Efficient Data Encoding and Decoding for Quantum Computing

Noisy Intermediate-Scale Quantum (NISQ) devices face many critical challenges that limit their usefulness for practical applications. A primary challenge is classical-to-quantum (C2Q) data encoding, which requires specific circuits for quantum state initialization, particularly for I/O intensive applications. The required state initialization circuits are often complex, and violate decoherence constraints. Another critical challenge for quantum computers is quantum state readout or quantum-to-classical (Q2C) data decoding. The general approach for Q2C involves repeated sampling of the quantum circuit, which often incurs significant overhead in the overall execution time. In this paper, we propose time-efficient methods for C2Q data encoding and Q2C data decoding for quantum algorithms. Decoherence optimized circuits for C2Q data encoding are presented along with analysis of their circuit depths. For Q2C, a novel approach based on more efficient sampling of the output state using the Quantum Wavelet Transform is proposed. The proposed methods are experimentally evaluated on a state-of-the-art quantum computing device from IBM Quantum using realistic multi-spectral data. Experimental results are consistent with our theoretical expectations and confirm the efficiency of our proposed methods compared to existing techniques. More specifically, our proposed C2Q method demonstrates a theoretical 2x reduction in circuit depth which resulted in improving the experimental execution time compared to the state-of-the-art, while our Q2C method achieved a maximum of 89% reduction in circuit sampling time.