Kvantum-informatika és kommunikáció 2015/2016 ősz A kvantuminformatika jelölésrendszere 2015. szeptember 11.
Mi lehet kvantumbit?
Kvantum eszközök (1)
15=53 Bacsárdi László, 2007. november 23. Képek forrása: IBM's Almaden Research Center (San Jose, CA.),
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Kvantum eszközök (2)
Bacsárdi László, 2007. november 23.
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Kvantum eszközök (3)
Fénykép: Roy Kaltschmidt, forrás: http://www.lbl.gov/Science-Articles/Archive/sabl/2005/June/02-quantum-comp.htm Forrás: http://wikis.lib.ncsu.edu/index.php/Image:Quantum_Computer.jpg
• Fluxuskvantumokon alapuló adiabatikus rendszer • 2007 Orion Systems, 16 kvantumbites gép bemutatója három alkalmazással: – Adatbázis keresés – Ülésrend tervezés – Sudoku fejtés
• 2009 Neural Information Processing Systems Conference – Képfelismerő rendszer betanítása Forrás: Galambos Máté előadása (BME)
• 2011, D-Wave One – 128 qubit – 10 000 000 $
• 2013, D-Wave Two – 512 qubit
„D-Wave Systems Raises an Additional $29M, Closing 2014 Financing at $62M” (Jan 29, 2015) Forrás: Galambos Máté előadása (BME)
Cégek D-wave : • Kanadai cég • 1999-ben alapították • Állításuk szerint kvantumszámítógépet árulnak
IdQuantique • • • •
Svájci cég Senatas-al együttműködésben 2001 óta létezik, University of Geneva Spinoff Kvantum kulcsszétosztás, randomszám generálás
MagiQ Technologies • Amerikai • 1999-ben alapították • Kvantum kulcsszétosztás
Quintessence Labs • Amerikai-ausztrál együttműködés • Kulcsszétosztás, randomszám generálás Forrás: Galambos Máté előadása (BME)
Slides for Quantum Computing and Communications – An Engineering Approach
Chapter 2 Quantum Computing Basics Sándor Imre Ferenc Balázs
Qubits and Qregisters "All of the books in the world contain no more information than is broadcast as video in a single large American city in a single year. Not all bits have equal value." Carl Sagan
Qubit • Dirac’s ‘ket’ and ‘bra’ notations: • Qubit: contains both classical states (computational basis states) at the same time in a so called superposition
• where a and b are probability amplitudes. They squared absolute value carries the information about the probabilities of obtaining a certain classical states after measurement (in that classical basis)
Remark • We strongly emphasize here again that before the measurement the qubit has both logical values, i.e., it is in both computational basis states at the same time • and the measurement let the qubit collapse into one of them. This completely differs from the classical approach which assumes that the coin is in one of the logical states before the measurement and the measurement only reveals this fact.
Superposition
a 0 b1 a, b C
2
2
a b 1.
Superposition a 0 b1
2
2
a b 1.
a, b C
L. Bacsardi, M. Galambos, S. Imre, A. Kiss. ”Quantum Key Distribution over Space-Space Laser Communication Links,” AIAA Space 2012, Pasadena, California, Sept, 2012.
Superposition 1
A2
B2
0
1
0
0
1
i1
2
2
M. Galambos, S. Imre, “Visualizing the Effects of Measurements and Logic Gates On Multi-Qubit Systems Using Fractal Representation,” International Journal on Advances in Systems and Measurements, Vol. 5, No. 1-2, 2012, pp. 1–10.
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Merging qubits to qregisters • Two-qbit example of 4th Postulate
0
General case: n-qubit register
The Postulates of Quantum Mechanics "The belief that there is only one truth and that oneself is in possession of it seems to me the deepest root of all evil that is in the world." Max Born
1st Postulate (state space) • The actual state of any closed physical system can be described by means of a so called state vector v having complex coefficients and unit length in a Hilbert space V, i.e., a complex linear vector space (state space) equipped with inner product.
2nd Postulate (evolution) • The evolution of any closed physical system in time can be characterized by means of unitary transforms depending only on the starting and finishing time of the evolution. • 2nd Postulate can be interpreted as v’ (t2) = U(t1, t2)v(t1) and v’ V . • The above definition describes the evolution between discrete time instants, which is more suitable in context of quantum computing. Its original continuous-time form is known as Schrödinger equation
• Relationship between H and U
3rd Postulate (measurement) • Any quantum measurement can be described bymeans of a set of measurement operators {Mm}, where m stands for the possible results of the measurement. The probability of measuring m if the system is in state v can be calculated as • and the system after measuring m gets in state
•
Because classical probability theory requires that
•
Completeness relation:
4th Postulate (composite systems)
• The state space of a composite physical system W can be determined using the tensor product of the individual systems W = V Y . Furthermore having defined v V and y Y then the joint state of the composite system is w = v y.
