  Randomized benchmarking (RB) protocols are widely used to measure an average
error rate for a set of quantum logic gates. However, the standard version of
RB is limited because it only benchmarks a processor's native gates indirectly,
by using them in composite $n$-qubit Clifford gates. Standard RB's reliance on
$n$-qubit Clifford gates restricts it to the few-qubit regime, because the
fidelity of a typical composite $n$-qubit Clifford gate decreases rapidly with
increasing $n$. Furthermore, although standard RB is often used to infer the
error rate of native gates, by rescaling standard RB's error per Clifford to an
error per native gate, this is an unreliable extrapolation. Direct RB is a
method that addresses these limitations of standard RB, by directly
benchmarking a customizable gate set, such as a processor's native gates. Here
we provide a detailed introduction to direct RB, we discuss how to design
direct RB experiments, and we present two complementary theories for direct RB.
The first of these theories uses the concept of error propagation or scrambling
in random circuits to show that direct RB is reliable for gates that experience
stochastic Pauli errors. We prove that the direct RB decay is a single
exponential, and that the decay rate is equal to the average infidelity of the
benchmarked gates, under broad circumstances. This theory shows that group
twirling is not required for reliable RB. Our second theory proves that direct
RB is reliable for gates that experience general gate-dependent Markovian
errors, using similar techniques to contemporary theories for standard RB. Our
two theories for direct RB have complementary regimes of applicability, and
they provide complementary perspectives on why direct RB works. Together these
theories provide comprehensive guarantees on the reliability of direct RB.
