Kavli Affiliate: Ke Wang
| First 5 Authors: Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang
| Summary:
The optimal control problem for open quantum systems can be formulated as a
time-dependent Lindbladian that is parameterized by a number of time-dependent
control variables. Given an observable and an initial state, the goal is to
tune the control variables so that the expected value of some observable with
respect to the final state is maximized. In this paper, we present algorithms
for solving this optimal control problem efficiently, i.e., having a
poly-logarithmic dependency on the system dimension, which is exponentially
faster than best-known classical algorithms. Our algorithms are hybrid,
consisting of both quantum and classical components. The quantum procedure
simulates time-dependent Lindblad evolution that drives the initial state to
the final state, and it also provides access to the gradients of the objective
function via quantum gradient estimation. The classical procedure uses the
gradient information to update the control variables.
At the technical level, we provide the first (to the best of our knowledge)
simulation algorithm for time-dependent Lindbladians with an $ell_1$-norm
dependence. As an alternative, we also present a simulation algorithm in the
interaction picture to improve the algorithm for the cases where the
time-independent component of a Lindbladian dominates the time-dependent part.
On the classical side, we heavily adapt the state-of-the-art classical
optimization analysis to interface with the quantum part of our algorithms.
Both the quantum simulation techniques and the classical optimization analyses
might be of independent interest.
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