Local tensor-train surrogates for quantum learning models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910174339399680 |
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| author | Nair, Sreeraj Rajindran Ferrie, Christopher |
| author_facet | Nair, Sreeraj Rajindran Ferrie, Christopher |
| contents | A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical tensor-train surrogates of fully trained quantum machine learning models within local patches of their input data space. The approach combines Taylor polynomial approximation with a tensor-train (TT) representation and embeds it in a statistical learning paradigm via empirical risk minimization. In our analysis, the Taylor-TT construction serves as a deterministic error certificate proving that the TT hypothesis class contains a good approximation; empirical risk minimization then provably recovers a surrogate with controlled generalization error and explicit bounds. This translates into three independently controllable error sources: (i) Taylor truncation error controlled by the patch radius $r$ and polynomial degree $p$, (ii) TT approximation error controlled by the bond dimension $χ$, and (iii) statistical estimation error. While the parameter count scales polynomially in the number of data dimensions $N$, i.e., $d_{\mathrm{eff}} = N(p+1)χ^2$ rather than the naive $(p+1)^N$, the worst-case constants inherit an exponential factor through the tensor-product feature norm during Taylor polynomial embedding onto TT. This cleanly separates representation complexity from feature-induced constants. Our risk bounds and sample complexity depend explicitly on the local patch radius $r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25631 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local tensor-train surrogates for quantum learning models Nair, Sreeraj Rajindran Ferrie, Christopher Quantum Physics A key bottleneck in quantum machine learning is the computational cost of repeated quantum circuit evaluations during the inference phase. To address this, we present a framework for constructing fast, cheap, provably accurate classical tensor-train surrogates of fully trained quantum machine learning models within local patches of their input data space. The approach combines Taylor polynomial approximation with a tensor-train (TT) representation and embeds it in a statistical learning paradigm via empirical risk minimization. In our analysis, the Taylor-TT construction serves as a deterministic error certificate proving that the TT hypothesis class contains a good approximation; empirical risk minimization then provably recovers a surrogate with controlled generalization error and explicit bounds. This translates into three independently controllable error sources: (i) Taylor truncation error controlled by the patch radius $r$ and polynomial degree $p$, (ii) TT approximation error controlled by the bond dimension $χ$, and (iii) statistical estimation error. While the parameter count scales polynomially in the number of data dimensions $N$, i.e., $d_{\mathrm{eff}} = N(p+1)χ^2$ rather than the naive $(p+1)^N$, the worst-case constants inherit an exponential factor through the tensor-product feature norm during Taylor polynomial embedding onto TT. This cleanly separates representation complexity from feature-induced constants. Our risk bounds and sample complexity depend explicitly on the local patch radius $r$. |
| title | Local tensor-train surrogates for quantum learning models |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.25631 |