Siheon Park

Simulating open quantum systems is essential for modeling realistic dynamics beyond closed-system Hamiltonian evolution. Such dynamics are described by the Lindblad master equation for Markovian systems and arise in fields ranging from condensed matter and quantum chemistry to quantum optics and noise analysis in quantum devices. Existing algorithms typically rely on sparse-access or linear-combination-of-unitaries input models. We propose an alternative framework, Wave Matrix Lindbladization, inspired by density matrix exponentiation for sample-based Hamiltonian simulation. In this model, Hamiltonians and Lindblad operators are encoded directly into program states, enabling sample-based Lindbladian simulation. We present algorithms for this task, analyze their sample and gate complexities, and demonstrate both efficiency and optimality. We also show that our algorithms achieve better sample complexity than any tomographic strategy for Lindbladian simulation. This further suggests a form of quantum copy-protection, where program states allow Lindbladian simulation without revealing the operators they encode.