Optimal Hamiltonian simulation by quantum signal processing

Cited from Hamiltonian simulation for Theorem 3: a d-sparse Hamiltonian, with entries specified to m bits, simulated for time t to error ε with success probability at least 1 minus 2ε. The query count is on the order of t d times the largest absolute entry, plus log of one over ε divided by log log of one over ε. The paragraph after the theorem limits that asymptotic reading to the regime where the time parameter is on the order of that same logarithmic term. Their 2019 qubitization paper is the block-encoding statement, and it is a separate record.