Error Bounds for Variational Quantum Time Evolution

Variational quantum time evolution (VarQTE) allows us to simulate dynamical quantum systems with parameterized quantum circuits. We derive a posteriori, global phase-agnostic error bounds for real and imaginary time evolution based on McLachlan's variational principle that can be evaluated efficiently. Rigorous error bounds are crucial in practice to adaptively choose variational circuits and to analyze the quality of optimization algorithms. The power of the new error bounds, as well as, the performance of VarQTE are demonstrated on numerical examples.