014), Article ID:48723,4 pages
DOI:10.4236/jqis.2014.43015
Josephson Fourier Spectrometer Based on HTSP: Construction and Quantum Computer Realization Problem
Dresvyannikov Maxim, Zherikhina Larisa, Murzin Vladimir, Tskhovrebov Andrey
The Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
Email: dresvjannikovm@gmail.com
Copyright © 2014 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
Received 17 June 2014; revised 19 July 2014; accepted 5 August 2014
Abstract
The possibility of creating a spectrometer of THz range, which is based on non-stationary Josephson effect in HTSP is considered. Simple design of Josephson junction adjustable at cryogenic conditions is proposed. Using of such device for solving the problem of factorization of high value numbers, which in fact is the only motivation for creating a quantum computer, is discussed.
Keywords: High-Temperature Superconductors, Josephson Effect, Quantum Computer
1. Introduction: Non-Stationary Josephson Effect in HTSC Systems and Its Applications
Previously we have investigated non-stationary Josephson effect via dot junction, which was performed by crossing of edges of two prisms of Y1Ba2Cu3O7−δ. Josephson effect [1] is a phenomenon, where it is possible to observe persistent and phase-dependent current in tunnel structures (weak link):
(1)
(2)
(3)
where―critical current,
―“phase difference”
across the junction,
―voltage,
―tunneling conductance. In our case junction
is exposed to radiation, thus we have:
which gives us the next equation for Josephson current:
.
From this equation, it follows that under irradiation of Josephson junction it is
possible to observe steps on a current-voltage characteristic with
amplitude. The experiment conditions corresponded to so-called inverse non-stationary
Josephson effect with external electromagnetic microwave radiation (in our case
). We observed Shapiro steps on
the curve of the current-voltage characteristic that pointed on an appearance of
Josephson effect [1]
[2] , and enabled drawing a conclusion about high microwave radiation sensitivity
of the contact (Figure 1). Also it’s worth mentioning
that our junction is cheap and easy to produce; that’s very important in case of
breakdown. So it is viable to construct a fast spectrum analyzer with the high microwave
radiation sensitivity based on HTSP Josephson junction
[3] . Such a device could record THz radiation, as
, and Y1Ba2Cu3O7−δ
possesses a wider superconductivity gap Δ in comparison with traditional superconductors.
The action of the analyzer comes to recording current-voltage characteristic, recognition
of Shapiro steps, and restoration of signal spectrum based on them.
2. Method of Analogy Simulating of the Quantum Computer with the Help of the Single Josephson Contact: Discussion of the Scheme of the Device
One of the most interesting modern problems, which demand quick production of Fourier
transform, is the realization of quantum computer [4]
. At present, there are a lot of research centers, which try to find ways of realization
of quantum computer. Yet, there is the only applied problem for such a devise. It
is the problem of factorization of multidigit numbers,which provides the framework
for code-breakingof the high defensive codes in cryptography
[5] . The method of factorization is based on the classical Euclid algorithm
[6] . For factorization of an integer number
on prime factors it is necessary to find periods of the function
, where
is the residue of division
by
,
―natural number. Then
one takes the lowest period
, and defines the proper
divisor
, where
is the greatest common divisor of
and
.
This simple algorithm for solving the problem of factorization of numbers could
be realized with the help of quantum computer. As the period of function
corresponds to the maximum of its Fourier-spectrum, it is enough to find appropriate
coordinates of the extremum. The quantum computer permits to do such operation for
a few measurements of
register. Registers
and
form entangled state, when all combinations of
-bites, which correspond to domain of
definition, are present at the
, due to quantum fluctuation
and appropriate values of
are in register
. We propose alternative
approach for finding an effective substitution of the non-polynominal algorithm,
which is based on the use of a spectrum analyzer with Josephson HTSP junction. In
our case the role of quantum parallelism is substituted by the modeling of function
. Indeed, as a periodic function
contains the whole superposition (not quantum) of Fourier harmonics, which form
this function supposing time
is fixed, when it is multiple of the period
. In some way this is an
analog of the quantum parallelism, when register
of a quantum computer contains in the form of superposition all possible values
of
due to indefinite states of all
-bits. The block scheme of such device, which includes
Josephson junction and is intended for factorization of numbers on prime factors,
is presented on Figure 2. Here, voltage
is applied to M1, thus the output of integrator is
. Further, in accordance
with Richardson formula we observe current
on diode
, and by zero shifting
of integrator M2 we can compensate term
in order to receive
on M3 input (we assume for convenient that
, thus
). Next we compare
with the analog signal
(it is generated via M7) on comparator M4. If
exceeds
, then M4 generates pulse
with amplitude, which is defined by M7 and M5. These pulses form step stair function
after integrating on M6. Difference between signal
and step stair function is residue-
,
Figure 1. Rightand left-hand
bolts are identical constructively. They have different thread pitch between higher
and lower parts, that allows to displace electrodes of HTSP toward/outward by
per one turn. Junction is shifted out of center for additional accuracy of adjustment
of contact, that permit to use principle of lever.
Figure 2. The block scheme
demonstrates the realization of process of factorization on prime factors via Fourier
spectrum analyzer, which is based on HTSP Josephson junction. Left-hand out of the
capacity C (M1 - M8)—block of formation of. Right-hand out of C (M9
- M11)—Josephson spectrum analyzer. M1—integrator with a constant voltage at the
entrance; M2—integrator of currents; M3—wide band differential operational amplifier;
M4—comparator; M5—digital analog multiplier; M6—stepped integrator; M7—digital-to-analog
converter; M8—tact generator; M9—strobe storage memory; cross-Josephson junction;
M10—digital-to-analog converter; M11—analog-to-digital converter.
which is needed for prime numbers factorization. From M3 residue is applied to M8, and after discretization it is applied to Josephson junction, where Fourier conversion is occurred.
3. Conclusion
Of course, during development, analog computing systems yielded to digital one in produced calculations. However, in our opinion in the field of quantum computers that moment will not come very soon.
Acknowledgements
This work was supported by the program “Strongly Correlated Electrons in Semiconductors, Metals, Superconductors and Magnetic Materials” of the Department of Physical Sciences of the Russian Academy of Sciences (project No. II-3).
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