Quantum simulation algorithms based on quantum trajectories
AbstractQuantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed by the Lindblad master equation, has received attention recently with the current state-of-the-art algorithms having an input model query complexity of $O(T\mathrm{polylog}(T/\epsilon))$, where $T$ and $\epsilon$ are the desired time and precision of the simulation respectively. For the Hamiltonian simulation problem it has been show that the optimal Hamiltonian query complexity is $O(T + \log(1/\epsilon))$, which is additive in the two parameters, but for Lindbladian simulation this question remains open. In this work we show that the additive query complexity to a Lindbladian's jump operators is reachable for the simulation of a large class of Lindbladians by constructing a novel quantum algorithm based on quantum trajectories.Featured image: Trajectory CircuitPopular summarySimulating quantum mechanical systems has been a key target application for quantum computation ever since the introduction of quantum computation as a concept. This has been due to the difficulty in designing classical algorithms that can simulate quantum systems that are efficient and the belief that simulating quantum systems using a quantum mechanical system should be more "natural". In general quantum systems can be categorized into closed or open. Closed quantum mechanical systems are ones that are completely shielded from noise due to the environment, while open quantum systems are ones that are not shielded from such an environment. Quantum algorithms built to simulate closed quantum systems have been explored first, and it has been only recently that quantum algorithms built to simulate open quantum systems have been explored. When designing a quantum algorithm to simulate a quantum system one needs to give the quantum computer access to the
