We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.
We describe a general approach to modeling rational decision-making agents who adopt either quantum or classical mechanics based on the Quantum Bayesian (QBist) approach to quantum theory. With the additional ingredient of a scheme by which the properties of one agent may influence another, we arrive at a flexible framework for treating multiple interacting quantum and classical Bayesian agents. We present simulations in several settings to illustrate our construction: quantum and classical agents receiving signals from an exogenous source, two interacting classical agents, two interacting quantum agents, and interactions between classical and quantum agents. A consistent treatment of multiple interacting users of quantum theory may allow us to properly interpret existing multi-agent protocols and could suggest new approaches in other areas such as quantum algorithm design.
Abstract In multi-agent systems, Bayesian networks are pivotal for inference and decision-making under uncertainty, yet they face significant challenges, such as high computational complexity and slow decision speed. Quantum computing, leveraging superposition and entanglement, offers potential advantages for solving certain complex problems. Therefore, exploring Bayesian networks within the quantum multi-agent framework promises enhanced inference and decision-making capabilities. While quantum Bayesian networks for inference have been extensively studied, quantum dynamic Bayesian networks for inference and quantum decision networks for decision-making remain underexplored. In the noisy intermediate-scale quantum (NISQ) era, quantum computers struggle to process the long-term temporal structures of dynamic Bayesian networks due to limited resources. To address this, we propose a recursive quantum-classical hybrid Bayesian network inference method, which decomposes dynamic Bayesian networks into smaller subnetworks along the time series. Each subnetwork is represented by a reduced-scale quantum circuit, and the forward and backward operators are computed recursively, enabling efficient filtering and smoothing inference. In addition, we propose an optimal decision-making method based on quantum decision networks, which maps utility values to quantum probabilities and identifies the optimal action by determining the quantum state corresponding to the maximum expected probability. We validate the effectiveness of these algorithms using the IonQ quantum simulator and compare their performance with classical methods. The results demonstrate that our proposed quantum algorithms can effectively perform inference and decision-making tasks well on NISQ devices. The proposed methods provide a foundation for collaborative inference and decision-making within the quantum multi-agent framework.
Imagine a Bayesian decision agent who is keen to invest only in technologies or businesses that are conductive to achieving a sustainable economic future. Being initially keen to invest in a certain technology, subsequently two pieces of new information are received that both individually reduce the agent’s inclination to make that investment. In such a situation, it would be natural to assume that the simultaneous consideration of both pieces of information should further reduce the agent’s initial enthusiasm; after all the Bayesian method has been called “ nothing but common sense reduced to calculation.” Somewhat surprisingly, making general statements like this about the double conditional probability requires substantial additional assumptions in classical Bayesian probability theory. We investigate four schemes of assumptions that allow ‘reasonable’ conclusions about the double conditional probability. We compare this with two schemes for the quantum probability model where the double conditional results from sequential updating through projections.
Abstract Although quantum Bayesian networks provide a promising paradigm for multi-agent decision-making, their practical application faces two challenges in the noisy intermediate-scale quantum (NISQ) era. Limited qubit resources restrict direct application to large-scale inference tasks. Additionally, no quantum methods are currently available for multi-agent collaborative decision-making. To address these, we propose a hybrid quantum–classical multi-agent decision-making framework based on hierarchical Bayesian networks, comprising two novel methods. The first one is a hybrid quantum–classical inference method based on hierarchical Bayesian networks. It decomposes large-scale hierarchical Bayesian networks into modular subnetworks. The inference for each subnetwork can be performed on NISQ devices, and the intermediate results are converted into classical messages for cross-layer transmission. The second one is a multi-agent decision-making method using the variational quantum eigensolver (VQE) in the influence diagram. This method models the collaborative decision-making with the influence diagram and encodes the expected utility of diverse actions into a Hamiltonian and subsequently determines the intra-group optimal action efficiently. Experimental validation on the IonQ quantum simulator demonstrates that the hierarchical method outperforms the non-hierarchical method at the functional inference level, and the VQE method can obtain the optimal strategy exactly at the collaborative decision-making level. Our research not only extends the application of quantum computing to multi-agent decision-making but also provides a practical solution for the NISQ era.
We offer a realist interpretation of non-relativistic quantum mechanics in which dynamical properties are properly possessed by the system in question, and are supposed to have definite values at any time. Like the QBists, we employ Bayesian probability, but we adopt something closer to the Bayesian statistics of E. T. Jaynes than to the subjective Bayesian statistics of B. de Fenetti employed by the QBists. Accordingly, we view calculated Bayesian probabilities as rational degrees of expectation of dynamical property values rather than as personal degrees of expectation of future (measurement) experiences. Probabilities are, for us, based on knowledge of the value of some dynamical property of the system, not on knowledge of previous experiences unassociated with system dynamical properties. As some Bayesians might, we take a probability equal to 1 not generally to indicate certainty but only (full) expectation; and we disallow probabilities of conjunctions of propositions claiming incompatible properties. Then, by reinterpreting and adding a little to the quantum formalism, we argue that we can maintain the advantages of the QBist interpretation. So, for us (as for the QBists), there is no unexplained collapse of the wave function, no need for ‘spooky action at a distance’, and no problem raised by the double slit experiment, the Kochen-Specker paradox or Bell type theorems. By holding on to a realist perspective, modelling (of ideal measurements, of system preparation processes etc.) is possible, and we can claim certain dynamical laws of quantum mechanics without leading to contradiction.
Purpose: Decision-making under uncertainty remains a foundational challenge in cognitive science and artificial intelligence. Classical Bayesian Probability Models (CBM) often fail to explain paradoxical cognitive behaviors such as order effects, ambiguity aversion, and context-dependent reasoning. This study seeks to compare Quantum Probability Theory (QPT) and Classical Bayesian Models in their ability to capture the dynamics of human decision-making. It aims to determine which framework more accurately reflects the cognitive mechanisms underlying reasoning under uncertainty. Methodology: A qualitative, exploratory research design was adopted, involving in-depth semi-structured interviews with 16 experts across psychology, philosophy, artificial intelligence, and cognitive neuroscience. Participants were purposively selected for their theoretical and empirical expertise in probabilistic reasoning. Data were analyzed using reflexive thematic analysis, guided by the Dual-Process Theory and Busemeyer’s Quantum Cognition framework. The analysis emphasized participants’ perspectives on theoretical assumptions, cognitive plausibility, and predictive utility between QPT and CBM paradigms. Findings: Thematic findings reveal that Quantum Probability Theory offers superior explanatory power in contexts involving cognitive ambiguity, contextual dependence, and non-commutativity of mental operations. Participants consistently reported that QPT better models real-world reasoning tasks where classical logic collapses, capturing the fluid and context-sensitive nature of human judgment. Conversely, while CBM remains effective in structured, low-uncertainty scenarios, it fails to accommodate superposition and interference effects inherent in human cognition. Unique Contribution to Theory, Practice, and Policy (Recommendations): The study contributes theoretically by demonstrating how quantum probabilistic models expand existing theories of bounded rationality and probabilistic reasoning in cognitive science. Practically, it encourages interdisciplinary collaboration between cognitive scientists, AI researchers, and philosophers to refine decision models that mirror human intuition more closely. Policy-wise, the findings support the integration of quantum-inspired approaches in the design of intelligent decision-support systems and cognitive architectures. The study recommends continued empirical validation of QPT within applied domains—such as behavioral economics, machine learning, and cognitive modeling—to strengthen its predictive and explanatory robustness.
Can an agent's predictions reveal whether its reasoning is based on a classical or a quantum model? Using known results on matrix factorizations, here we show that quantum Bayesian retrodiction can produce one-step-ahead forecasts incompatible with every classical Bayesian explanation based on learning about a fixed but unknown sampling law from conditionally independent observations. The separation has a sharp threshold in the number of outcomes: for any measurement with at most four outcomes, the quantum predictions admit a classical realization, irrespective of the prior state and the finite Hilbert-space dimension, whereas a five-outcome measurement on a single qubit already violates an explicit classical bound. This bound holds for arbitrary classical latent states, prior probabilities, and sampling laws, and involves only the agent's initial and updated predictions. Thus, in this setting, quantum Bayesian retrodiction is strictly more expressive than classical Bayesian learning, and this difference can be witnessed without observing or specifying the agent's internal description.