A Quantum Optimization Algorithm for Optimal Electric Vehicle Charging Station Placement for Intercity Trips

TL;DR

This work tackles the NP-hard charging station location problem for intercity EV trips by formulating it as a gate-based quantum optimization using Grover Adaptive Search (GAS) and Quantum Phase Estimation (QPE). By constructing a resource-efficient quantum oracle that marks valid station combinations and counts their density, the method achieves a quadratic speedup over classical exact approaches and targets a complexity near $O(1.4^n)$ compared to $O(2^n)$. The authors implement a detailed quantum circuit design, including initialization, isolation detection, labeling, restoration, and counting via QPE, and validate the approach on a 7-node Illinois network using a simulator due to hardware limits. The results demonstrate the potential for exact quantum solutions to CSLP and provide a foundation for scaling with future quantum hardware, while outlining avenues to incorporate capacity and reliability constraints in future work.

Abstract

Electric vehicles (EVs) play a significant role in enhancing the sustainability of transportation systems. However, their widespread adoption is hindered by inadequate public charging infrastructure, particularly to support long-distance travel. Identifying optimal charging station locations in large transportation networks presents a well-known NP-hard combinatorial optimization problem, as the search space grows exponentially with the number of potential charging station locations. This paper introduces a quantum search-based optimization algorithm designed to enhance the efficiency of solving this NP-hard problem for transportation networks. By leveraging quantum parallelism, amplitude amplification, and quantum phase estimation as a subroutine, the optimal solution is identified with a quadratic improvement in complexity compared to classical exact methods, such as branch and bound. The detailed design and complexity of a resource-efficient quantum circuit are discussed.

Figures (21)

• Figure 1: Representation of a Pauli-X gate. The X gate flips the state of a qubit from $\ket{0}$ to $\ket{1}$ and vice versa.
• Figure 2: Representation of a Hadamard gate. The Hadamard gate creates a superposition state by transforming $\ket{0}$ to $\ket{+}$ and $\ket{1}$ to $\ket{-}$.
• Figure 3: Representation of CNOT gate. (A) When the control qubit is $\ket{0}$, the target qubit remains unchanged. (B) When the control qubit is $\ket{1}$, the target qubit is flipped.
• Figure 4: Representation of the phase gate: $\ket{0}$ remains unchanged, while $\ket{1}$ is mapped to $\exp(2\pi i/2^n) \ket{1}$.
• Figure 5: Illustration of the initial superposition state in Grover's algorithm. (A) Solution states (green dots) and non-solution states (black dots) illustrating uniform amplitudes. The dashed line represents the mean amplitude of the system. (B) Representation of the state vector $\ket{\psi}$ spanning across solution $\ket{\omega}$ and non-solution spaces $\ket{\bar{\omega}}$.

Theorems & Definitions (2)

• Theorem 1
• proof