Entangled solitons and stochastic q-bits (original) (raw)

ŠOEoe'…›… '…•‹ƒˆˆ‚ "ˆ ‡ˆŠ… TWO INTERACTING SPINS IN EXTERNAL FIELDS AND APPLICATION TO QUANTUM COMPUTATION

2020

We study the four-level system given by two quantum dots immersed in a time-dependent magnetič eld, which are coupled to each other by an effective Heisenberg-type interaction. We describe the construction of the corresponding evolution operator in a special case of different time-dependent parallel external magneticˇelds. Weˇnd a relation between the externalˇeld and the effective interaction function. The obtained results are used to analyze the theoretical implementation of a universal quantum gate.ˆ § ÊÎ ¥É¸Ö Î¥ÉÒ·¥ÌÊ·μ¢´¥¢ Ö¸¨¸É¥³ , μÉ¢¥Î ÕÐ Ö ¤¢Ê³ ±¢ ´Éμ¢Ò³ ÉμÎ± ³¸¢ § ¨³μ¤¥°¸É¢¨¥³ ƒ¥° §¥´¡¥·£ , ¶μ³¥Ð¥´´Ò³ ¢μ ¢´¥Ï´¥¥ § ¢¨¸ÖÐ¥¥ μÉ ¢·¥³¥´¨³ £´¨É´μ¥ ¶μ²¥. μ¸É·μ¥´μ ¶¥· Éμ· Ô¢μ²ÕÍ¨¨¤²Ö¸²ÊÎ Ö, ±μ£¤ ³ £´¨É´Ò¥ ¶μ²Ö ¢ ± ¦¤μ°ÉμÎ±¥ ¶ · ²²¥²Ó´Ò. "± § ´ ¸¢Ö §Ó ³¥¦¤Ê ³ £´¨É´Ò³¨ ¶μ²Ö³¨¨ÔËË¥±É¨¢´μ°ËÊ´±Í¨¥°¢ § ¨³μ¤¥°¸É¢¨Ö¸ ¶¨´μ¢. ¡¸Ê¦¤ ¥É¸Ö ¶·¨³¥´¥´¨¥ ¶μ²ÊÎ¥´´ÒÌ ·¥ §Ê²ÓÉ Éμ¢ ± ¶μ¸É·μ¥´¨Õ Ê´¨¢¥·¸ ²Ó´μ£μ ±¢ ´Éμ¢μ£μ ±²ÕÎ .

Two interacting spins in external fields and application to quantum computation

Physics of Particles and Nuclei Letters, 2009

A Pedagogical Approach to Quantum Computing using Spin-1/2 particles

2006 Sixth IEEE Conference on Nanotechnology

This paper discusses the important primitives of superposition and entanglement in QIP from physics of spin-1/2 particles. System of spin-1/2 particles present a logical and conceptual candidate to understand Quantum Computing. A pedagogical approach to abstract quantum information processing is considered in more concrete physical terms here.

Entanglement generation by collisions of quantum solitons

arXiv (Cornell University), 2009

We present analytic expressions describing generation of the entanglement in collisions of initially uncorrelated quantum solitons. The results, obtained by means of the Born's approximation (for fast solitons), are valid for both integrable and non-integrable quasi-one-dimensional systems supporting soliton states.

Quantum systems in regular and stochastic fields. Creation and destruction of the coherence

2007

The problem of the coherent state generation with deˇnite parameters for multilevel quantum systems is investigated. The interaction with external environment and stochasticˇelds can destroy the coherence. The competition of these processes is considered on the basis of FokkerÄPlanck equations approach, derived from master equation for the density matrix of the system. Examples of the coherent states dynamics for two-level atoms in an external stochasticˇeld in a nonideal resonator are considered. Average over the realizations of stochasticˇelds is performed for the case of white Gaussian noise and KuboÄAnderson process. Explicit formulas for probability and shape of radiation line are obtained.¸¸² ¥¤μ¢ ´ ¶•μ¡²¥³ £¥´¥• Í¨¨±μ£¥•¥´É´ÒÌ¸μ¸ÉμÖ´¨°¤²Ö ³´μ£μÊ•μ¢´¥¢ÒÌ ±¢ ´Éμ¢ÒÌ¸¨-É¥³. ‚ § ¨³μ¤¥°¸É¢¨¥¸¢´¥Ï´¨³ μ±•Ê¦¥´¨¥³¨¸ÉμÌ ¸É¨Î¥¸±¨³¨¢´¥Ï´¨³¨ ¶μ²Ö³¨• §•ÊÏ ¥É ±μ-£¥•¥´É´μ¸ÉÓ. Šμ´±Ê•¥´Í¨Ö ÔÉ¨Ì ¶•μÍ¥¸¸μ¢¨ §ÊÎ¥´ ´ μ¸´μ¢¥ ¶μ¤Ìμ¤ Ê• ¢´¥´¨°"μ±±¥• Ä² ´± , ¢Ò¢¥¤¥´´ÒÌ¨ § ±¨´¥É¨Î¥¸±μ£μ Ê• ¢´¥´¨Ö ¤²Ö ³ É•¨ÍÒ ¶²μÉ´μ¸É¨¸¨¸É¥³Ò. ¸¸³μÉ•¥´ ¶•¨³¥• ¤¨´ ³¨±¨±μ£¥•¥´É´ÒÌ¸μ¸ÉμÖ´¨°¤²Ö ¤¢ÊÌÊ•μ¢´¥¢ÒÌ Éμ³μ¢ ¢μ ¢´¥Ï´¥³¸ÉμÌ ¸É¨Î¥¸±μ³ ¶μ²¥ ¢ ¥¨¤¥ ²Ó´μ³ •¥ §μ´ Éμ•¥. ‚Ò ¶μ²´¥´μ Ê¸•¥¤´¥´¨¥ ¶μ •¥ ²¨ § Í¨Ö³¸ÉμÌ ¸É¨Î¥¸±μ£μ ¶μ²Ö ¢¸²ÊÎ ÖÌ ¡¥²μ£μ £ Ê¸¸μ¢ ÏÊ³ ¨ ¶•μÍ¥¸¸ ŠÊ¡μÄ´¤¥•¸μ´. ‚Ò¢¥¤¥´Ò Ö¢´Ò¥ Ëμ•³Ê²Ò ¤²Ö ¢¥•μÖÉ´μ¸É¥° °É¨ Éμ³´ ¢¥•Ì´¥³¨´¨¦´¥³ Ê•μ¢´¥¨±μ´ÉÊ• ²¨´¨¨¨ §²ÊÎ¥´¨Ö.

J. of PhysA Math&Gen32-631-646 (1999)

2013

For a quantum open system the so-called Schrödinger-Langevin picture has been revisited. In a second-order perturbation it is shown that a non-Markovian evolution for the stochastic state vector leads to a dissipative generator which has a Kossakowski-Lindblad form. In this context it is possible to analyse the completely positive condition. The equivalence of this picture with the trace-out technique in the weak coupling approximation has been proved.

0 Ju l 2 00 2 Introduction to Quantum Information Processing

2008

2 Quantum Information 4 2.1 The Quantum Bit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Processing One Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Two Quantum Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 Processing Two Qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Using Many Quantum Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.6 Qubit Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.7 Mixtures and Density Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.8 Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.9 Resource Accounting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.10 From Factoring to Phase Estimation . . . . . . . . . . . . . . . . . . . . ...

An outline of quantum probability

1 INDEX Introduction (1a.) Foundations of quantum theory (1b.) Quantum probability and the paradoxes of quantum theory (1c.) Von Neumann' s measurement theory (1d.) Contemporary measurement theory (1e.) Open systems and quantum noise (1f.) Stochastic calculus (1g.) Laws of large numbers and central limit theorems (1h.) Conditioning PART I: ALGEBRAIC PROBABILITY THEORY (2.) Algebraic probability spaces (3.) Algebraic random variables (4.) Stochastic Processes (5.) The local algebras of a stochastic process (6.) Independence (7.) Example: quantum spin systems (8.) A combinatorial lemma (9.) The Boson law of large numbers for independent random variables (10.) The central limit theorem for product maps (11.) Boson and Fermion Gaussian maps (12.) The quantum commutation relations as GNS representations (13.) The quantum commutation relations (14.) De Finetti' s theorem (15.) Conditioning: expected subalgebras (16.) Conditional amplitudes on B(H o ) (17.) Transition expectations and Markovian operators (18.) Markov chains, stationarity, ergodicity (19.) Conditional density amplitudes, potentials and invariant weights (20.) Multiplicative functionals and the discrete Feynman integral (21.) Quantum Markov chains and high temperature superconductivity models (22.) Kümmerer's Markov chains (23.) The algebraic states of Fannes, Nachtergaele and Slegers (24.) 1-dependence and the Ibragimov-Linnik conjecture (25.) 1-dependent quantum Markov chains 2 (26.) Commuting conditional density amplitudes (27.) Diagonalizable states (28.) A nonlinear chain of harmonic oscillators (29.) Generalized random walks (30.) The diffusion limit of the coherent chain (31.) Cecchini' s Markov chains PART II : STOCHASTIC CALCULUS (32.) Simple stochastic integrals (33.) Semimartingales and integrators (34.) Forward derivatives (35.) The o(dt)-notation (36.) Stochastic differential equations (37.) Meyer brackets and Ito tables (38.) The weak Itô formula (39.) The unitarity conditions (40.) The Boson Lévy theorem PART III : CONDITIONING (41.) The standard space of a von Neumann algebra (42.) The ϕ-conditional expectation

Entangled solitons and stochastic q-bits (original) (raw)

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