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arXiv:2610.04247

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

Archie Butterworth, Jens Renders, Jingbo Wang

On Aqora:Jingbo WangJingbo Wang
quant-phSubmitted Oct 3, 2026• Announced Oct 6, 2026• 0 citations
v1 · Oct 3, 2026v2 · Oct 28, 2026
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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.

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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 MMM nnn-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 O(Mn)\mathcal{O}(Mn)O(Mn) to O(n)\mathcal{O}(n)O(n). Applied to a real-world (128\times256) ultrasound dataset, Q-MERGE achieves an infidelity of 1.066×10−81.066\times10^{-8}1.066×10−8, compared with 3.413×10−13.413\times10^{-1}3.413×10−1 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=107M=10^7M=107 segments, supporting the scalability of Q-MERGE for encoding massive classical datasets.
Quantum state preparation (QSP) for a general nnn-qubit state requires O(2n)O(2^n)O(2n) 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))O(poly(n))O(poly(n)) for a broad class of compressible data. The method first applies a classical compression step to obtain a ddd-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.
Preparation and verification of specific quantum states is an important capability for quantum devices to realise advantages over classical computations and algorithms. In this work, we have demonstrated an end-to-end framework that combines resource-efficient quantum state preparation with rapid, robust fidelity verification on near-term quantum hardware. By experimentally preparing and validating a structured complex quantum state encoding a digitized acoustic signal on the Quantinuum H2-1 trapped-ion platform, we achieved a high hardware fidelity of Fhw=0.929F_{\mathrm{hw}} = 0.929Fhw​=0.929. Crucially, this milestone was realized without relying on idealized assumptions or deep fault-tolerant overhead, but rather through resource-minimal circuits optimized for NISQ-era and early fault-tolerant devices. Furthermore, we addressed a key limitation in current quantum state certification. While validation methods like shadow overlap work well for random states, their sample complexity can become prohibitively high for the structured states used in practical algorithms. We mitigate this by introducing a pre-measurement basis-change technique that reduces the verification parameter, τττ, by over 10 orders of magnitude for structured targets. This approach tightens the theoretical certification guarantees of the shadow overlap method and integrates tensor-network preparation and shadow validation into a unified workflow. These results shift the paradigm of how structured classical data can be mapped to and verified on quantum hardware under realistic noise and measurement budgets. By compressing a robust verification procedure to just 1,000 measurement shots, this framework offers an immediate, scalable benchmarking standard.
We propose a hybrid quantum state preparation method based on the Walsh--Hadamard transform within the dense-to-sparse quantum state preparation framework. The method approximately prepares structured classical data in a quantum circuit through an indirect approach. Instead of directly preparing the dense amplitude-encoded state, the method first transforms the classical data into the Walsh domain and prepares only the largest-magnitude coefficients using a sparse state-preparation algorithm. The original state can then be approximately recovered through a parallel layer of Hadamard gates. Since this reconstruction requires no CNOT gates and has circuit depth 1, the proposed method introduces no additional CNOT or circuit-depth overhead, and its quantum preparation cost is determined by the underlying sparse state-preparation algorithm. Numerical results on representative benchmark signals demonstrate that the proposed method enables accurate state preparation for signals admitting sparse or approximately sparse representations in the Walsh domain.
Quantum state preparation is the process of producing a target quantum state that will be used as the input to a quantum circuit. Many quantum algorithms require an input state where amplitudes, phases, or basis probabilities encode problem data, and the cost of preparing this state can be significant in gate count and circuit depth. This review summarizes common goals, assumptions, and methods for quantum state preparation, with emphasis on preparing states from classical vectors, probability distributions, and feature data used in quantum machine learning. We organize approaches by the information they load and by the resources they require, including gate count, circuit depth, qubit overhead, and classical preprocessing. It also compares exact and approximate preparation procedures, and discusses how precision targets affect cost. The review highlights links between families of methods, typical sources of resource estimates, and criteria that help match a preparation method to a task and hardware constraints.
Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data loading tailored to a given input vector and target error tolerance. By explicitly exploiting the trade-off between exact and approximate state preparation, our approach systematically partitions the total error budget between precision and approximation errors, thereby minimizing quantum resource costs. The framework supports a comprehensive suite of state-of-the-art methods, including multiplexer-based loaders, quantum read-only memory (QROM) constructions, sparse encodings, matrix product states (MPS), Fourier series loaders (FSL), and Walsh transform-based diagonal operators. We demonstrate the effectiveness of our framework across several applications, where it consistently uncovers non-obvious, resource-efficient strategies enabled by controlled approximation. In particular, we analyze a computational fluid dynamics workflow where the automated selection of MPS state preparation and Walsh transform-based encoding, combined with a novel Walsh-based measurement technique, leads to resource reductions of over four orders of magnitude compared to previous approaches. We also introduce two independent advances developed through the framework: a more efficient circuit for d-diagonal matrices, and an optimized block encoding for kinetic energy operators. Our results underscore the indispensable role of automated, approximation-aware compilation in making large-scale quantum algorithms feasible on resource-constrained hardware.
We present a protocol for encoding NNN real numbers stored in NNN memory registers into the amplitudes of the quantum superposition that describes the state of log2N{log}_{2}Nlog2​N qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scales linearly with the number of qubits in the processing register and hence logarithmically with NNN. The average time needed to successfully perform the encoding scales logarithmically with the number of qubits, in addition to being inversely proportional to the acceptable error in the encoded amplitudes. It also depends on the structure of the dataset in such a way that the protocol is most efficient for nonsparse data.