Fast-forwarding of Hamiltonians and exponentially precise measurements.

ABSTRACT: The time-energy uncertainty relation (TEUR) [Formula: see text] holds if the Hamiltonian is completely unknown, but can be violated otherwise; here we initiate a rigorous study describing when and to what extent such violations can occur. To this end, we propose a computational version of the TEUR (cTEUR), in which Δt is replaced by the computational complexity of simulating the measurement. cTEUR violations are proved to occur if and only if the Hamiltonian can be fast forwarded (FF), namely, simulated for time t with complexity significantly smaller than t. Shor's algorithm provides an example of exponential cTEUR violations; we show that so do commuting local Hamiltonians and quadratic fermion Hamiltonians. A general FF method is ruled out, but finding further examples, as well as exper

SUBMITTER: Atia Y 

PROVIDER: S-EPMC5691059 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature