This paper demonstrates that some nonclassical models of human decision-making can be run successfully as circuits on quantum computers. Since the 1960s, 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 2020s, 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：本文证明，一些非经典的人类决策模型可以成功地在量子计算机上作为电路运行。自20世纪60年代以来，许多观察到的认知行为已被证明违反了基于经典概率和集合论的规则。例如，提问的顺序会影响参与者回答“是”或“否”的方式，因此对两个问题都回答“是”的人群无法被建模为两个固定集合的交集。然而，它可以被建模为按不同顺序进行的投影序列。这一例子及其他类似现象已通过量子概率成功描述，量子概率依赖于比较子空间之间的角度而非子集之间的体积。如今在21世纪20年代初，量子计算机已发展到足以在量子硬件上实现并研究部分量子认知模型的阶段，即将心理状态表示在量子比特寄存器中，并使用不同的量子门与测量操作来表征认知操作与决策。本文针对量子认知模型开发了此类量子电路表示，特别关注对顺序效应和不确定性下的决策进行建模。我们的主张并非人类大脑显式地使用量子比特和量子电路（正如布尔集合论的使用并不要求大脑基于经典比特工作），而是量子认知与量子计算之间共享的数学结构激发了利用量子计算机进行认知建模的探索。关键的量子特性包括叠加、纠缠和坍缩，这些数学元素为认知模型、量子硬件和电路实现提供了共同语言。