  Given its importance to many other areas of physics, from condensed matter
physics to thermodynamics, time-reversal symmetry has had relatively little
influence on quantum information science. Here we develop a network-based
picture of time-reversal theory, classifying Hamiltonians and quantum circuits
as time-symmetric or not in terms of the elements and geometries of their
underlying networks. Many of the typical circuits of quantum information
science are found to exhibit time-asymmetry. Moreover, we show that
time-asymmetry in circuits can be controlled using local gates only, and can
simulate time-asymmetry in Hamiltonian evolution. We experimentally implement a
fundamental example in which controlled time-reversal asymmetry in a
palindromic quantum circuit leads to near-perfect transport. Our results pave
the way for using time-symmetry breaking to control coherent transport, and
imply that time-asymmetry represents an omnipresent yet poorly understood
effect in quantum information science.
