Quantum computers are expected to contribute more efficient and accurate ways of modeling economic processes. Quantum hardware is currently available at a relatively small scale, but effective algorithms are limited by the number of logic gates that can be used, before noise from gate inaccuracies tends to dominate results. Some theoretical algorithms that have been proposed and studied for years do not perform well yet on quantum hardware in practice. This encourages the development of suitable alternative algorithms that play similar roles in limited contexts. This paper implements this strategy in the case of quantum counting, which is used as a component for keeping track of position in a quantum walk, which is used as a model for simulating asset prices over time. We introduce quantum approximate counting circuits that use far fewer 2-qubit entangling gates than traditional quantum counting that relies on binary positional encoding. The robustness of these circuits to noise is demonstrated. We compare the results to price change distributions from stock indices, and compare the behavior of quantum circuits with and without mid-measurement to trends in the housing market. The housing data shows that low liquidity brings price volatility, as expected with the quantum models.

翻译：量子计算机有望为经济过程建模提供更高效、更精确的方法。当前量子硬件的规模相对较小，但有效算法受限于逻辑门的使用数量——超过一定限度后，门操作不精确性带来的噪声将主导计算结果。一些经过多年研究和理论验证的算法在实际量子硬件上表现不佳，这促使人们开发在有限场景中发挥类似作用的替代算法。本文以量子计数为案例实施这一策略：量子计数作为量子游走中位置追踪的组件，而量子游走则被用于模拟资产价格随时间演化的模型。我们引入了比传统依赖二进制位置编码的量子计数使用更少双量子比特纠缠门的近似量子计数电路，并证明了这些电路对噪声的鲁棒性。我们将结果与股票指数价格变化分布进行比较，同时对比了含中间测量与不含中间测量的量子电路在房地产市场趋势中的表现。住房数据表明，低流动性会导致价格波动，这与量子模型的预期一致。