  Powerful hardware services and software libraries are vital tools for quickly
and affordably designing, testing, and executing quantum algorithms. A robust
large-scale study of how the performance of these platforms scales with the
number of qubits is key to providing quantum solutions to challenging industry
problems. This work benchmarks the runtime and accuracy for a representative
sample of specialized high-performance simulated and physical quantum
processing units. Results show the QMware simulator can reduce the runtime for
executing a quantum circuit by up to 78% compared to the next fastest option
for algorithms with fewer than 27 qubits. The AWS SV1 simulator offers a
runtime advantage for larger circuits, up to the maximum 34 qubits available
with SV1. Beyond this limit, QMware can execute circuits as large as 40 qubits.
Physical quantum devices, such as Rigetti's Aspen-M2, can provide an
exponential runtime advantage for circuits with more than 30 qubits. However,
the high financial cost of physical quantum processing units presents a serious
barrier to practical use. Moreover, only IonQ's Harmony quantum device achieves
high fidelity with more than four qubits. This study paves the way to
understanding the optimal combination of available software and hardware for
executing practical quantum algorithms.
