[Paper Review] Quantum computer: an appliance for playing market games

Edward W. Piotrowski, Jan Sładkowski|ArXiv.org|May 5, 2003

Quantum Mechanics and Applications4 citations

TL;DR

This paper proposes a quantum game-theoretic framework for financial markets, modeling traders' strategies using qubits and quantum operations to enable interference and entanglement effects that can yield superior payoffs. It demonstrates that quantum strategies in a market context can outperform classical ones due to quantum interference and non-local correlations, offering a theoretical foundation for quantum advantage in trading and market design.

ABSTRACT

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The authors have recently proposed a quantum description of financial market in terms of quantum game theory. The paper contain an analysis of such markets that shows that there would be advantage in using quantum computers and quantum strategies.

Motivation & Objective

• To explore how quantum computation and quantum game theory can be applied to model and enhance financial market dynamics.
• To investigate whether quantum strategies—represented as qubits and governed by quantum operations—can provide a competitive advantage in market games.
• To analyze the role of quantum interference, entanglement, and non-classical correlations in shaping trader behavior and market outcomes.
• To propose a theoretical model of a 'quantum market' where quantum strategies lead to new forms of market efficiency and profit generation.

Proposed method

• Traders' strategies are represented as qubits in a two-dimensional Hilbert space, parameterized by complex amplitudes |z⟩ = |0⟩ + z|I⟩, with |0⟩ and |I⟩ denoting low and high price acceptance.
• Quantum interference is modeled via the Fourier transform (Hadamard gate), mapping strategies between conjugate bases (|0⟩,|I⟩) and (|0′⟩,|I′⟩), representing supply and demand perspectives.
• Entanglement is used to correlate strategies across traders, enabling non-classical correlations that cannot be replicated by classical communication.
• Quantum teleportation protocols are applied to transfer strategies between players using Bell-state measurements and classical communication, preserving quantum information.
• The model incorporates quantum operations such as the Hadamard transform and controlled operations (e.g., CX) to simulate tactical moves and alliances.
• The framework allows for collective quantum market games where players form alliances, and quantum entanglement is used to implement fair division protocols like Banach-Knaster.

Experimental results

Research questions

• RQ1 Can quantum strategies modeled as qubits lead to higher profits than classical strategies in a market game setting?
• RQ2 How does quantum interference between traders' decisions affect market outcomes and equilibrium behavior?
• RQ3 To what extent can quantum entanglement and non-local correlations be leveraged to create advantageous market positions or alliances?
• RQ4 Can quantum teleportation be used to securely and efficiently transfer trading strategies between market participants?
• RQ5 What are the implications of quantum game theory for the design of fair and efficient market mechanisms in financial systems?

Key findings

• Quantum strategies parameterized by complex amplitudes |z⟩ exhibit interference effects that can alter the probability distribution of market outcomes, even when classical probabilities remain unchanged.
• The phase φ of the complex parameter z influences buying probabilities in the Fourier-transformed basis, demonstrating a purely quantum effect absent in classical models.
• Entangled states such as |0′⟩_A|0⟩_B + |I′⟩_A|I⟩_B enable secure and concise communication of market intentions, detectable upon eavesdropping due to coherence collapse.
• Quantum teleportation allows a player to transfer their strategy to another player using only classical communication and shared entanglement, enabling strategy sharing without cloning.
• Alliances in collective quantum games can be formed using quantum operations, and the Banach-Knaster protocol can be implemented via quantum operations to ensure envy-free strategy distribution.
• The no-cloning and no-reducing theorems imply that quantum strategies cannot be duplicated or reduced by classical means, preserving strategic integrity in quantum markets.