Surrogate-Guided Quantum Discovery in Black-Box Landscapes with Latent-Quadratic Interaction Embedding Transformers

TL;DR

The paper addresses the challenge of discovering diverse, high-utility configurations under expensive black-box evaluations by learning a PSD quadratic proxy from data. It introduces the Latent-Quadratic Interaction Embedding Transformer (QET) to capture higher-order variable dependencies via self-attention and projects them into a valid QUBO/Ising Hamiltonian for use with QAOA, reframing QAOA from pure optimization to diversity-oriented sampling. Empirical results on an enterprise IDP risk discovery benchmark show that QET-QAOA achieves competitive utility while enhancing structural diversity and exclusive discovery, with an emphasis on tail-risk configurations; an ablation against Factorization Machines demonstrates how higher-order modeling improves extreme discovery. The work suggests that surrogate-guided quantum sampling can provide robust, hardware-efficient discovery under budget constraints and points to broader applicability, including transferability of learned embeddings and multi-objective extensions.

Abstract

Discovering configurations that are both high-utility and structurally diverse under expensive black-box evaluation and strict query budgets remains a central challenge in data-driven discovery. Many classical optimizers concentrate on dominant modes, while quality-diversity methods require large evaluation budgets to populate high-dimensional archives. Quantum Approximate Optimization Algorithm (QAOA) provides distributional sampling but requires an explicit problem Hamiltonian, which is unavailable in black-box settings. Practical quantum circuits favor quadratic Hamiltonians since higher-order interaction terms are costly to realize. Learned quadratic surrogates such as Factorization Machines (FM) have been used as proxies, but are limited to pairwise structure. We extend this surrogate-to-Hamiltonian approach by modelling higher-order variable dependencies via self-attention and projects them into a valid Positive Semi-Definite quadratic form compatible with QAOA. This enables diversity-oriented quantum sampling from learned energy landscapes while capturing interaction structure beyond pairwise terms. We evaluate on risk discovery for enterprise document processing systems against diverse classical optimizers. Quantum-guided samplers achieve competitive utility while consistently improving structural diversity and exclusive discovery. FM surrogates provide stronger early coverage, whereas ours yields higher-fidelity surrogate landscapes and better extreme-case discovery. Our method recovers roughly twice as many structurally tail-risk outliers as most classical baselines and identify an exclusive non-overlapping fraction of high-utility configurations not found by competing methods, highlighting that an effective mechanism for learning higher-order interaction structure and projecting it into quadratic surrogate Hamiltonians for quantum-assisted black-box discovery.

Figures (2)

• Figure 1: The QET-QAOA Discovery Framework. (A) Latent-Quadratic Interaction Embedding Transformer: Contextualizes latent embeddings $V$ via self-attention in Transformer $\mathcal{T}_\theta$ to capture higher-order dependencies, predicting $\hat{y}$ via Factorization Machine pooling. (B) QUBO and Hamiltonian Projection: The learned contextual embeddings $V_{\text{eff}}$ forms a Gram matrix $Q = V_{\text{eff}} V_{\text{eff}}^T$, projecting the learned topology onto a valid PSD matrix that defines the QUBO coefficients, which are mapped to an equivalent Ising Hamiltonian $H_C$. (C) QAOA Sampling: This proxy $H_C$ drives a QAOA circuit to sample diverse high-quality configurations, which are evaluated by the Oracle and fed back to iteratively refine the surrogate.
• Figure 2: Tail distribution plot across all methods, for 24D and 27D regimes.