  We present two complementary viewpoints for combining quantum computers and
the foundations of quantum mechanics. On one hand, ideal devices can be used as
testbeds for experimental tests of the foundations of quantum mechanics: we
provide algorithms for the Peres test of the superposition principle and the
Sorkin test of Born's rule. On the other hand, noisy intermediate-scale quantum
(NISQ) devices can be benchmarked using these same tests. These are
deep-quantum benchmarks based on the foundations of quantum theory itself. We
present test data from Rigetti hardware.
