Internship Software Engineer Applied Math Jobs in Illinois

We are seeking a Quantum Software Engineer with expertise in quantum-inspired classical machine learning and quantum machine learning (QML). This role will focus on developing advanced ML models and algorithms that leverage tensor networks and related structured representations, supporting applications across quantum computing and quantum sensing platforms.
As a member of the Quantum Software division, you will work closely with teams spanning quantum computing and sensing hardware and algorithms to design scalable learning architectures that operate in hybrid classical-quantum workflows. The ideal candidate brings strong foundations in machine learning and mathematical physics, along with hands-on experience developing novel model architectures for structured, high-dimensional data.
This position offers the opportunity to contribute to next-generation ML techniques that bridge classical and quantum paradigms for real-world deployment.
Job Responsibilities
The duties and responsibilities outlined below include essential functions of the role. Depending on business needs, this role may perform a combination of some or all of the following duties. Duties, responsibilities, and activities may change, or new ones may be assigned:

• Develop and implement quantum-inspired machine learning models, including tensor network-based architectures (e.g., MPS/TTN/PEPS-inspired models) for structured data analysis
• Design and evaluate quantum machine learning algorithms suitable for near-term and fault-tolerant quantum computers
• Build hybrid classical-quantum workflows integrating classical ML pipelines with quantum processors and/or quantum sensors
• Develop ML models for signal processing, state estimation, calibration, and noise mitigation in quantum sensing systems
• Collaborate with hardware and experimental teams to translate physical system characteristics into learning-based models
• Optimize models for performance, scalability, and deployment in HPC and low-SWaP environments
• Stay current with emerging research in tensor networks, quantum information science, and advanced ML architectures
• Contribute to research publications, technical reports, and conference presentations
• Provide technical mentorship and contribute to a collaborative, interdisciplinary research environment

Requirements
Required Qualifications

• BS or MS in Computer Science, Physics, Applied Mathematics, Electrical Engineering, or a closely related field
• Strong experience developing, training, and optimizing machine learning models
• Demonstrated experience with tensor networks, structured linear algebra, or physics-informed ML architectures
• Proficiency in Python and modern ML frameworks (e.g., PyTorch, JAX, TensorFlow)
• Experience working in scientific computing and HPC environments leveraging GPU acceleration
• Strong mathematical foundation in linear algebra, probability, and optimization
• Ability to communicate complex theoretical and experimental concepts clearly across teams and to external customers
• Demonstrated ability to work effectively in a collaborative, cross-functional, and fast-paced R&D environment
• Resourceful problem-solver with a track record of delivering research ideas into prototype or production systems
• Willingness to travel domestically and potentially internationally up to 10%

Preferred Qualifications

• Ph.D. in Computer Science, Physics, Applied Mathematics, or a related field
• Research experience in quantum machine learning and/or quantum information science
• Experience implementing variational quantum algorithms, parameterized quantum circuits, or quantum kernel methods
• Experience developing tensor network algorithms for large-scale modeling or simulation
• Familiarity with quantum SDKs (e.g., Qiskit, Cirq, Braket, PennyLane)
• Strong publication record in machine learning, quantum computing, or computational physics
• Experience working with quantum sensor data or quantum hardware calibration workflows

Benefits

• Salary range: $135,000 to $160,000

• 100% company-paid medical, dental, vision, short/long-term disability
• Employer-funded Health Savings Account
• Unlimited PTO
• 401(k) match
• Company-paid Life and AD&D Insurance
• Flexible Savings Account
• Paid FMLA, Maternity/Paternity Leave
• Employee Assistance Program
• Student Loan Repayment
• Equity Program