Quantum trajectories for time-dependent adiabatic master equations

Abstract

We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension $N$ instead of a complex density matrix of dimension $N^2$, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor $N$ advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor $N^2$ is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for $8$-qubit quantum annealing examples. We also apply the quantum trajectories method to a $16$-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.

18 pages, 8 figures; v2: Phys. Rev. A version

References in corpus (8)

• Quantum trajectories and open many-body quantum systems
• Non-Markovian quantum jumps
• Genuine quantum trajectories for non-Markovian processes
• Decoherence in adiabatic quantum computation
• Open system dynamics with non-Markovian quantum jumps
• Stochastic jump processes for non-Markovian quantum dynamics
• Stochastic unraveling of positive quantum dynamics
• Jump probabilities in the non-Markovian quantum jump method

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• Reverse quantum annealing of the $p$-spin model with relaxation
• Improving quantum annealing of the ferromagnetic $p$-spin model through pausing
• HOQST: Hamiltonian Open Quantum System Toolkit
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Adaptive variational simulation for open quantum systems
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence
• Breakdown of the weak coupling limit in quantum annealing
• Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity
• Implementing quantum stochastic differential equations on a quantum computer
• Geometric phases along quantum trajectories
• Nonadiabatic evolution and thermodynamics of a time-dependent open quantum system
• QTM: computational package using MPI protocol for quantum trajectories method