  The transport of conserved quantities like spin and charge is fundamental to
characterizing the behavior of quantum many-body systems. Numerically
simulating such dynamics is generically challenging, which motivates the
consideration of quantum computing strategies. However, the relatively high
gate errors and limited coherence times of today's quantum computers pose their
own challenge, highlighting the need to be frugal with quantum resources. In
this work we report simulations on quantum hardware of infinite-temperature
energy transport in the mixed-field Ising chain, a paradigmatic many-body
system that can exhibit a range of transport behaviors at intermediate times.
We consider a chain with $L=12$ sites and find results broadly consistent with
those from ideal circuit simulators over 90 Trotter steps, containing up to 990
entangling gates. To obtain these results, we use two key problem-tailored
insights. First, we identify a convenient basis$\unicode{x2013}$the Pauli $Y$
basis$\unicode{x2013}$in which to sample the infinite-temperature trace and
provide theoretical and numerical justifications for its efficiency relative
to, e.g., the computational basis. Second, in addition to a variety of
problem-agnostic error mitigation strategies, we employ a renormalization
strategy that compensates for global nonconservation of energy due to device
noise. We expect that these techniques will prove useful beyond the specific
application considered here.
