Stacking the Odds: Full-Stack Quantum System Design Space Exploration

Design space exploration (DSE) plays an important role in optimising quantum circuit execution
by systematically evaluating different configurations of compilation strategies and hardware 
settings. In this paper, we conduct a comprehensive investigation into the impact of various
layout methods, qubit routing techniques, and optimisation levels, as well as device-specific properties
such as different variants and strengths of noise and imperfections, the topological structure of qubits, connectivity densities, and back-end sizes.
By spanning through these dimensions, we aim to understand the interplay between compilation choices and 
hardware characteristics. A key question driving our exploration is whether the optimal selection of device
parameters,  mapping techniques, comprising of initial layout strategies and routing heuristics can mitigate
device induced errors beyond standard error mitigation approaches. Our results show that carefully selecting software strategies
(e.g., mapping and routing algorithms) and tailoring hardware characteristics (such as minimising noise and leveraging topology and connectivity density) significantly improve
the fidelity of circuit execution outcomes, and thus the expected correctness or success probability of the computational result. We provide estimates based on key metrics such as circuit depth, 
gate count and expected fidelity.
Our results highlight the importance of 
hardware–software co-design, particularly as quantum systems scale to larger dimensions,
and along the way towards fully error corrected quantum systems:
Our study is based on computationally noisy simulations,
but considers various implementations of
quantum error correction (QEC) using the same approach as for other algorithms.
The observed sensitivity of circuit fidelity
to noise and connectivity suggests that co-design principles will be equally
critical when integrating QEC in future systems. Our exploration provides practical
guidelines for co-optimising physical mapping, qubit routing, and hardware
configurations in realistic quantum computing scenarios.