Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and membership for quantum correlations. Most of these results rely on reductions from a handful undecidable problems, such as halting problem, tiling Post correspondence or matrix mortality problem. All common property: they an NP-hard bounded version. This work establishes relation between...

Evaluating the expectation of a quantum circuit is classically difficult problem known as mean value (QMV). It used to optimize approximate optimization algorithm and other variational eigensolvers. We show that such an can be improved substantially by using approximation rather than exact expectation. Together with efficient classical sampling algorithms, minimal gate count thus improve effici...