💻 computer science

Towards Quantum Decision Intelligence: A Four-Qubit Architecture for Venture Capital's Non-Linear Dilemmas on a 156-Qubit IBM Heron Processor

This paper presents HQDIS, a four-qubit variational quantum circuit tested on IBM's 156-qubit Heron processor for venture capital screening, which demonstrates high hardware-simulation fidelity and performance comparable to classical models on a small synthetic benchmark, though it is outperformed by classical algorithms on a second synthetic dataset, highlighting the current limitations of quantum advantage in this domain.

Original authors: Enrique Díaz de León López

Published 2026-09-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Enrique Díaz de León López

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Making money on new technology is one of the most difficult tasks in the business world. When investors look at a startup that has a brilliant idea but no sales and no history, they cannot use the standard math that works for established companies. There are no past profits to calculate, and the market might not even exist yet. Instead, investors must rely on gut feelings about intangible things: Is the team honest? Is the technology real? Can the founders take criticism? These decisions often involve complex trade-offs where a great team can make up for a risky product, or a dishonest founder can kill a perfect idea instantly. For decades, researchers have tried to build computer models to help with this, but standard computers struggle to capture these messy, non-linear human judgments without getting confused or making simple mistakes.

A new study explores whether a different kind of computer, one that uses the strange rules of quantum physics, might handle these tricky decisions better. Quantum computers do not just calculate numbers in a straight line; they can hold many possibilities at once and let them interact in ways that mimic how human minds weigh conflicting factors. The researchers built a small, specialized model to see if this approach could work in the real world. They did not test it on a massive database of real companies, because such data is often secret or too messy to use. Instead, they created a carefully crafted set of 45 fictional investment scenarios that perfectly represented the difficult choices described in decades of business research. They then ran their quantum model against these scenarios and compared the results to the best standard computer programs available today.

The team, led by Enrique Díaz de León López at Tecnológico de Monterrey, designed a system called HQDIS. It is a very small quantum circuit, using only four quantum bits, or qubits, to represent the four main factors an investor considers: the technology's readiness, the founder's credibility, the market fit, and early signs of success. The researchers had to be very careful with how they programmed the machine. In early tests, they found that when a startup looked perfect on paper, the quantum math would sometimes flip the result, telling them to reject a great idea. They discovered a specific mathematical glitch that caused this and fixed it by adjusting how the information entered the machine, ensuring that better scores always led to better chances of funding.

Once the model was calibrated, the researchers put it to the test. They ran the 45 scenarios through the quantum system and compared its decisions to those made by three standard computer methods: a simple linear calculator, a random forest of decision trees, and a gradient boosting algorithm. The quantum model performed remarkably well, getting the right answer about 80% of the time. This was statistically indistinguishable from the performance of the complex tree-based programs, which are known for being very good at spotting patterns. Interestingly, a simpler linear calculator actually scored slightly higher in this specific test, though the difference was not large enough to say for sure that it was better. The key finding was that the tiny quantum model could match the performance of much larger, more complex systems using only a handful of adjustable settings.

To prove that this was not just a simulation, the team took their model to a real quantum computer. They used a 156-qubit processor from IBM, a powerful machine that exists in a laboratory today. They sent all 45 cases to the physical hardware and watched how the machine handled the noise and interference that naturally occurs in real quantum devices. The results were striking. The physical machine made the correct decision in 93% of the cases, and its choices matched the perfect simulation 98% of the time. This showed that the model was robust enough to survive the imperfect conditions of a real quantum processor. The researchers also demonstrated that the system could be audited. They could take a single borderline case and slowly change one factor, like the founder's experience, to see exactly where the decision flipped from "reject" to "fund." This level of transparency is something that many modern artificial intelligence systems cannot provide.

However, the study also revealed the limits of this technology. The researchers created a second set of 500 fictional cases designed specifically to be extremely difficult and non-linear, the kind of problem where quantum computers are supposed to shine. In this tougher test, the quantum model did not win. It was significantly outperformed by the standard tree-based computer program, and it did not beat the simple linear calculator either. The quantum model showed a slight, but not statistically proven, edge in ranking the best opportunities, but it did not make more correct decisions than the classical methods. This suggests that while the quantum approach is viable and can match current technology on certain types of problems, it has not yet found a clear advantage where it beats the best traditional tools.

The value of this work lies less in a sudden breakthrough in prediction and more in what it proves is possible today. The researchers showed that a quantum decision system can be built, tuned to avoid specific errors, and run on real hardware with high accuracy. They also showed that these systems can offer a clear, auditable trail of how a decision was made, which is crucial for investors who need to explain their choices to boards and regulators. The study concludes that while quantum decision intelligence is not yet a magic bullet that solves all investment dilemmas, it is a functional tool that is ready for the next stage of development. It offers a new way to think about complex choices, one that respects the messy, non-linear nature of human judgment while running on the most advanced hardware available.

Technical Summary: Towards Quantum Decision Intelligence (HQDIS)

Problem Statement
Early-stage venture capital screening involves navigating non-linear, compensatory trade-offs that traditional linear scoring models fail to capture. In seed and pre-revenue stages, investors face "Knightian uncertainty" where decisions rely on intangible assets (e.g., team tenacity, coachability) rather than historical cash flows. The paper identifies three structural limitations in current decision support systems (DSS):

Sample Scarcity: High-quality venture records are scarce, leading to overfitting in deep neural networks.
Modeling Failure: Standard models assume additive utility, failing to capture "quantum-like" cognitive interference where evaluation dimensions interact non-commutatively (e.g., a strong team offsetting high technical risk, or a flawed team vetoing a good market).
Governance Deficit: Deep learning models lack geometric interpretability, making them unsuitable for institutional auditability.

Methodology
The author proposes HQDIS (Hybrid Quantum Decision Intelligence System), a parsimonious 4-qubit Variational Quantum Circuit (VQC) designed to model these non-linear dilemmas.

Data Architecture: The study utilizes Benchmark A, a synthetic dataset of $N=45$ cases. The author explicitly states this is not a digitized historical record but a literature-motivated construction based on the qualitative findings of Bachher, Diaz De Leon, and Guild (1999) and Diaz De Leon and Guild (2003). The data maps four decision constructs (Technological Readiness, Founder Credibility, Strategic Market Fit, Early Traction) onto a 4-qubit register.
Mathematical Formulation:
- Feature Map: The author introduces a Monotonic Angular Scaling Protocol ( $\pi/4$ ) for the input feature map. This mathematically resolves a "phase-inversion aliasing" failure mode where high-scoring inputs (near $x_k=1$ ) would otherwise trigger a destructive $\pi$ phase shift, causing catastrophic rejection of excellent proposals.
- Ansatz: The circuit consists of 13 trainable parameters (12 rotation angles + 1 classical bias). It employs a 3-layer structure with $R_y$ rotations and $CZ$ entanglement gates (linear and circular) to map inputs into a high-dimensional Hilbert space.
- Optimization: Parameters are optimized using the derivative-free COBYLA algorithm with a smoothed margin loss function.
Validation Protocol:
- Statistical Reliability: Evaluated via Repeated Stratified 5-Fold Cross-Validation (100 runs) and Leave-One-Out Cross-Validation (LOOCV) against Logistic Regression, Random Forest, and Gradient Boosting.
- Ablation: Circuit variants were tested to isolate the contribution of the feature map's entanglement versus the ansatz's entanglement.
- Hardware Execution: The calibrated model was deployed on the 156-qubit IBM Heron processor (ibm_fez) using Qiskit Runtime Primitives V2 with Twirled Readout Error Extrapolation (TREX).
- Stress Testing: A second synthetic benchmark (Benchmark B) was constructed with explicit non-linear generative rules (disjunctive thresholds) to test the model's capacity against linear baselines.

Key Results

Performance on Benchmark A: HQDIS achieved 80.33% accuracy (±2.72% 95% CI). This is statistically indistinguishable from Random Forest (83.00%) and Gradient Boosting (82.78%) ( $p > 0.7$ ). Logistic Regression achieved a nominally higher 91.56%, but the difference was not statistically significant ( $p=0.133$ ), likely due to low statistical power at $N=45$ .
Ablation Findings: Removing the ansatz's entanglement resulted in a nominal 7-point accuracy drop (73.44% vs. 80.33%) with a medium effect size ( $d \approx 0.51$ ), but this difference was not statistically significant ( $p \approx 0.32$ ). Removing the feature map's entanglement had no negative impact on accuracy, though the monotonic scaling protocol remained essential to prevent phase-inversion errors.
Hardware Fidelity: On the IBM Heron processor, the model achieved 93.33% accuracy against ground truth, with 97.78% concordance with noise-free simulation ( $\kappa = 0.9552$ ). The expectation values correlated at $r = 0.9943$ .
Benchmark B (Non-Linear Stress Test): In a synthetic environment explicitly designed to favor non-linear rules, HQDIS was significantly outperformed by Random Forest in both accuracy and AUC-ROC. Logistic Regression significantly outperformed HQDIS in accuracy ( $p=0.025$ ), while HQDIS showed a non-significant nominal advantage in AUC-ROC ( $p=0.141$ ).
Auditability: The system demonstrated a reproducible counterfactual audit mechanism, identifying the exact threshold (Founder Credibility $\approx 4.6/7$ ) where a decision flips from "Pass" to "Fund" for a boundary case.

Significance and Claims
The paper adopts a modest, rigorous stance regarding its contributions:

Proof of Concept for NISQ Governance: The primary contribution is demonstrating that a quantum decision architecture can be executed with high fidelity on current 156-qubit superconducting hardware while maintaining decision retention.
Mathematical Correction: The identification and resolution of the "phase-inversion aliasing" error via monotonic angular scaling is a specific technical contribution to the stability of quantum feature maps.
Governance over Prediction: The author argues that HQDIS's value lies in governance and auditability (e.g., Bloch-sphere trajectories, counterfactual stress-testing) rather than superior predictive accuracy. The model offers a geometrically interpretable alternative to black-box deep learning.
Honest Reporting of Limitations: The paper explicitly acknowledges that Benchmark A is synthetic and small ( $N=45$ ), limiting claims of predictive validity against real-world venture outcomes. It reports that on a benchmark designed to favor non-linearities, HQDIS did not statistically outperform classical baselines, framing this as a necessary finding to distinguish defensible empirical claims from sampling artifacts.
Parameter Efficiency: The author claims that HQDIS matches the performance of complex ensemble methods (Random Forest/Gradient Boosting) with only 13 parameters, though they concede it does not outperform the even simpler Logistic Regression (5 parameters) in this specific context.

In summary, the paper presents HQDIS not as a superior predictor for venture capital, but as a technically viable, auditable, and hardware-ready framework for modeling non-linear decision dilemmas, with a clear path for future validation on larger, real-world datasets.

Technical Summary: Towards Quantum Decision Intelligence (HQDIS)

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