  Quantum computers have the potential to efficiently simulate the dynamics of
many interacting quantum particles, a classically intractable task of central
importance to fields ranging from chemistry to high-energy physics. However,
precision and memory limitations of existing hardware severely limit the size
and complexity of models that can be simulated with conventional methods. Here,
we demonstrate and benchmark a new scalable quantum simulation
paradigm--holographic quantum dynamics simulation--which uses efficient quantum
data compression afforded by quantum tensor networks along with opportunistic
mid-circuit measurement and qubit reuse to simulate physical systems that have
far more quantum degrees of freedom than can be captured by the available
number of qubits. Using a Honeywell trapped ion quantum processor, we simulate
the non-integrable (chaotic) dynamics of the self-dual kicked Ising model
starting from an entangled state of $32$ spins using at most $9$ trapped ion
qubits, obtaining excellent quantitative agreement when benchmarking against
dynamics computed directly in the thermodynamic limit via recently developed
exact analytical techniques. These results suggest that quantum tensor network
methods, together with state-of-the-art quantum processor capabilities, enable
a viable path to practical quantum advantage in the near term.
