Research using matrix product state (MPS) representations instead of state vectors

[gstenzel]

Investigate the potential benefits and challenges of adopting matrix product state (MPS) representations for quantum circuits in qandle, as an alternative to traditional state vector methods. Tasks include:

• Review literature on MPS and its applications in quantum circuit simulation.
• Evaluate how MPS could improve memory efficiency and scalability for large, weakly entangled circuits.
• Analyze integration challenges and differences with the current state vector implementation.
• Compare simulation accuracy, performance, and implementation complexity between MPS and state vector approaches.
• Link this research and potential implementation to improvements in circuit splitting algorithms (see issue Research and improve circuit splitting algorithms using graph theory #6).