AQER: a scalable and efficient data loader for digital quantum computers

TL;DR

This work addresses the challenge of loading classical and quantum data into quantum circuits by introducing a unified AQL framework and information-theoretic bounds that tie loading accuracy to the target state's entanglement via $\mathcal{S}$. It then proposes AQER, a scalable AQL that greedily reduces entanglement, uses explicit product-state approximations, and refines parameters to minimize infidelity, leading to improved gate efficiency and trainability. Across synthetic and real-world classical datasets and quantum many-body states up to 50 qubits, AQER outperforms TN- and circuit-based baselines and remains robust to noise, showcasing practical potential for scalable quantum data processing. The paper provides both theoretical guarantees (entanglement-based bounds) and empirical evidence of AQER's effectiveness, along with public code, signaling a concrete step toward real-world quantum-data-enabled quantum computing applications.

Abstract

Digital quantum computing promises to offer computational capabilities beyond the reach of classical systems, yet its capabilities are often challenged by scarce quantum resources. A critical bottleneck in this context is how to load classical or quantum data into quantum circuits efficiently. Approximate quantum loaders (AQLs) provide a viable solution to this problem by balancing fidelity and circuit complexity. However, most existing AQL methods are either heuristic or provide guarantees only for specific input types, and a general theoretical framework is still lacking. To address this gap, here we reformulate most AQL methods into a unified framework and establish information-theoretic bounds on their approximation error. Our analysis reveals that the achievable infidelity between the prepared state and target state scales linearly with the total entanglement entropy across subsystems when the loading circuit is applied to the target state. In light of this, we develop AQER, a scalable AQL method that constructs the loading circuit by systematically reducing entanglement in target states. We conduct systematic experiments to evaluate the effectiveness of AQER, using synthetic datasets, classical image and language datasets, and a quantum many-body state datasets with up to 50 qubits. The results show that AQER consistently outperforms existing methods in both accuracy and gate efficiency. Our work paves the way for scalable quantum data processing and real-world quantum computing applications.

Figures (19)

• Figure 1: The general framework of AQL. Typical AQLs are separated into two categories: TN–based methods and circuit-based methods, both of which aim to construct quantum circuits from a given gate set $\mathcal{U}$ that approximately prepare the target state.
• Figure 2: The workflow of the AQER algorithm. (a) An overview of AQER, which consists of three steps. (b) Step I: entanglement reduction. This step iteratively appends two-qubit gate blocks to progressively reduce the entanglement of the input $|\bm{v}_{\rm target}\rangle$ with the circuit $V_T(\bm{\alpha})$. (c) Step II: product state approximation. This step approximates the low-entanglement state $|\bm{v}_T\rangle$ by applying single-qubit rotations $\{R_Z(\bm{\beta}_n)\}_{n=1}^{N}$ and $\{R_Y(\bm{\gamma}_n)\}_{n=1}^{N}$ to the initial state ${|0\rangle}^{\otimes N}$. (d) Step III: parameter refinement. This step finetunes all circuit parameters in $\bm{\theta}=(\bm{\alpha}, \bm{\beta}, \bm{\gamma})$ to minimize the infidelity and obtain the final AQL $U_{\rm AQER}(\bm{\theta}^*)$.
• Figure 3: Performance of AQER across MNIST, CIFAR-10, SST-2, S-RQC, and GS-TFIM datasets, distinguished by different colors and markers. (a) Infidelity versus the entanglement measure value $S$ after Step II of AQER, averaged over $M$ samples. Color bars from light to dark indicate increasing $T$. Dashed lines indicate the linearized upper (U.B.) and lower (L.B.) bounds in Theorem \ref{['AQER_method_tn_init_projection_prop']}, which neglect higher-order terms. (b) Infidelity versus different $T$ values after Step III of AQER across all datasets. (c) Infidelity versus different measurement shots for the GS-TFIM dataset, with different $T \in \{10,20,40,100\}$.
• Figure 4: Performance of AQER on the GS-TFIM dataset. (a) Infidelity during Step III optimization across different $T$ values with $N=50$ qubits. (b) Infidelity for different qubit numbers $N$ and Step I iteration times $T$. (c) Expectation values of the averaged magnetization $\langle X\rangle$ measured on AQER-loaded GS-TFIM states for different $g/J$ values with $N=10$. Each curve corresponds to a different $T \in \{10,20,40\}$.
• Figure 5: Downstream performance of AQER on classical data. (a) Reconstructed MNIST and CIFAR-10 images using AQER with $T \in \{20,40,80\}$. (b) Classification error on the SST-2 dataset using AQER-loaded states with $T \in \{10,20,40,60,80,100\}$, compared to exact loading (black dashed line).

Theorems & Definitions (22)

• Theorem 3.1
• Corollary 3.2: informal
• Lemma B.1
• proof
• Lemma B.2
• proof
• Lemma B.3
• proof
• Theorem B.4
• proof