Quantum stochastic walks on networks for decision-making

Abstract

Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce’s response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process’ degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

Application of Quantum—Markov Open System Models to Human Cognition and Decision

“…One way is to directly solve the differential equation, perhaps using numerical methods. A second way, described by [ 11 , 22 ], is to vectorize the state by stacking each column of on top of each other to form a vector. (Note that is a linear operation.)…”

“…In addition to these lines of evidence, quantum dynamics have been used to account for violations of rational decision making [ 11 ], as well as several dynamic decision inconsistencies [ 12 ].…”

“…Instead, at each moment, the decision maker is in a superposed state with several different levels of evidence having potential to be realized, so that the decision maker has internal uncertainty about the level of evidence. Open system models are ideally suited for combining these two different types of dynamics into a single unified process [ 11 , 14 , 15 , 16 , 17 ].…”

Can Biological Quantum Networks Solve NP‐Hard Problems?

“…Further search along the lines of "quantum games", "quantum decisions" and "quantum finance" opens up a world of quantum applications for rational decision making. [182][183][184][185][186][187][188] All these fields are variants of optimization problems, usually involving Ising-type quantum spin Hamiltonians generalising classical binary problems. To provide quantum advantage (i.e., exponential speedup) the algorithms must run on quantum hardware.…”

Quantum-like dynamics applied to cognition: a consideration of available options

“…This uniform mixture of possible opinions would correspond to a classical mental state, given by a normalized identity matrix. Other examples for such open system modeling occur in political science, in the complex dynamics of election campaigns where potential voters are submerged in a high intensity information flow from various external sources [39,40], or they occur in connectionist approaches describing the decision-maker embedded in her surrounding environment [41].…”