Qavis Inc.

Overview

Qavis Technologies builds Qoordinate, a hybrid quantum-AI optimization platform. We integrate classical solvers with quantum computing backends to solve large-scale combinatorial optimization problems for logistics and industrial operations.

Our platform serves the logistics sector with vehicle routing and delivery scheduling, achieving 240× faster planning and up to 29% fuel reduction. We are now expanding into manufacturing and production scheduling — and we need strong mathematical foundations to do it right.

The Problem

Job-Shop Scheduling at a Glance

The Job-Shop Scheduling Problem (JSSP) is one of the most important combinatorial optimization problems in manufacturing:

• N jobs must be processed, each consisting of a sequence of operations
• M machines are available; each operation requires a specific machine for a specific duration
• Each machine can process only one operation at a time
• Operations within a job must follow a prescribed order (precedence constraints)
• Objective: minimize the makespan (total completion time)

JSSP is NP-hard. Even modest instances (15 jobs × 15 machines) challenge state-of-the-art solvers.

Why Encoding Efficiency Matters

To solve JSSP on quantum solvers, we formulate it as a binary optimization problem (QUBO). The standard approach uses a binary variable $x(j,m,t)$ for each job-machine-timeslot combination. A 10×10×100 instance yields 10,000 binary variables = 10,000 qubits.

Recent work on the Linear Ramp QAOA (LR-QAOA) protocol (Montañez-Barrera & Michielsen, npj Quantum Information, 2025) shows that quantum success probability scales as $P(x*) \approx 2^{(–\eta(p)\cdot N_q + C)}$. Every qubit eliminated from the formulation exponentially improves the chance of finding the optimal solution.

This is why we ask: what is the most qubit-efficient way to formulate JSSP?

The Research Questions

Question 1 — Formulation How should JSSP be encoded as a binary optimization problem with minimal variables? What are the decision variables, objective, and how are constraints expressed as quadratic penalties?

Question 2 — Penalties How should penalty coefficients be chosen? Can we derive bounds? How sensitive is solution quality to penalty weights?

Question 3 — Decomposition For large instances, how can the problem be split into smaller sub-problems while preserving solution quality?

Project Scope

Core Deliverables

The focus is mathematical formulation and analysis. No quantum hardware, no production software. The team builds the mathematical model; Qavis handles the engineering.

Bonus (If Time Permits)

These are extras, not expectations. The core deliverables above are what we need.

No quantum hardware is needed for any part of this project.

Timeline & Working Style

How We Work Together

Qavis provides a mentor who meets with the team daily for approximately 1 hour. These are collaborative working sessions, not status reports. The mentor provides domain context, answers questions, suggests directions, and helps the team stay on track. The pace is guided: each day builds naturally on the previous day’s work.

Think of it as a supervised research sprint. The team does the mathematical heavy lifting; the mentor ensures the work stays relevant and steers around dead ends.

Week 1: M2PI Training

No project deliverables

Qavis preparation during this week:

• Share a short reading list: 2–3 papers on JSSP formulations + the LR-QAOA paper for motivation
• Brief introductory call if M2PI schedule allows (“Here’s who we are, here’s what we’re building”)

Week 2: Build the Formulation (Project Week 1)

The goal this week is simple: end with a complete, correct QUBO formulation of JSSP on paper.

Week 3: Analyze, Decompose and Deliver (Project Week 2)

The goal this week: understand how the formulation behaves at scale, propose a decomposition, and write it all up.

The Bigger Picture

The formulation you produce is not a standalone exercise — it is the mathematical foundation for a concrete product pipeline:

Qavis Optimization Roadmap

• STEP 1 — Mathematical Formulation (this M2PI project) Produce a qubit-efficient binary formulation of JSSP with penalty analysis and decomposition strategy.
• STEP 2 — Solver Integration & Validation (Qavis, post-M2PI) Encode the formulation into solver-ready formats. Validate on classical and quantum-inspired solvers. Integrate into the Qoordinate platform.
• STEP 3 — Quantum Execution via LR-QAOA (Qavis, near-term) Execute the compact encoding on quantum hardware using the LR-QAOA protocol. The team’s qubit scaling analysis directly determines feasibility.
• STEP 4 — Manufacturing Deployment Deploy JSSP optimization to manufacturing clients across automotive, electronics, textiles, and food processing.

Your work is Step 1 — everything else builds on it. The encoding quality determines quantum feasibility, the penalty analysis ensures solution quality, and the decomposition shapes how we scale.

Interested in continuing beyond M2PI? Steps 2–3 offer natural follow-on research — quantum hardware experiments, benchmarking papers, or ongoing consulting. We welcome that conversation.

Intellectual Property & Publication

Fully compatible with M2PI’s public final report:

• Published: The JSSP formulation, penalty analysis, decomposition strategy, and scaling assessment. Mathematical methodology, fully publishable.
• Not shared: Qavis’s proprietary optimization engine, AI preprocessing, solver logic, and customer data. Not involved in this project.
• Boundary: The team works on “what to solve” (formulation). Qavis handles “how to solve” (engineering). Zero IP conflict.

Ideal Team Profile

We would benefit from 4-5members with backgrounds in some or all of:

• Combinatorial / discrete optimization (integer programming, complexity theory)
• Operations research (scheduling theory, resource allocation)
• Linear algebra and graph theory (for coupling analysis and decomposition)
• Scientific computing / Python (helpful, not required)

No quantum computing experience is required. Qavis provides all necessary quantum context through the reading list and daily meetings.

Why This Project

• For the team: JSSP is a canonical NP-hard problem. Designing qubit-efficient encodings is an active research question. Your work has a path to a published paper, and you gain hands-on understanding of how formulation choices impact quantum feasibility.
• For Qavis: Your formulation becomes the mathematical core of our manufacturing product. It directly shapes our product roadmap and opens a new customer segment.
• For the field: Qubit-conscious JSSP formulations with scaling analysis are rare. This contributes to both operations research and quantum computing communities.

Resources Provided by Qavis

Key References

• [1] Montañez-Barrera & Michielsen, “Toward a linear-ramp QAOA protocol,” npj Quantum Information 11, 131 (2025). DOI: 10.1038/s41534-025-01082-1
• [2] LR-QAOA benchmark: quantumbenchmarkzoo.org/content/application-level-benchmark/protocols/lr-qaoa
• [3] OR-Library JSSP instances: people.brunel.ac.uk/~mastjjb/jeb/orlib/jobshopinfo.html