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arXiv · 2305.15398

Learning t-doped stabilizer states

Lorenzo Leone·Salvatore F. E. Oliviero·Alioscia Hamma
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Abstract

In this paper, we present a learning algorithm aimed at learning states obtained from computational basis states by Clifford circuits doped with a finite number $t$ of $T$-gates. The algorithm learns an exact tomographic description of $t$-doped stabilizer states in terms of Pauli observables. This is possible because such states are countable and form a discrete set. To tackle the problem, we introduce a novel algebraic framework for $t$-doped stabilizer states, which extends beyond $T$-gates and includes doping with any kind of local non-Clifford gate. The algorithm requires resources of complexity $\text{poly}(n,2^t)$ and exhibits an exponentially small probability of failure.

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Lorenzo Leone, Salvatore F. E. Oliviero, Alioscia Hamma. 2023-05-24. Learning t-doped stabilizer states. https://doi.org/10.22331/q-2024-05-27-1361

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