Hybrid Quantum State Preparation via Data Compression

TL;DR

This work tackles the exponential cost of general quantum state preparation by introducing an ancilla-free hybrid classical–quantum framework that uses reversible transform-based compression to obtain a $d$-sparse representation and a quantum inverse transform to reconstruct the target state, achieving $O( ext{poly}(n))$ resources for compressible data. The method comprises Phase I classical compression (transform, thresholding, normalization) and Phase II quantum decompression (sparse-state preparation plus inverse transform), enabling scalable QSP without variational training or ancilla qubits. Extensive simulations on synthetic and biomedical signals (Fourier and Haar-based transforms) demonstrate substantial reductions in CNOT counts and circuit depth relative to exact amplitude encoding, while maintaining high fidelity; performance is competitive with, and sometimes superior to, the Fourier Series Loader (FSL) depending on data structure and sparsity. The approach highlights a practical pathway to efficient data loading for near-term quantum devices, with potential extensions to more efficient sparse-state preparation methods or inclusion of ancillary resources to further reduce quantum overhead. Overall, the findings suggest that classical sparsification paired with quantum decompression can be a robust, scalable strategy for high-dimensional QSP in realistic, nonstationary data domains.

Abstract

Quantum state preparation (QSP) for a general $n$-qubit state requires $O(2^n)$ CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid classical-quantum strategy that reduces this cost to $O(poly(n))$ for a broad class of compressible data. The method first applies a classical compression step to obtain a $d$-sparse representation of the input, loads this sparse vector using a sparse-state preparation routine, and then reconstructs the target state through a polynomial-depth quantum inverse transform. We evaluate the framework on synthetic benchmark signals and real biomedical time series using Fourier and Haar transforms, demonstrating substantial reductions in CNOT counts and circuit depth compared to EAE, together with competitive performance relative to the Fourier Series Loader (FSL). The quantum simulation results show that combining classical data compression with quantum decompression provides a scalable framework for efficient QSP, reducing quantum overhead without requiring variational training or ancillary registers.

Figures (9)

• Figure 1: (a) Original multi-frequency periodic signal (light blue) and its exact reconstruction (red) via hybrid QSP. (b) Frequency-domain representation obtained via DFT, revealing four non-zero coefficients.
• Figure 2: Hybrid QSP circuit for the multi-frequency periodic signal in Fig. \ref{['fig:multi-periodic-signal']}. The 4-sparse frequency-domain state is initialized using a single $R_y(2\theta)$ rotation with $\theta \approx 0.9505$ radians and prepared with only 14 CNOT gates and 15 single-qubit rotations. An inverse QFT is then applied to recover the exact original time-domain signal. For resource estimation, each Toffoli gate could be decomposed into 6 CNOTs and 9 single-qubit gates nielsen2010quantum.
• Figure 3: Illustrative representation of the original piecewise-constant signal (light blue) versus its quantum preparation using the proposed hybrid algorithm (red).
• Figure 4: Hybrid QSP for the piecewise-constant signal. (a) The quantum circuit for the hybrid QSP, including the sparse preparation operator $\mathcal{P}$ and a 7-level inverse packet QHWT for data decompression. (b) Expanded view of $\text{QHWT}_8^{-1}$ block.
• Figure 5: Approximate hybrid QSP of a sinc signal using the Haar wavelet basis. The reconstructed signal (red) closely matches the original (light blue), demonstrating strong fidelity after high compression.