  Parameterized Quantum Circuits (PQC) have obtained increasing popularity
thanks to their great potential for near-term Noisy Intermediate-Scale Quantum
(NISQ) computers. Achieving quantum advantages usually requires a large number
of qubits and quantum circuits with enough capacity. However, limited coherence
time and massive quantum noises severely constrain the size of quantum circuits
that can be executed reliably on real machines. To address these two pain
points, we propose QuantumSEA, an in-time sparse exploration for noise-adaptive
quantum circuits, aiming to achieve two key objectives: (1) implicit circuits
capacity during training - by dynamically exploring the circuit's sparse
connectivity and sticking a fixed small number of quantum gates throughout the
training which satisfies the coherence time and enjoy light noises, enabling
feasible executions on real quantum devices; (2) noise robustness - by jointly
optimizing the topology and parameters of quantum circuits under real device
noise models. In each update step of sparsity, we leverage the moving average
of historical gradients to grow necessary gates and utilize salience-based
pruning to eliminate insignificant gates. Extensive experiments are conducted
with 7 Quantum Machine Learning (QML) and Variational Quantum Eigensolver (VQE)
benchmarks on 6 simulated or real quantum computers, where QuantumSEA
consistently surpasses noise-aware search, human-designed, and randomly
generated quantum circuit baselines by a clear performance margin. For example,
even in the most challenging on-chip training regime, our method establishes
state-of-the-art results with only half the number of quantum gates and ~2x
time saving of circuit executions. Codes are available at
https://github.com/VITA-Group/QuantumSEA.
