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

This paper from TISI Inc. and Osaka University, with contributions from RIKEN’s Center for Quantum Computing, introduces Pauli Correlation Encoding, or PCE, as a qubit-efficient alternative to direct QAOA-style binary encoding. Instead of assigning one qubit to each decision variable, PCE maps variables to signs of k-body Pauli expectation values, using k=n/2 so the available correlator count grows combinatorially as m=3 choose n k, while all correlators remain measurable in only three global X, Y, and Z bases. The authors apply a two-stage hybrid workflow to electric power demand portfolio optimization: a 24-hour time-averaged QUBO initializes a time-resolved optimization, followed by sign decoding and greedy post-processing. Using 61 days of hourly data from 2143 consumers in the Energy Management System Open Data platform, with mixup augmentation for larger portfolios, simulations cover m=18 to m=10296 and achieve normalized cost gaps on the order of 0.0001 against Gurobi solutions with certified optimality. The variational circuits use depth 5, BFGS optimization, and Qulacs state-vector simulation. Hardware validation on IonQ Forte through Amazon Braket uses 4001 shots per basis: post-processing recovers high-quality solutions despite noise, although performance approaches random-greedy initialization at the largest sizes. The central finding is that PCE’s success depends on correlator resolution: small systems show discrete decoding instability, while larger systems behave more continuously and transmit relaxed optimization improvements more reliably. The work demonstrates representational scalability, not end-to-end quantum advantage, since dense objective evaluation and sampling costs remain significant.