Dhrumil Patel, Mark M. Wilde

Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

  • Mathematical Physics
  • Statistics and Probability
  • Statistical and Nonlinear Physics
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Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator [Formula: see text] is encoded into a quantum state [Formula: see text]. Then, given access to [Formula: see text] copies of the state [Formula: see text], the task is to simulate the corresponding Markovian dynamics for time [Formula: see text]. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses [Formula: see text] samples of [Formula: see text] to achieve the target dynamics, with an approximation error of [Formula: see text].

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