Since the 1990's, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can however be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020's, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modelling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.

翻译：自20世纪90年代以来，大量观察到的认知行为已被证明违背基于经典概率和集合论的规则。例如，问题提出的顺序会影响参与者回答"是"或"否"，因此对两个问题均回答"是"的人群无法被建模为两个固定集合的交集。然而，这可以被建模为按不同顺序执行的投影序列。这一案例及其他实例已成功运用量子概率理论进行描述，该理论依赖子空间之间的夹角比较而非子集之间的体积比较。进入21世纪20年代初期，量子计算机的发展已达到可部分实现并研究这些量子认知模型的阶段——在量子硬件上，通过量子比特寄存器表征心理状态，并利用不同量子门与测量操作表征认知过程与决策。本文针对量子认知模型开发此类量子电路表征方法，重点研究顺序效应与不确定性下的决策建模。本文并非主张人脑显式使用量子比特与量子电路（正如布尔集合论的应用并不要求人脑使用经典比特），而是强调量子认知与量子计算共享的数学基础为探索量子计算机用于认知建模提供了动力。核心量子特性包括叠加、纠缠与坍缩，这些数学元素为认知模型、量子硬件与电路实现之间构建了共同语言。