Superposition Seekers

Computing wildfire index around lake Tahoe
Results of QAOA optimization
Downsampling lake Tahoe

Inspiration

As wildfires continue to grow more frequent and devastating, we were driven to find a more efficient way to help emergency services stay ahead of the flames. The summer of 2024, marked by destructive fires across Canada and California, and the beginning of 2025 with the Palisades Fire — the most devastating blaze in modern history in Los Angeles County — hit especially close to home.

Each of us lives in either California or Canada, and every team member personally knows someone who has lost their property or been in danger due to recent wildfires. That connection made this problem deeply personal. As engineers, we feel a responsibility to build for a safer future. We believe that traditional methods of resource allocation can — and must — be improved, especially in vast, high-risk regions.

At YQuantum 2025, we saw an opportunity to combine our skills with a cause we care about. Motivated by our shared experiences and guided by modern quantum tools, we worked with a sense of urgency and purpose — to help protect communities and contribute meaningful knowledge to the field.

What it does

We have developed an innovative quantum optimization model leveraging the Quantum Approximate Optimization Algorithm (QAOA) to strategically position firefighting crews for wildfire suppression. Given limited resources, our goal is to maximize efficiency by precisely deploying crews based on predictive analytics derived from real historical wildfire data and current weather conditions.

Our model begins by generating a heat probability map, translating geographical data points into a matrix representing potential wildfire locations. Traditionally, wildfire probability calculations rely solely on localized factors such as temperature and humidity. However, we have introduced a novel enhancement by incorporating spatial interactions between neighboring points. Specifically, we utilize a two-dimensional Gaussian distribution to model the influence of high-risk locations on their surrounding areas, with parameters dynamically adjusted based on wind speed, direction, and elevation.

To manage resource allocation effectively, our approach introduces a dual-structured crew constraint with a quadratic capacity constraint ensuring the deployment of firefighting crews does not exceed available resources and a linear cost-saving incentive encouraging solutions that use fewer resources when possible, promoting cost efficiency.

Additionally, our model addresses operational practicality through a clustering constraint, discouraging overly concentrated crew deployments. While intense wildfire scenarios might justify clustering resources, the algorithm inherently promotes dispersal of crews to cover larger affected areas efficiently while still be able to cluster at a penalty.

The resulting optimization problem is succinctly formulated as a quadratic unconstrained binary optimization (QUBO) equation:

x^T (Q-K-D)x

Here, x is a binary vector where each element indicates whether a firefighting crew is deployed (1) or not (0) at a specific geographic location. The matrices in the equation represent:

Q: Encodes the wildfire probabilities and spatial interactions derived from our probability maps and Gaussian influence model.
K: Represents the quadratic penalty enforcing the crew capacity constraints, ensuring resources are not exceeded.
D: Captures the clustering penalty, discouraging excessive concentration of crews and encouraging balanced resource distribution.

Leveraging QAOA, which synergizes quantum and classical computations, we encode our problem into a quantum state manipulated through cost and mixer Hamiltonians. This innovative approach efficiently navigates the solution space, identifying near-optimal placements for firefighting crews.

Ultimately, the algorithm outputs a clear, actionable deployment strategy as a binary vector, pinpointing exact locations where firefighting crews should be positioned to effectively combat wildfires. Our methodology demonstrates significant potential in enhancing wildfire response effectiveness, optimizing resource usage, and contributing valuable insights into quantum computing's practical application for real-world crisis management.

Implementation

We implemented our solution using Python and NumPy to efficiently gather and process historical and real-time wildfire probability data based on geographic coordinates (longitude and latitude), which allowed us to compute the essential Q, K, and D matrices. To solve the resulting QUBO optimization problem, we employed Qiskit with a 5-qubit quantum simulation. While currently limited to small-scale simulations, our approach can seamlessly scale with future advancements in computational and quantum hardware capabilities.

Challenges we ran into

Throughout our project, we encountered several significant challenges. The primary challenge was formulating the wildfire resource allocation problem in a manner compatible with quantum computation. Since the QUBO framework inherently requires binary variables, we faced difficulty in directly representing scenarios that typically use positive integer variables for resource allocation. We addressed this by conceptualizing resources as firefighting crews rather than individual pieces of equipment. Additionally, we explored potential solutions to the continuity problem, such as incrementally adding crews or encoding integer variables into binary form; however, due to time constraints, we didn't implement these methods fully in our initial proof of concept.

Another significant hurdle was the limitation of simulating quantum computations using classical hardware. Locally, we could effectively simulate only around five qubits, restricting the complexity of our simulations. While this currently presents a constraint, advancements in quantum hardware capabilities are anticipated to resolve this issue and enable the practical scaling of our solution in the future. As we move from the NISQ era to the fault-tolerant where quantum computers have increased computing power our algorithm will be able to run and aid wildfire suppression in the real world.

Accomplishments that we're proud of

We're proud that we successfully modeled a complex, real-world emergency logistics problem using a QUBO formulation and ran it effectively on a quantum computer. Despite the problem's inherent complexity, our model was able to identify optimal and near-optimal placements for firefighting resources under varying levels of fire risk and resource availability.

We also integrated a hybrid classical-quantum workflow that compared quantum solver results with classical optimization approaches, helping us validate the usefulness and performance of quantum methods.

Additionally, we created a system flexible enough to scale with more detailed geospatial inputs and constraints, which sets a strong foundation for real-world deployment. Most importantly, we're proud that our work could someday help real communities better prepare for wildfires and make emergency response more effective and intelligent.

What we learned

We deepened our understanding of quantum computing, QUBO optimization, and how to translate real-world logistics into mathematical models. We tried experimenting with neutral atoms with the pennylane library but we didn't have enough knowledge on this library so we reverted to Qiskit. We also gained experience working with hybrid quantum-classical workflows, tuning hyperparameters, and analyzing output from stochastic solvers.

What's next for Superposition Seekers

Next, we plan to incorporate real geospatial data and fire probability maps, refining the model with satellite-derived inputs for greater accuracy and real-world relevance. We also aim to develop an interactive visualization dashboard, allowing fire agencies to explore suggested resource layouts and simulate fire spread versus response efficiency in various scenarios.

In addition, we intend to improve the Gaussian distribution model by potentially modeling it as an attention blocks with weights for query, value matrices learned from historical data that represent relationships between geographical data points. This approach could enhance the model’s accuracy by removing the naive bias of Gaussian distributions — bringing us closer to a deployable, intelligent emergency response planning tool.