Abstract Decision’s biggest challenge is uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Decision-making under uncertainty is the unification of people’s subjective beliefs and the objective world. Quantum density operator as value operator which we call it quantum circuit is proposed to simulate people’s subjective beliefs. Quantum circuit guides people to choose corresponding actions based on their subjective beliefs through objective world. The quantum circuit is a decision tree constructed from quantum gates and logic operations. The genetic programming can be used to optimize and auto-generate quantum circuits. Our proposed synapse’s quantum circuit hypothesis states that the combination of neurotransmitter and receptor functioned as quantum circuit open or close ion channels probabilistically which determines the excitation or inhibition of synapse.
Abstract Decision’s biggest challenge is uncertainty. We propose a quantum expected value theory for decision-making under uncertainty. Decision-making under uncertainty is the unification of people’s subjective beliefs and the objective world. Quantum density operator as value operator which we call it quantum circuit is proposed to simulate people’s subjective beliefs. Quantum circuit guides people to choose corresponding actions based on their subjective beliefs through objective world. The quantum circuit is a decision tree constructed from quantum gates and logic operations. The genetic programming can be used to optimize and auto-generate quantum circuits. Our proposed synapse’s quantum circuit hypothesis states that the combination of neurotransmitter and receptor functioned as quantum circuit open or close ion channels probabilistically which determines the excitation or inhibition of synapse.
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.
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.
Decision making in stochastic autonomous systems, which considers uncertainty of many factors, is always a challenge. The problem can typically be addressed by probabilistic methods such as approximate stochastic optimization or Monte Carlo (MC) simulation. The potential solution may usually be constrained by the system's computing power, due to the size of the probabilistic problem. This paper aims to present and implement a quantum probabilistic comparison (QPC) algorithm that can help to find a desired solution or make decision between two random variables under uncertainty. This approach takes advantage of quantum computing to perform parallel comparison and fast calculation of the probability of matched state vectors. In the presented scheme, two random variables have different values (e.g., 2, 4, 8, or more values) and different probability distributions. The data of the variables are encoded to the basis states of the corresponding qubits. The quantum probabilistic comparator is used to make up the quantum output matrix that stores the comparison solutions as well as their probability probabilities. Moreover, unlike the existing quantum comparator algorithm, which uses bit string comparison approaches, the proposed probabilistic comparator is not only comparing the basis state, but also accumulating the outcome's probabilities. The calculation results of the quantum probabilistic comparator circuit are compared with those from classical computation and quantum circuit simulation as well as on an IBM quantum computer, for analysis and verification.
Quantum circuit optimization is a crucial step in realizing the full potential of quantum computing. However, the inherent uncertainty in quantum gate fidelities and measurement outcomes presents a significant challenge. Traditional optimization methods often fail to adequately address this probabilistic nature. This paper proposes a novel dynamic programming approach for quantum circuit optimization that explicitly incorporates uncertainty. The algorithm constructs an optimal circuit path by minimizing the expected cost, which accounts for the potential error associated with each gate operation and measurement. This framework allows for a more accurate and robust optimization process, leading to circuits with reduced error and improved performance. The core claim is that dynamic programming can be effectively applied to quantum circuit optimization, acknowledging and utilizing the probabilistic elements. The key mechanism involves a structured, iterative process to evaluate and select the best circuit paths based on a quantified uncertainty model. This approach avoids the limitations of purely deterministic optimization techniques when dealing with quantum systems.
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).
Can quantum theory provide new answers to puzzling results from decision research that have resisted formal explanations so far? This chapter presents several new contributions that quantum theory provides to decision research. However, in order to locate where quantum theory can make an important new contribution, we first need to provide some necessary background on decision theory and what has already been accomplished. Decision science is a highly developed field that has produced a variety of sophisticated mathematical theories (Gilboa, 2009; Wakker, 2010). Some of these theories are rational theories, which prescribe optimal ways to make decisions. Others are psychological theories that describe the way people actually make decisions. One of the most important rational decision theories is von Neumannn and Morgenstern's expected utility (EU) theory (von Neumann & Morgenstern, 1944). Expected utility theory is designed for decisions under risk ; that is, a choice among actions defined as an objective probability distribution over possible payoffs. An important extension of (EU) theory is Savage's (1954) subjective expected utility (SEU) theory . This extends utility theory to decisions under uncertainty ; that is, a choice among actions defined as functions that map un-certain events into payoffs, and the events may not have objective probabilities. A more general theory designed for decisions under both uncertainty and risk was presented by Anscombe and Aumann (1963). All of these theories are rational, in the sense that they are based on a small set of compelling axioms and the prescribed action logically follows from the axioms.