Introduction to Quantum Dynamics with Quantum Superposition

Ciaran Hughes, Joshua Isaacson, Anastasia Perry +2 more

Abstract In this section, we review the concepts of classical and quantum superposition. Quantum superposition is the framework for understanding all quantum phenomena. As we do not observe quantum phenomena in our everyday lives, it may seem confusing at first. However, as unintuitive as the quantum world may appear, there are a vast number of experiments which conclusively show that the universe really does operate according to the law of quantum superposition at the smallest distances accessible today. Before going into specific details on quantum superposition, it is useful to explain how the term “superposition” is used in different contexts in both classical and quantum physics. At the end of the chapter, we present the related activities and questions. After gaining experience with quantum superposition from working through these problems, it will become more intuitive. The more experience you gain by advancing through this book, the more quantum superposition will make sense.

Jesús Fernández‐Villaverde, Isaiah Hull

We introduce a novel approach to solving dynamic programming problems, such as those in many economic models, on a quantum annealer, a specialized device that performs combinatorial optimization. Quantum annealers attempt to solve an NP-hard problem by starting in a quantum superposition of all states and generating candidate global solutions in milliseconds, irrespective of problem size. Using existing quantum hardware, we achieve an order-of-magnitude speed-up in solving the real business cycle model over benchmarks in the literature. We also provide a detailed introduction to quantum annealing and discuss its potential use for more challenging economic problems.

Azeddine Ennabati

This paper extends the Relative Cosmic Equilibrium (RCE) framework to the foundations of quantum mechanics. We demonstrate that the Schrödinger equation emerges naturally from the linearized dynamics of a single scalar energy deviation field ΔE(x, t) near equilibrium, without imposing quantization postulates. Planck’s constant ℏ appears as a derived quantity — the minimal topological action unit of the field. Quantum superposition is reinterpreted as a stable multimodal dynamical equilibrium in which the field coherently populates degenerate minima of the effective action. Measurement is physically defined as the introduction of an external energy gradient that breaks this degeneracy, triggering an exponential relaxation toward a single definite outcome. A key result is the derivation of a falsifiable, energy-dependent collapse time: τ ≈ ℏ / ΔE_meas For conventional measurements (ΔE ~ eV), the collapse is extremely fast (~10^{-16} s). However, in weak measurements with very low energy exchange (ΔE ~ 1 neV), the theory predicts an observable collapse time of approximately 0.66 μs. A feasible table-top optical experiment using single photons and time-resolved correlation measurements is proposed to test this prediction. This work transforms the quantum measurement problem from a philosophical puzzle into a concrete, experimentally testable question. Keywords: Quantum measurement problem, Objective collapse, Quantum superposition, Dynamical equilibrium, Energy-dependent collapse, RCE theory, Weak measurement, Foundations of quantum mechanics

Jack Cohn