Q-MERGE: Parallelising Quantum State Preparation for Large-Scale Classical Data

Abstract

Quantum processing of classical data fundamentally relies on efficiently mapping classical datasets onto the amplitudes of quantum states. Preparing large amplitude-encoded states, however, remains a major bottleneck in quantum computing. In this paper, we introduce a novel state-preparation framework we call Q-MERGE, that addresses this bottleneck by partitioning a large target state into $M$ $n$-qubit segments, preparing these segments independently and in parallel, and then coherently combining them into a single amplitude-encoded state using SELECT-SWAP operations and measurement. Q-MERGE is agnostic to the segment-level preparation method, allowing existing techniques to be applied to smaller subproblems while providing a tunable trade-off between circuit depth and qubit count. With mid-circuit measurement and preparation-register reuse, the required ancilla qubits can be reduced from $\mathcal{O}(Mn)$ to $\mathcal{O}(n)$. Applied to a real-world \(128\times256\) ultrasound dataset, Q-MERGE achieves an infidelity of $1.066\times10^{-8}$, compared with $3.413\times10^{-1}$ for direct preparation using the same underlying method, a seven-order of magnitude improvement. We demonstrate its feasibility experimentally on the Quantinuum System Model H2 trapped-ion quantum computer and validate the prepared state using shadow-overlap tomography. Numerical analysis of Haar-random states indicates consistent success probability for up to $M=10^7$ segments, supporting the scalability of Q-MERGE for encoding massive classical datasets.