aiqbench analysis
This research establishes the theoretical limits for blind single-copy compression of quantum states using autoencoders, identifying a balanced regime between narrow nonuniversal architectures and overparameterized universal ones. The study proves that specific encoder ancilla counts are necessary to achieve optimal fidelity while showing that isometric decoders suffice for many practical cases despite not being universally sufficient. These findings provide critical benchmarks for optimizing circuit width in quantum machine learning applications without sacrificing information-theoretic performance.
Toward the Goldilocks Blind Compression of Quantum States
arXiv:2605.01258v2 Announce Type: replace Abstract: Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.
Abstract:Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.
arXiv:2605.01258 [quant-ph]
(or arXiv:2605.01258v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.01258 Focus to learn more arXiv-issued DOI via DataCite
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