Farzad Qassemi, Université de Sherbrooke
Kristan Temme, Massachusetts Institute of Technology
Linmei Liang, National University of Defense Technology, China
Juan Jose Garcia Ripoll, Instituto de Física Fundamental
Igor Radchenko, Russian Academy of Sciences
Eduardo Martin-Martinez, Institute for Quantum Computing
Chris Herdman, The University of Vermont
I will introduce the field of quantum simulations from a wide
scientific perspective. Then, I will discuss the relevance of quantum
simulations for reproducing different aspects of quantum physics:
nonrelativistic and relativistic quantum dynamics, physical and unphysical
quantum operations, as well as strong and ultrastrong light-matter
interactions. Finally, I will give examples in the context of trapped-ion
and circuit QED technologies.
We derive new Heisenberg-type uncertainty relations for both joint measurability and the error- disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever.
We provide a quantum algorithm for simulating the
dynamics of sparse Hamiltonians with complexity sublogarithmic in
the inverse error, an exponential improvement over previous methods.
Unlike previous approaches based on product formulas, the query
complexity is independent of the number of qubits acted on, and for
time-varying Hamiltonians, the gate complexity is logarithmic in the
norm of the derivative of the Hamiltonian. Our algorithm is based on
a significantly improved simulation of the continuous- and