Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits

Abstract The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified expansion using single device. calls device to implement simple circuit constant depth on 2D lattice qubits. output can be verified classically in linear time, and guaranteed contain polynomial number random bits assuming used generate operated (classical or quantum) sub-logarithmic depth. This assumption contrasts with locality certification based Bell inequality violation more recent proposals computational assumptions. Furthermore, demonstrate it sufficient sample ideal distribution within statistical distance. Our procedure inspired by work Bravyi et al. (Science 362(6412):308–311, 2018), who introduced relational problem solved constant-depth circuit, but provably cannot any develop discovery into framework robust expansion. results lead new proposal demonstrated advantage has some advantages compared existing proposals. First, our does not rest complexity-theoretic conjectures, relies physical adversarial being tested implements Second, success easily time. Finally, noise-tolerant than other only tolerate multiplicative error, require additional conjectures complexity theory; contrast, we are able allow small additive error total variation distance between sampled distributions.