  Designing performant and noise-robust circuits for Quantum Machine Learning
(QML) is challenging -- the design space scales exponentially with circuit
size, and there are few well-supported guiding principles for QML circuit
design. Although recent Quantum Circuit Search (QCS) methods attempt to search
for performant QML circuits that are also robust to hardware noise, they
directly adopt designs from classical Neural Architecture Search (NAS) that are
misaligned with the unique constraints of quantum hardware, resulting in high
search overheads and severe performance bottlenecks.
  We present \'Eliv\'agar, a novel resource-efficient, noise-guided QCS
framework. \'Eliv\'agar innovates in all three major aspects of QCS -- search
space, search algorithm and candidate evaluation strategy -- to address the
design flaws in current classically-inspired QCS methods. \'Eliv\'agar achieves
hardware-efficiency and avoids an expensive circuit-mapping co-search via
noise- and device topology-aware candidate generation. By introducing two
cheap-to-compute predictors, Clifford noise resilience and Representational
capacity, \'Eliv\'agar decouples the evaluation of noise robustness and
performance, enabling early rejection of low-fidelity circuits and reducing
circuit evaluation costs. Due to its resource-efficiency, \'Eliv\'agar can
further search for data embeddings, significantly improving performance.
  Based on a comprehensive evaluation of \'Eliv\'agar on 12 real quantum
devices and 9 QML applications, \'Eliv\'agar achieves 5.3% higher accuracy and
a 271$\times$ speedup compared to state-of-the-art QCS methods.
