Testing Quantum Mechanics using Noisy Quantum Computers

We outline a proposal to test quantum mechanics using noisy intermediate-scale quantum (NISQ) devices in the high-complexity quantum advantage regime. We are motivated by the possibility that quantum mechanics is not fundamental, but instead emerges from a theory with less computational power, such as classical mechanics. We show that our proposal can significantly rule out this possibility with 2000 logical qubits and a modest gate infidelity of 10^-5, although useful experiments can already be conducted with e.g. 80 qubits and gate infidelity 10^-3. Our procedure involves simulating a non-Clifford random circuit, followed by its inverse, and then checking that the resulting state is the same as the initial state. We show that quantum mechanics predicts that the fidelity of this procedure decays exponentially with circuit depth (due to noise in NISQ computers). However, if quantum mechanics emerges from a theory with significantly less computational power, then we expect the fidelity to decay significantly more rapidly than the quantum mechanics prediction for sufficiently deep circuits, which is the experimental signature that we propose to search for.