  Optimizing of a portfolio of financial assets is a critical industrial
problem which can be approximately solved using algorithms suitable for quantum
processing units (QPUs). We benchmark the success of this approach using the
Quantum Approximate Optimization Algorithm (QAOA); an algorithm targeting
gate-model QPUs. Our focus is on the quality of solutions achieved as
determined by the Normalized and Complementary Wasserstein Distance, $\eta$,
which we present in a manner to expose the QAOA as a transporter of
probability. Using $\eta$ as an application specific benchmark of performance,
we measure it on selection of QPUs as a function of QAOA circuit depth $p$. At
$n = 2$ (2 qubits) we find peak solution quality at $p=5$ for most systems and
for $n = 3$ this peak is at $p=4$ on a trapped ion QPU. Increasing solution
quality with $p$ is also observed using variants of the more general Quantum
Alternating Operator Ans\"{a}tz at $p=2$ for $n = 2$ and $3$ which has not been
previously reported. In identical measurements, $\eta$ is observed to be
variable at a level exceeding the noise produced from the finite number of
shots. This suggests that variability itself should be regarded as a QPU
performance benchmark for given applications. While studying the ideal
execution of QAOA, we find that $p=1$ solution quality degrades when the
portfolio budget $B$ approaches $n/2$ and increases when $B \approx 1$ or
$n-1$. This trend directly corresponds to the binomial coefficient $nCB$ and is
connected with the recently reported phenomenon of reachability deficits.
Derivative-requiring and derivative-free classical optimizers are benchmarked
on the basis of the achieved $\eta$ beyond $p=1$ to find that derivative-free
optimizers are generally more effective for the given computational resources,
problem sizes and circuit depths.
