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Specifing recurses for stochastics Schorödinger deriven to n-step probabilities in measurements

Autor:

JUAN JOSE MOLINA GONZALEZ

https://orcid.org/0000-0001-6256-8898
jjmg@edu.es
jjmg@um.es
jjmg@um.edu
Prof. Asis. Sr. Juan José Molina González
University of Murcia

A derivation of stochastic Schr¨odinger equations is given using quantum filtering theory. We study an

open system in contact with its environment, the electromagnetic field. Continuous observation of the

field yields information on the system: it is possible to keep track in real time of the best estimate of the

system’s quantum state given the observations made (Markovian). This estimate satisfies a stochastic Schr¨odinger

equation, which can be derived from the quantum stochastic differential equation for the interaction

picture evolution of system and field together.

There are many stochastic processes in mathematics. In this chapter, we will study a special kind of

stochastic process, called Markov Chain, where the next state of the system depends only on the present

state. Before to start, just recall that Markov Chain where introduced in 1906 by the Russian

mathematician Andrei Andreyevich Markov (1856 – 1922) and were named in his honor. Some a

countable set and each i I n  is a state, then I is called a state-space. In this chapter, we will work in the

probability space (  ,Ŧ,  ) where  is a set of outcomes, Ŧ the set of subsets of  and for any A  Ŧ , 

( A ) is a probability of A .Our goal is to study a sequence n/ 0 X  where 1 2 X X, , are taking from the

set I .

Specifing recurses for stochastics Schorödinger deriven to n-step probabilities in measurements of

The function X :   I is called a random variable, where the values of X belong the state-space  . [1,9]

Definition 4.3. Let  =( : i  i ) be a row vector. Then  is called measure if for all i I , i  . In the

special case, when   (0,0,...,1,...,0), it is longest probability vector given anteriorely.We will denote  = i 

. In sum the state of X :   I depend of past states in an randon walk due for n-steps that in Mathlab

receivent the nom of bar for the unicity of the convolution of states determinated in    then  is a

probability measure or probability vector . Thus determine the states of Qubits possibles in the fields

(  ,Ŧ,  ) where the probability of 1 bar depend of the state  for the possibles fields for the stochastics

processes of Schorödinger tratted some an Markovian for the unicity 1 bar

The Monte Carlo particle numbering scheme presented here isintended to facilitate interfacing between

event generators, detectorsimulators, and analysis packages used in particle physics. Thenumbering

scheme was introduced in 1988 [1] and a revisedversion [2,3] was adopted in 1998 in order to allow

systematic inclusionof quark model states which are as yet undiscovered and hypotheticalparticles such as

SUSY particles. The numbering scheme is used inseveral event generators, e.g. HERWIG and

PYTHIA/JETSET, andin the /HEPEVT/ [4] standard interface.The general form is a 7–digit number:

±nnrnLnq

This encodes information about the particle’s spin, ﬂavor content, and

internal quantum numbers. The details are as follows:Particles are given positive numbers, antiparticles

negativenumbers. The PDG convention for mesons used, so that Kand B are particles. Quarks and

leptons are numbered consecutively starting from 1+and 11 respectively; to do this they are ﬁrst ordered

by family and within families by weak isospin. In composite quark systems (diquarks, mesons, and

baryons)n are quark numbers used to specify the quark content, whilethe rightmost digit nq1-3=2J + 1

gives the system’s spin (exceptfor the K0/S and K0_L-J). The scheme does not cover particles of spinJ>4.

Diquarks have 4-digit numbers with nq1= nq2and n=0. The numbering of mesons is guided by the

nonrelativistic (L–Sdecoupled) quark model, The numbers specifying the meson’s quark content

conformto the convention nq1=0andn. The special case K0_L/q2= nq is the sole exception to this rule.

Getting an API Key

From here we can start building out the definition of the problem that we would like to solve. We'll start with an NP Hard problem called Maximum Weighted Cut. We can define a graph we would like to cut by supplying a list of edges and their weights.

graph = [ (0, 1, 1.0), (0, 2, 1.0), (0, 4, 1.0), (1, 2, 1.0), (2, 3, 1.0), (3, 4, 1.0), ]

We can then give this graph to our "Application" which will define what we want to do with it and how to translate it into the quantum world and back. Q3AS defines multiple such problem domains that you can us

from q3as.app import Maxcut app = Maxcut(graph)

We now need to define a solver for our problem. We will use a Variational Quantum Eigensolver or VQE for shor

from q3as import VQE vqe = VQE.builder().app(app)

Now we can send the job to the Q3AS, and let the server handle the computation and the visualization of the intermediate result that resul for API key the computation of graph for the possibles trf/domain-graph in sets to (1,2,3,4) eigenvalues random path possibles for the determinated probability space (  ,Ŧ,  ) where  is a set of outcomes .

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