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Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

NeurIPS 2026 · Architectures and efficiency › RNNs and normalization · approach: Scalable approximation and equivariant compute · 0 citations (OpenAlex)

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Proposes TNQE, which encodes classical images into quantum circuits by compiling quantized tensor-train cores into shallow unitary circuits (full, core-wise, and unitary-aware variants), reporting up to 0.04x amplitude-encoding depth on MNIST and runs on IBM hardware.

Problem

Quantum data encoding of classical data (e.g., images) typically yields deep, resource-heavy circuits such as amplitude encoding, which limits scalability on quantum hardware.

Approach

Represent images as quantized tensor-train cores and convert them to circuits either via right-canonical MPS isometries completed to unitaries (TNQE-full), per-core amplitude-encoded sub-circuits (TNQE-core), or by directly optimizing parameterized block unitaries whose first columns define the cores (TNQE-unitary).

Key results

• TNQE-unitary reaches circuit depth 81 vs 2028 for amplitude encoding on 32x32 MNIST (about 0.04x) with MSE 0.011249 and PSNR 20.58.
• TNQE-core with the referenced-image protocol achieves MSE 0.002182, PSNR 28.49, SSIM 0.983 on MNIST.
• On IBM Heron QPUs (ibm_torino, ibm_fez, ibm_boston) with 100 MNIST images, TNQE-unitary-based encoding gives PSNR around 15-16 dB vs about 9.7-9.9 dB for amplitude encoding.

Surprising findings

• Amplitude encoding already fails on real hardware for only 16x16 images, per the authors' hardware stress test.
• Amplitude encoding's SSIM on real hardware drops to nearly zero (0.0003-0.02), indicating hardware noise dominates deep circuits.

Limitations

• No noise-aware training or error mitigation; hardware performance degrades substantially with resolution.
• Performance is bounded by the quality of the underlying tensor network decomposition.
• Lacks a theoretical characterization of the TNQE-unitary optimization landscape and convergence.

Experimental setup

Datasets: MNIST Cameraman Girl with a Pearl Earring synthetic Gaussian blob images

Benchmarks: MNIST

Metrics: MSE BCE PSNR SSIM classification accuracy qubit count circuit depth operation count

Baselines: amplitude encoding automatic encoding basis encoding CNN-based hybrid encoding MPS-based encoding

Builds on: quantized tensor train matrix product state amplitude encoding quantum shannon decomposition hardware-efficient ansatz

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