  The quantum volume test is a full-system benchmark for quantum computers that
is sensitive to qubit number, fidelity, connectivity, and other quantities
believed to be important in building useful devices. The test was designed to
produce a single-number measure of a quantum computer's general capability, but
a complete understanding of its limitations and operational meaning is still
missing. We explore the quantum volume test to better understand its design
aspects, sensitivity to errors, passing criteria, and what passing implies
about a quantum computer. We elucidate some transient behaviors the test
exhibits for small qubit number including the ideal measurement output
distributions and the efficacy of common compiler optimizations. We then
present an efficient algorithm for estimating the expected heavy output
probability under different error models and compiler optimization options,
which predicts performance goals for future systems. Additionally, we explore
the original confidence interval construction and show that it underachieves
the desired coverage level for single shot experiments and overachieves for
more typical number of shots. We propose a new confidence interval construction
that reaches the specified coverage for typical number of shots and is more
efficient in the number of circuits needed to pass the test. We demonstrate
these savings with a $QV=2^{10}$ experimental dataset collected from Quantinuum
System Model H1-1. Finally, we discuss what the quantum volume test implies
about a quantum computer's practical or operational abilities especially in
terms of quantum error correction.
