Quantum-Inspired AI Rapidly Finds Optimal Solutions in Complex, Uncharted Problem Spaces

Researchers are tackling the persistent problem of identifying both valuable and diverse configurations within complex, black-box systems where evaluations are costly and limited. Saisubramaniam Gopalakrishnan and Dagnachew Birru, both from Quantiphi India, USA, alongside et al., present a novel approach leveraging quantum computing to enhance this discovery process. This work is significant because it moves beyond limitations of existing optimisation techniques, which often favour common solutions or require extensive computational resources. By employing a learned surrogate model based on self-attention and projecting higher-order variable dependencies into a quadratic form suitable for Quantum Approximate Optimisation Algorithm, the team enables diversity-oriented quantum sampling and captures interaction structures beyond simple pairwise terms, ultimately achieving improved structural diversity and the exclusive discovery of high-utility configurations.

Challenges in efficiently exploring high-dimensional non-convex search spaces

Scientists are increasingly focused on discovering configurations that are simultaneously high-utility and structurally diverse in complex black-box landscapes. This need for high-coverage discovery spans domains such as de novo molecular design, financial stress testing, and the reliability assurance of Intelligent Document Processing (IDP) systems.

Such problems are typically governed by expensive black-box oracles and strict query budgets, rendering exhaustive search infeasible. Classical approaches rely primarily on population-based heuristics, yet they exhibit well-known limitations under tight evaluation budgets. Evolutionary and swarm-based Methods effectively exploit local information but often suffer from mode collapse, converging to narrow clusters around dominant basins of attraction.

Quality-Diversity (QD) Methods such as MAP-Elites explicitly enforce behavioral diversity through archive-based illumination, but their archive-filling dynamics are frequently sample-inefficient in high-dimensional spaces. Bayesian Optimisation (BO) and reinforcement learning (RL) Methods are query-efficient for sequential decision-making, but are typically formulated to optimise scalar objectives or expected return, and require additional novelty or entropy regularization to support diverse solution set discovery.

Quantum optimisation offers a complementary mechanism for maintaining solution diversity through probabilistic sampling over an energy landscape. Nevertheless, such models are limited in their ability to represent higher-order dependencies and are typically applied to optimisation rather than diverse discovery.

To address these limitations, researchers propose the Latent-Quadratic Interaction Embedding Transformer (QET), a surrogate-guided quantum discovery framework that learns a quadratic proxy Hamiltonian directly from observational data. QET employs a Transformer encoder with self-attention to model higher-order dependencies among decision variables, and projects the learned interactions into a valid positive semi-definite (PSD) quadratic form compatible with Ising/QUBO representations.

This surrogate Hamiltonian is then used within QAOA at low alternating-operator depth, enabling the quantum circuit to function as a structured diversity-oriented sampler rather than a traditional ground-state optimizer. By adjusting circuit parameters and mixing operators, the sampler concentrates probability mass around multiple low-energy basins while preserving multi-modal coverage.

Researchers empirically evaluate the framework on high-dimensional reliability testing of enterprise Intelligent Document Processing (IDP) systems, which serves as a representative High-dimensional Expensive Problem (HEP) setting. The search space is combinatorial, the oracle is computationally costly, and the resulting risk landscape is fragmented and non-differentiable.

The underlying structure of assembling discrete document components to optimise a black-box risk score makes this benchmark representative of a broader class of other scientific discovery problems. The contributions of this work are as follows: Firstly, a novel surrogate architecture, Latent-Quadratic Interaction Embedding Transformer (QET), is introduced, bridging deep learning and quantum.

Unlike standard FM limited to fixed pairwise interactions, QET employs a self-attention mechanism to capture complex, higher-order dependencies in the black-box objective. A projection layer maps these latent embeddings onto a valid, Positive Semi-Definite (PSD) quadratic form, effectively constructing a realizable Ising Hamiltonian from observational data.

Secondly, QAOA is reframed from ground state optimisation to diversity sampling. The induced wavefunction leverages quantum superposition to simultaneously populate distinct low-energy basins, effectively bypassing the mode collapse typical of greedy classical heuristics. Thirdly, through set-theoretic analysis, the framework isolates a distinct utility subspace (4, 5% of yield exclusive to the union of other baselines) and, alongside FM-surrogate, ranks amongst the top in discovering tail 1% edge cases, making it an important surrogate mechanism for robust quantum-based discovery.

Transformer-based Quadratic Surrogate Modelling for Diversity-oriented Quantum Optimisation

A Latent-Quadratic Interaction Embedding Transformer (QET) forms the core of a novel surrogate-guided quantum discovery framework used to address challenges in black-box optimisation. The research directly tackles the need for both high-utility and structurally diverse configurations under strict query budgets, a common problem in areas like enterprise document processing.

QET initially models higher-order variable dependencies using a Transformer encoder equipped with self-attention mechanisms, allowing it to capture complex relationships beyond simple pairwise interactions. Experiments were conducted on risk discovery within enterprise document processing systems, comparing the performance of QET-guided samplers against various classical optimizers.

Evaluation involved assessing both the utility of discovered configurations and their structural diversity, with a particular emphasis on identifying extreme-case outliers. Specifically, the study demonstrates that QET, QAOA methods recover approximately twice as many structurally tail-risk outliers compared to most classical baseline methods.

Furthermore, the approach identifies an exclusive, non-overlapping fraction of around 4, 5% of high-utility configurations that remain undiscovered by competing techniques. This highlights the effectiveness of learning higher-order interaction structures and translating them into quadratic surrogate Hamiltonians for quantum-assisted black-box discovery, offering a significant advancement over Factorization Machines which, while providing stronger initial coverage, yield less accurate surrogate landscapes.

Enhanced outlier detection via deep learning and quantum-inspired optimisation

Latent-Quadratic Interaction Embedding Transformer methods recover approximately twice as many structurally tail-risk outliers compared to most classical baselines. The research identifies an exclusive, non-overlapping fraction of 4, 5% of high-utility configurations that were not discovered by competing methods, demonstrating a unique capability in configuration space exploration.

This work introduces a novel surrogate architecture, the Latent-Quadratic Interaction Embedding Transformer, which bridges deep learning and quantum computation for black-box discovery. Unlike Factorization Machines limited to pairwise interactions, this transformer employs a self-attention mechanism to capture complex, higher-order dependencies within the objective function.

A projection layer maps these latent embeddings onto a valid, Positive Semi-Definite quadratic form, constructing a realizable Ising Hamiltonian from observational data. Empirical validation on high-dimensional reliability testing of enterprise Intelligent Document Processing systems demonstrates superior predictive fidelity, achieving an R2 value of approximately 0.84.

Set-theoretic analysis reveals the isolation of a distinct utility subspace exclusive to this method, further highlighting its effectiveness in uncovering novel and valuable configurations. This approach utilises a Transformer-based Latent-Quadratic Interaction embedding to capture complex relationships beyond simple pairwise interactions, enabling diversity-oriented discovery within limited evaluation budgets.

The resulting method improves the identification of extreme-case outliers and exclusive high-utility configurations compared to classical optimisation techniques. Evaluations conducted on risk discovery within enterprise document processing systems demonstrate the framework’s effectiveness. Quantum-guided samplers achieve competitive utility alongside consistent improvements in structural diversity and the discovery of unique solutions.

While Factorization Machines offer broader initial coverage, the new method generates more accurate surrogate landscapes and excels at identifying rare, high-impact scenarios. The learned embedding also functions as a feature map, potentially extending its application to other optimisation and search problems.

The authors acknowledge that the performance of pairwise surrogates is strong in certain regimes, indicating a trade-off between broad coverage and precise tail discovery. Future research will focus on transferring learned embeddings to related tasks and adapting the framework for constrained and multi-objective optimisation problems. This work establishes a pathway for leveraging quantum-assisted methods in black-box discovery, offering a means to navigate complex data landscapes and uncover valuable, previously hidden configurations.