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The effect of realistic noise models on quantum error correction thresholds

Mauricio Gutierrez, Georgia Institute of Technology

(Session 9a : Friday from 5:00pm - 5:30pm)

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code (QECC). In this context, it is common to model the noise as a depolarizing channel by inserting Pauli gates randomly throughout the circuit [1]. However, it is not clear how sensitive a code's threshold is to the noise model, and whether or not a depolarizing channel is a good approximation for realistic non-stabilizer errors. Within the stabilizer formalism, we have shown that for a single qubit more accurate approximations can be obtained by including in the noise model Clifford operators and Pauli operators conditional on measurement [2]. Independent work by Magesan et al. has also shown the utility of adding Clifford operators to error models [3]. We now examine the feasibility of employing these error approximations at the single-qubit level to obtain better estimates of a QECC's threshold. For several codes and various noise models, we simulate an error-correction step and compute the pseudo-threshold by determining the noise strength above which encoding reduces the qubit fidelity. We compare the pseudo-threshold values for the real noise with its Pauli and expanded Pauli approximations. In most cases, the expanded Pauli channel provides a significantly better approximation to the real pseudo-threshold suggesting that our expanded error models will lead to more accurate stabilizer-based threshold estimations for realistic noise models. [1] A.M. Steane, Phys. Rev. A 68, 042322 (2003) [2] M. Gutiérrez, L. Svec, A. Vargo, and K. R. Brown, Phys. Rev. A. 87, 030302(R) (2013) [3] E. Magesan, D. Puzzuoli, C. E. Granade, D. G. Cory, Phys. Rev. A 87, 012324 (2013)