Scalable Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization

As quantum hardware remains limited in qubit count, researchers face a bottleneck when mapping large-scale classical combinatorial optimization problems to quantum circuits. This paper investigates whether Pauli correlation encoding (PCE) can effectively compress high-dimensional binary optimization problems—specifically electric power demand portfolio optimization—into a compact quantum representation that remains solvable on near-term devices.

The authors utilize Pauli correlation encoding, which represents classical binary variables as the expectation values of multi-body Pauli operators. By choosing a correlation order of $k=n/2$, they maximize the number of available correlators for a given number of qubits $n$. The optimization is performed in two stages: a time-averaged model provides initialization, followed by a time-resolved model that handles specific hourly fluctuations. The framework relies on a variational quantum circuit to generate these correlators, which are then optimized via a classical outer loop and refined through greedy post-processing.

The study demonstrates that PCE can successfully represent dense quadratic optimization problems with real-valued, nonuniform coefficients. Numerical simulations across problem sizes ranging from $m=18$ to $10,296$ show normalized cost gaps on the order of $10^{-4}$ compared to certified optimal solutions. The authors identify that the optimization performance is governed by the effective resolution of the correlator representation, where larger systems exhibit more consistent behavior. Furthermore, the approach was validated on trapped-ion quantum hardware, showing that high-quality solutions can be recovered despite hardware noise and finite sampling.