MatchCake: Exploring Classically Simulable Quantum Circuits for Machine Learning

We introduce MatchCake, a Python package that implements a new PennyLane device for simulating matchgate circuits (also known as matchcircuits). Matchgates form a restricted class of two-qubit unitaries that preserve parity and act on nearest-neighbor qubits. These circuits are equivalent to non-interacting Majorana fermion systems, which makes them classically simulable in polynomial time while retaining rich quantum structure. MatchCake provides a practical framework for exploring this class of circuits within PennyLane and PyTorch, enabling research on classically simulable quantum machine learning models. We demonstrate its capabilities through applications in quantum kernel methods, including classification [arXiv:2404.19032], regression, and beyond.