Scaling Quantum Simulation-Based Optimization: Demonstrating Efficient Power Grid Management with Deep QAOA Circuits

TL;DR

The paper assesses the optimization component of Quantum Simulation-based Optimization (QuSO) for industrially relevant problems by applying a diagonalized QAOA to the unit commitment problem on the IEEE 57-bus grid. By performing extensive classical precomputation and using a precomputed diagonal cost unitary, the authors simulate QAOA with over 1000 layers on up to 20 qubits and compare against simulated annealing, finding competitive solution quality and favorable time-to-solution in many cases. The results demonstrate that the optimization component can scale to deep QAOA layers while maintaining stability across problem instances, highlighting the practical potential of QuSO when paired with quantum-simulation components. While promising, the work is limited by problem size and reliance on classical precomputation, suggesting that future gains depend on advances in quantum hardware and larger-scale datasets.

Abstract

Quantum Simulation-based Optimization (QuSO) is a recently proposed class of optimization problems that entails industrially relevant problems characterized by cost functions or constraints that depend on summary statistic information about the simulation of a physical system or process. This work extends initial theoretical results that proved an up-to-exponential speedup for the simulation component of the QAOA-based QuSO solver proposed by Stein et al. for the unit commitment problem by an empirical evaluation of the optimization component using a standard benchmark dataset, the IEEE 57-bus system. Exploiting clever classical pre-computation, we develop a very efficient classical quantum circuit simulation that bypasses costly ancillary qubit requirements by the original algorithm, allowing for large-scale experiments. Utilizing more than 1000 QAOA layers and up to 20 qubits, our experiments complete a proof of concept implementation for the proposed QuSO solver, showing that it can achieve both highly competitive performance and efficiency in its optimization component compared to a standard classical baseline, i.e., simulated annealing.

Figures (7)

• Figure 1: Quantum circuit addressing a QuSO problem of the form $\arg\min_x f(x) = u(s(x))$, as outlined in \ref{['thm:quso']}. A possible implementation of QSim is detailed in Ref. stein2024exponentialquantumspeedupsimulationbased. The symbol indicates ancillary qubits initialized in the $\ket{0}$ state, which can be reused for subsequent calculations. This circuit is taken from Ref. stein2024exponentialquantumspeedupsimulationbased.
• Figure 2: This IEEE 57-bus test case represents a simple approximation of the American Electric Power system (in the U.S. Midwest) from the early 1960s BusSystemPic. The data were provided by I. Dabbagchi and converted into the IEEE Common Data Format by R. Christie at the University of Washington in August 1993 BusSystemsArchive. This bus test case system has 57 buses, 7 generators, and 42 loads.
• Figure 3: Solution quality comparison between QAOA and SA showing the approximation ratio across all load percentages averaged over all qubits. The shaded area represents the 95% confidence interval.
• Figure 4: Model scaling performance showing the approximation ratio for 20 Qubits across all load percentages.
• Figure 5: Performance Heatmap showing the approximation ratio across all qubit and load percentage permutations. The colorbar is centered equally for both plots.

Theorems & Definitions (6)

• Definition 1
• Definition 2: Summary Statistic Information
• Definition 3: Quantum Simulation-based Optimization (QuSO)
• Theorem 1: QuSO Solver Architecture stein2024exponentialquantumspeedupsimulationbased
• Definition 4: Unit Commitment Problem (UCP)
• Theorem 2: QSim implementation for the UCP stein2024exponentialquantumspeedupsimulationbased