Hamiltonian Simulation
On Hamiltonian Simulation:
1) Hamiltonian simulation with nearly optimal dependence on all parameters (Dominic W. Berry, Andrew M. Childs, Robin Kothari)
Latest result in 2015 that has running time linear in norm of H, t and d (sparseness)
Previous result in 2014 with sparse Hamiltonian – https://arxiv.org/pdf/1312.
and his lecture note version: https://www.cs.umd.
On Quantum Walk (Discrete- vs Continuous-time)
2) Andrew Child’s On the relationship between continuous- and discrete-time quantum walk
and his lecture notes version: https://www.cs.umd.
3) Black-box Hamiltonian simulation and unitary implementation – Andrew Childs, Dominic Berry
The first paper that describes simulation of Hamiltonian based on quantum walk approach
On Fractional Query model:
4) Kothari Robin’s thesis
This summarizes the proof that simulation fractional query model using discrete query model takes polylog(1/epsilon) time
[To be continued]
