Learning t-doped stabilizer states

Lorenzo Leone; Salvatore F. E. Oliviero; Alioscia Hamma

doi:10.22331/q-2024-05-27-1361

Learning t-doped stabilizer states

Lorenzo Leone^1,2, Salvatore F. E. Oliviero^1,3, and Alioscia Hamma^4,5

¹Physics Department, University of Massachusetts Boston, 02125, USA
²Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
³NEST, Scuola Normale Superiore and Istituto Nanoscienze, Consiglio Nazionale delle Ricerche, Piazza dei Cavalieri 7, IT-56126 Pisa, Italy
⁴Dipartimento di Fisica `Ettore Pancini', Università degli Studi di Napoli Federico II, Via Cintia 80126, Napoli, Italy
⁵INFN, Sezione di Napoli, Italy

Published:	2024-05-27, volume 8, page 1361
Eprint:	arXiv:2305.15398v6
Doi:	https://doi.org/10.22331/q-2024-05-27-1361
Citation:	Quantum 8, 1361 (2024).

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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 $\operatorname{poly}(n,2^t)$ and exhibits an exponentially small probability of failure.

► BibTeX data

@article{Leone2024learningtdoped,
  doi = {10.22331/q-2024-05-27-1361},
  url = {https://doi.org/10.22331/q-2024-05-27-1361},
  title = {Learning t-doped stabilizer states},
  author = {Leone, Lorenzo and Oliviero, Salvatore F. E. and Hamma, Alioscia},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1361},
  month = may,
  year = {2024}
}

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