Hybrid Quantum State Preparation via Data Compression

TL;DR

This paper presents a hybrid classical-quantum approach to quantum state preparation that leverages data compression to significantly reduce quantum circuit complexity for certain data types, making it more feasible for near-term quantum devices.

Contribution

The authors introduce a novel ancilla-free hybrid method combining classical data compression with quantum state preparation, reducing complexity from exponential to polynomial for compressible data.

Findings

Significant reduction in CNOT gates and circuit depth compared to exact amplitude encoding.

Effective for synthetic and real biomedical signals using Fourier and Haar transforms.

Competitive performance with existing Fourier Series Loader methods.

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.