Quantum generative model on bicycle-sharing system and an application

TL;DR

This work addresses bicycle-sharing shortages by learning a quantum generative process that couples multi-port time-series data through quantum time evolution $U(\vec{\theta},t)$. It discretizes data with SAX into $N$ states, maps states to quantum qubits, and optimizes a correlation-aware loss $C(\vec{\theta})$ that combines $D_{KL}$ fidelity to observed transitions with inter-port correlation terms. The approach is demonstrated on Sendai's DATE BIKE data, where a three-group aggregation captures key daily dynamics and correlations, and a counterfactual Monte Carlo analysis estimates primary and secondary effects of pre-adding bicycles along with associated opportunity losses. The results show the quantum generator reproduces marginal dynamics and qualitative correlation structure and supports operational decision-support through scenario analysis, highlighting a scalable, probabilistic tool for mobility demand planning and policy evaluation.

Abstract

Recently, bicycle-sharing systems have been implemented in numerous cities, becoming integral to daily life. However, a prevalent issue arises when intensive commuting demand leads to bicycle shortages in specific areas and at particular times. To address this challenge, we employ a novel quantum machine learning model that analyzes time series data by fitting quantum time evolution to observed sequences. This model enables us to capture actual trends in bicycle counts at individual ports and identify correlations between different ports. Utilizing the trained model, we simulate the impact of proactively adding bicycles to high-demand ports on the overall rental number across the system. Given that the core of this method lies in a Monte Carlo simulation, it is anticipated to have a wide range of industrial applications.

Figures (11)

• Figure 1: Image of SAX. The horizontal axis represents time. In this example, the vertical axis is divided into three intervals (usually, those are taken so that the frequency of occurrence for each symbol is similar). By mapping values to the intervals, a time series is converted into a simple character sequence {$a,a,a,b,c,c,c,c,b,b,b,a$}
• Figure 2: The upper panel depicts an overview of the whole quantum circuit. The lower panel shows the specific structure of $U(\vec{\theta},t)$. The left panel shows the concrete structure of $V$, while the right panel details the orthogonal component $D$. We can also build $V$ as another combination pattern of CNOT, e.x, two qubits away, and those different $V$ can be layered horowitz2022quantum.
• Figure 3: For any port $d$ and time $t$, the state transitions between 0 and $t$ are aggregated to the probability transition matrix over the number of days in the given data set. For a transition matrix, the row expresses the state at time 0 and the column expresses the state at time $t$. The state at 0 corresponds to the quantum state at 0, and the state at $t$ corresponds to the measurement output at $t$.
• Figure 4: Cost change over the 300 iteration. "term1", "term2" shows the first and second term in formula (\ref{['eq:cost_func']}). The result shows that the cost-minimizing process is sufficiently converged.
• Figure 5: To obtain the bicycle count time series from the trained quantum circuit, we iteratively run and measure the circuit by incrementing the time parameter $t$. At each iteration, we set the measured states as the initial state of the next step. We finally obtain a bicycle count time series by accumulating the measurement results.