We show that a class of binary optimization problems with complex non-quadratic objectives or constraints can be reformulated as multi-objective quadratic unconstrained binary optimization problems. When the objective and constraints depend on a small number of quadratic features and are monotone with respect to their preferred directions, at least one globally optimal solution lies in the Pareto set of the associated MO-QUBO. This enables the constraints to be evaluated classically on Pareto-optimal candidates rather than encoded as penalties. We demonstrate the approach for binary portfolio optimization under a Conditional Value-at-Risk constraint. Using Quantum Approximate Multi-Objective Optimization on an illustrative 100-asset instance, we approximate the mean-variance Pareto front using an IBM Quantum computer and derive mean-CVaR fronts through classical post-processing. The hardware results recover the overall structure of the classical front and yield near-optimal feasible portfolios for different risk bounds.
Andres D. Ruiz, Soumyadip Ghosh, S. Woerner· 0 citations
Near-term quantum devices are limited by noise and hardware constraints, motivating algorithmic approaches that trade circuit complexity for increased sampling overhead. Quasi-probability decompositions (QPDs), for example, allow replacing non-local operations by multiple circuits with local operations, but the associated sampling overhead generally scales exponentially and limits their practicality. In this work, we introduce a reweighting strategy for QPDs for circuits with the same variational structure across parameter settings, reusing samples and thereby reducing the sampling overhead. We first demonstrate this approach by estimating fidelities between parameterized quantum states, a key primitive in variational time evolution and quantum kernel methods. Importantly, this setup allows controlling the exponential QPD sampling overhead while preserving the structure of the state-encoding ansatz. We then apply the method to estimate the real part of the quantum geometric tensor using the simultaneous perturbation stochastic approximation and find that, in the presence of realistic hardware noise, our method outperforms other standard estimation techniques. These results highlight the potential of reweighting strategies to extend the applicability of QPD-based methods in variational quantum algorithms.
Sara Santos, S. Woerner, V. Savona et al.· 0 citations
This work presents a simplified analytical characterization of DQI, and provides new empirical evidence that classical sampling algorithms can closely match DQI's optimization performance, offering a more nuanced perspective on the practical advantage of DQI.
Elies Gil-Fuster, Matan Ninio, Lennart Bittel et al.· 1 citation
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