  The execution of quantum circuits on real systems has largely been limited to
those which are simply time-ordered sequences of unitary operations followed by
a projective measurement. As hardware platforms for quantum computing continue
to mature in size and capability, it is imperative to enable quantum circuits
beyond their conventional construction. Here we break into the realm of dynamic
quantum circuits on a superconducting-based quantum system. Dynamic quantum
circuits involve not only the evolution of the quantum state throughout the
computation, but also periodic measurements of a subset of qubits mid-circuit
and concurrent processing of the resulting classical information within
timescales shorter than the execution times of the circuits. Using noisy
quantum hardware, we explore one of the most fundamental quantum algorithms,
quantum phase estimation, in its adaptive version, which exploits dynamic
circuits, and compare the results to a non-adaptive implementation of the same
algorithm. We demonstrate that the version of real-time quantum computing with
dynamic circuits can offer a substantial and tangible advantage when noise and
latency are sufficiently low in the system, opening the door to a new realm of
available algorithms on real quantum systems.
