Abstract Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a novel approach by transposing fundamental concepts of quantum mechanics—such as superposition, operator algebra, and path integrals—into the realm of macroeconomic modeling. Within this quantum framework, core economic variables (capital, labor, and technological progress) are redefined as non-commuting operators acting on Hilbert spaces, and the state of the economy is represented as a dynamic wave function governed by a time-dependent Hamiltonian. The evolution of this economic wave function follows a generalized Schrödinger equation, developed here through Dyson series and Magnus expansions. We also define a quantum production function as the expected value of a composite operator, capturing the probabilistic nature of economic output. By integrating uncertainty relations analogous to Heisenberg's principle, and modeling economic fluctuations via Langevin dynamics, we extend the model to include dissipation, feedback loops, and non-linear interactions between variables. Finally, a Feynman path integral formalism is constructed to provide an alternative trajectory-based interpretation of economic dynamics. This quantum-inspired framework offers a rigorous and flexible methodology to rethink macroeconomic modeling under radical uncertainty, with potential applications in dynamic policy simulations and innovation-driven growth.
Abstract Traditional economic growth theories, grounded in deterministic and often linear frameworks, fail to adequately capture the inherent uncertainty, non-commutativity, and complex interdependencies of modern economies. This paper proposes a novel approach by transposing fundamental concepts of quantum mechanics—such as superposition, operator algebra, and path integrals—into the realm of macroeconomic modeling. Within this quantum framework, core economic variables (capital, labor, and technological progress) are redefined as non-commuting operators acting on Hilbert spaces, and the state of the economy is represented as a dynamic wave function governed by a time-dependent Hamiltonian. The evolution of this economic wave function follows a generalized Schrödinger equation, developed here through Dyson series and Magnus expansions. We also define a quantum production function as the expected value of a composite operator, capturing the probabilistic nature of economic output. By integrating uncertainty relations analogous to Heisenberg's principle, and modeling economic fluctuations via Langevin dynamics, we extend the model to include dissipation, feedback loops, and non-linear interactions between variables. Finally, a Feynman path integral formalism is constructed to provide an alternative trajectory-based interpretation of economic dynamics. This quantum-inspired framework offers a rigorous and flexible methodology to rethink macroeconomic modeling under radical uncertainty, with potential applications in dynamic policy simulations and innovation-driven growth.
To address the practical impasse of mainstream economics—rooted in the deterministic worldview of Newtonian mechanics—where its mechanistic and linear analytical framework struggles to handle complex scenarios in the digital economy era, such as interactive decision-making, globally non-local correlations, and systemic mutations after sudden shocks, leading to a pronounced tension between theory and practice, this paper constructs a quantum economics analytical framework. Drawing on the inherent uncertainty revealed by quantum mechanics and based on the core isomorphism between economic systems and quantum systems (both centering on uncertainty, featuring superposition of multiple states, observer-induced interaction, and holistic correlations), it translates quantum core logics like superposition, entanglement, and transition into economic analytical tools. Methods such as entanglement entropy and quantum state transition probabilities are employed to quantify the complex correlations and state transformations of economic variables. Empirical studies of China’s macroeconomy validate the framework’s effectiveness, precisely capturing structural features like the strong correlation between money supply and economic growth, transmission frictions between money and prices, and paradigm shifts under policy shocks and event impacts. It further reveals the synergistic effect of a multi-variable system (“1+1+1>3”), quantifies the transitional characteristics and transformation laws of inflation states. The findings demonstrate that quantum economics elevates “uncertainty” to the theoretical core, transcending the paradigm limitations of traditional economics. It provides a novel quantitative perspective for understanding the complex essence and structural contradictions of economic systems, offering a systematic solution to the challenges of modern economic complexity.
Abstract Foundations of Quantum Economics unfolds a coherent theoretical thread, replacing the rational-agent premise of mainstream economics with the quantum-person hypothesis: before observation, decision-makers sustain multiple conflicting options encoded in probability amplitudes, and a decision corresponds to collapse triggered by measurement. The book first lays cognitive and mathematical foundations, demonstrating that human judgement inherently exhibits quantum features including superposition, interference and order dependence. Classical probability theory fails for non-commutative economic events, making Hilbert spaces and probability amplitudes indispensable languages for economic inquiry. It then reconstructs causality, information, uncertainty and risk, arguing that economic causes are not uniquely fixed before the collapse of consensus; uncertainty is endogenous to the system, and risk represents the spread of superposed distributions rather than exogenous noise. Built upon this architecture, the work revisits core microeconomic notions such as value, utility, game interaction, supply and demand, property rights, institutions and innovation. All conventional theories are recovered as special limits under zero interference and single eigenstates, while superposition and entanglement furnish fresh explanatory power for economic anomalies. The analysis further expands into macroeconomics, interpreting growth, business cycles, money, fiscal policy, trade and welfare as coherent superposition, phase transition and collapse of collective cognition and consensus, and concludes with the renovation of econometrics and economic governance. The book’s central thesis holds that superposition, interference, observation and collapse are not metaphors borrowed from quantum physics, but intrinsic properties of human cognition and economic practice. Economic realities are not predetermined facts waiting to be discovered; instead, they are generated through human cognition, consensus and practice in the act of measurement. Quantum economics is far more than a cosmetic revision of existing models. It constitutes a shift of research programme, abandoning Laplacian determinism and reconceiving the economy as an open, generative process. The book articulates five interconnected layers: the quantum person as ontological starting point, quantum features of cognition, superposition of collective consensus, endogenous uncertainty, and quantuminformed governance. It reminds researchers and policymakers that economic observation and policy intervention are performative, capable of reshaping the very system they examine. Economics abandons the pursuit of a single, determinate optimum and embraces endogenous uncertainty; policymakers cease to be omniscient system engineers and become prudent stewards of consensus and designers of measurement bases. This volume establishes the unified bedrock for the whole quantum economics series and calls for a new, more honest and realistic economics embedded within the economic process itself.
Abstract Since Adam Smith, economics has erected a grand edifice upon the foundations of rational agents, equilibrium analysis, and linear causality; however, the 2008 global financial crisis, the European sovereign debt crisis, and the COVID-19 pandemic have successively revealed its fundamental limitations when confronted with complex economic phenomena: bubbles that ought not to have existed, crises unforeseen by equilibrium models, non-linear ruptures brought about by technological revolutions, and self-fulfilling expectations—all of which call for a richer theoretical language. This book serves as the foundational introduction to the "Quantum Economics Textbook Series," as well as the first gateway into this entire series. It introduces the methodological framework, mathematical apparatus, and philosophical insights of quantum mechanics to economic analysis, grounding its approach in the core proposition of a practical ontology—that human economic practice itself possesses quantum attributes such as superposition, entanglement, constructibility, uncertainty, and emergence—thereby reconstructing the economic world as a quantum process of superposition and evolution. Six core concepts—superposition, entanglement, measurement collapse, the uncertainty principle, quantum transitions, and emergence—run throughout the work. Quantum economics does not represent a simple negation of classical theory; rather, it constitutes a dialectical sublation: under the classical limit—where decoherence is complete, the measurement basis is fixed, and entanglement vanishes—quantum theory precisely reduces to classical theory. This book comprises five parts and thirty chapters: Part I establishes the paradigm shift and theoretical framework, covering critiques of Newton's worldview, the quantum worldview, a foundational conceptual framework, mathematical foundations, and research methodologies; Part II reconstructs quantum microeconomic theory, encompassing consumers, producers, pricing, markets, the wave-particle duality of markets, quantum games, and welfare economics; Part III builds quantum macroeconomic theory, addressing national income accounting, money, inflation, economic cycles, policy, and open economies; Part IV explores quantum finance and market dynamics, including asset pricing, portfolio management, market sentiment, risk management, and trading theory; Part V extends the scope to organizations, innovation, institutions, development, economic ethics, and the digital economy, while offering insights into the future of this discipline. This volume is intended for undergraduate and graduate students, as well as researchers in economics and related fields, and serves as the essential first volume in the quantum economics series.
Quantum economics is an interdisciplinary field that combines the principles of quantum mechanics and economic theories. The research examines the main theoretical and practical aspects of quantum economics, starting with its theoretical foundations based on the principles of quantum mechanics, such as superposition, uncertainty and entanglement, and ending with practical applications and perspectives for further research. Special attention was paid to the potential impact of quantum technologies on finance, marketing, supply chain management, as well as on macroeconomic planning and policy. It discusses how quantum algorithms can transform traditional approaches in economic research and practice, providing new methods for analyzing complex data, improving forecasting of economic trends, and optimizing decisions under uncertainty. Quantum economics opens up new perspectives for understanding dynamic and interconnected processes in the global economy, which can fundamentally change our perception of economic laws and strategies. It is emphasized that the quantum economy is at the initial stage of its development, and scientists and practitioners face many challenges and questions that need to be solved. In the future, we can expect the development of new tools for economic analysis and decisionmaking based on quantum computing, which will allow us to cope with current and future economic challenges more effectively. The quantum economy can also offer new approaches to risk management and financial security, especially in light of growing cyber threats and the need to protect economic information. Quantum economics is an exciting and promising direction that can significantly enrich both theoretical and applied aspects of economic science.
This chapter explores the intricate dynamics between medium-sized and large enterprises in EU candidate countries through the lens of Bohm's interpretation of Bohr's complementarity principle and Heisenberg's uncertainty principle which are two fundamental concepts in quantum theory. By drawing parallels between quantum mechanics and economic behavior, the research posits that the growth trajectories of these enterprises are interrelated, exhibiting complementary relationships under uncertainty that reflect the principles of quantum duality. Employing a robust research methodology, the chapter presents empirical evidence showcasing the correlation between capital concentration and growth rates of medium-sized and large enterprises across various regions. Statistical analyses, including Pearson coefficients, reveal significant relationships that support the hypothesis of a higher share of medium enterprises correlating with an increased presence of large enterprises revalidating complementariness. Furthermore, the findings highlight important policy implications for regional economic development, emphasizing the need for tailored strategies that foster the growth of both enterprise sizes under uncertain conditions. By integrating quantum theory with economic dynamics, this chapter contributes a novel perspective to the discourse on entrepreneurship and regional growth, encouraging further exploration of interdisciplinary approaches in econophysics research.
This article explores the interdisciplinary interface between quantum computing and economic theory, with a particular emphasis on how foundational concepts from quantum mechanics reshape core methodological and epistemological assumptions in economics. Drawing on a comprehensive bibliographic methodology, the study synthesizes contributions from quantum physics, computational theory, and economic modeling to trace the impact of quantum logic -especially principles such as superposition, entanglement, and measurement irreversibility- on both theoretical constructs and applied frameworks. Particular attention is given to emblematic algorithms (e.g., Shor’s and Grover’s) as case studies for illustrating computational discontinuities in fields such as cryptographic trust, portfolio optimization, and decision-making under uncertainty. The article also surveys recent developments in quantum machine learning and quantum-inspired models relevant to economic forecasting and adaptive policy design. Ethical and distributional concerns are critically addressed, especially in relation to the asymmetric global access to quantum resources. By mapping this emerging field through a structured review of cross-disciplinary literature, the paper offers a conceptual framework for understanding how quantum technologies may influence future research in financial economics, risk theory, and the modeling of complex systems operating under deep informational constraints.