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Machine learning for Schrödinger’s cat paradox

Lizhi Xin, Kevin Z. Xin, Houwen Xin

Published Mar 30, 2023• 0 citations
Publisher

Abstract

Abstract Unlike other quantum models that explain the Schrödinger’s cat paradox through rigorous mathematical structure, we propose a computational model to describe and explain Schrödinger’s cat paradox based on Darwin’s natural selection. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer’s expected value. There is no Schrödinger differential equation and quantum probability in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to discovering the Born rule. We do not model with the usual wave function, but with quantum decision tree that simulates the observer’s decision process, a quantum decision tree can be constructed from eight basic quantum gates as well as three logic operations; each quantum decision tree includes a set of strategies; every time a decision is made, the observer chooses a strategy from the quantum decision tree’s strategy pool first, and then chooses an action (believe whether the cat is alive or dead)) based on the degree of belief which is evolved by genetic programming.

DOI
10.21203/rs.3.rs-2751586/v1

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Abstract Unlike other quantum models that explain the Schrödinger’s cat paradox through rigorous mathematical structure, we propose a computational model to describe and explain Schrödinger’s cat paradox based on Darwin’s natural selection. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer’s expected value. There is no Schrödinger differential equation and quantum probability in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to discovering the Born rule. We do not model with the usual wave function, but with quantum decision tree that simulates the observer’s decision process, a quantum decision tree can be constructed from eight basic quantum gates as well as three logic operations; each quantum decision tree includes a set of strategies; every time a decision is made, the observer chooses a strategy from the quantum decision tree’s strategy pool first, and then chooses an action (believe whether the cat is alive or dead)) based on the degree of belief which is evolved by genetic programming.
Abstract A macroscopic particle obeys Newton's law, and a microscopic particle obeys the principles of quantum mechanics - so where is the sharp boundary between the macroscopic and microscopic worlds? It was this "interpretation problem" that prompted Schrödinger to propose his famous thought experiment (a cat that is simultaneously both dead and alive) and sparked a great debate about the quantum measurement problem, and there is still no satisfactory answer yet. This is precisely the inadequacy of rigorous mathematical models in describing the laws of nature. We propose a computational model to describe and understand the laws of nature based on Darwin's natural selection. In fact, whether it's a macro particle, a micro electron or a security, they can all be considered as an entity, the change of this entity over time can be described by a data series composed of states and values. An observer can learn from this data series to construct theories (usually consisting of functions and differential equations). We don't model with the usual functions or differential equations, but with a state Decision Tree (determines the state of an entity) and a value Function Tree (determines the distance between two points of an entity). A state Decision Tree and a value Function Tree together can reconstruct an entity's trajectory and make predictions about its future trajectory. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer's expected value. There is no differential equation in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to rediscovering Newton's law, the Born rule (quantum mechanics) and the efficient market hypothesis (financial market).
We live in a world brimming with uncertainty, where we constantly have to make a lot of decisions under incomplete information. We are firm believers that our subjective belief cannot be computed by rigorous mathematical formula; instead based on Darwin's natural selection (the evolution process is simulated by machine learning with genetic programming), a proposed computational model that incorporates insights from quantum theory to describe and explain decision-making under uncertainty. Unlike other decision-making theories that explain the decision-making process through probability theory, our proposed decision theory discovers "laws" of thought by learning observed historical data. There is no differential equation and no transition probability in our decision theory, our decision model has an emphasis on machine learning, where decision-makers build-up their experience by being rewarded or punished for each decision they make and prepare them for making better decisions in the future. We do not model with the usual utility function, but with quantum decision tree that simulates people's decision process. Each quantum decision tree includes a set of strategies; every time a decision is made, the decision-maker first chooses a strategy from the quantum decision tree's strategy pool, and then chooses an action based on the degree of belief which is obtained by genetic programming based on maximizing expected value.
In order to know if the Schrodinger's cat is alive or dead without opening the box, observers have to play a game with nature. The observers have to "guess" (with degrees of belief) the state of the cat due to incomplete information; in other words, the observers' decision has to be made under uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Value operator is proposed to guide observers to choose corresponding actions based on their subjective beliefs through objective quantum world by maximizing the value from the measured historical results. The value operator, as a quantum decision tree, can be constructed from both quantum gates and logic operations. Genetic programming is applied to optimize quantum decision trees.
The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities (or eigen states).This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation.However, when a measurement is carried out on the system to determine the value of that property (say position), the system instantaneously transforms to one of the eigen states and thus we get only a single value as an outcome of the measurement.Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation.In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real-world and will identify the root cause behind the stochastic nature of events.Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement.In the process of development of model, we will explain Schrodinger cat paradox and will show how Born's rule for probability becomes a natural consequence of the measurement process.
Incorporating insights from quantum theory, we propose a machine learning-based decision-making model, including a logic tree and a value tree; a genetic programming algorithm is applied to optimize both the logic tree and value tree. The logic tree and value tree together depict the entire decision-making process of a decision-maker. We applied this framework to the financial market, and a "machine economist" is developed to study a time series of the Dow Jones index. The "machine economist" will obtain a set of optimized strategies to maximize profits, and discover the efficient market hypothesis (random walk).
What is the observer's role in quantum measurement? Obviously, observers prepare the apparatus, observe and interpret the measured results. Although the observer will have a certain influence on the measurement results by setting up the measuring apparatus, we don't believe human consciousness cause reducing of wave packet; also observers are certainly required to interpret the measured results with physical meanings. We believe observers build up their experience of the external world by playing games with nature, and then "decode" the nature based on their experiences. We propose a quantum decision theory approach to explain the role of the observer in quantum measurements, and pointed out that a set of quantum decision trees (strategies to answer natural questions with yes/no logic) can be optimized to deal with the challenges of nature through quantum genetic programming based on maximization of the expected value of the observers; Quantum decision trees can discover the dynamics rules of quantum entities and Just as classical mechanics uses the principle of least action to obtain the trajectories of particles, we use the principle of maximum expected value to approximately obtain the kinematic "trajectories" of quantum entities by learning from natural historical "events" (measured results); even we can "reconstruct" the past of quantum entity, because we don't know the prior information of quantum entity, it is very difficult to predict the future of the nature.