Abstract
The performance of error correction protocols are necessary for understanding the operation of potential quantum computers, but this requires physical error models that can be simulated efficiently with classical computers. The Gottesmann-Knill theorem guarantees a class of such error models. Of these, one of the simplest is the Pauli twirling approximation (PTA), which is obtained by twirling an arbitrary completely positive error channel over the Pauli basis, resulting in a Pauli channel. In this work, we test the PTA’s accuracy at predicting the logical error rate by simulating the 5-qubit code using a 9-qubit circuit with realistic decoherence and unitary gate errors. We find evidence for good agreement with exact simulation, with the PTA overestimating the logical error rate by a factor of 2 to 3. Our results suggest that the PTA is a reliable predictor of the logical error rate, at least for low-distance codes.
Highlights
The performance of error correction protocols are necessary for understanding the operation of potential quantum computers, but this requires physical error models that can be simulated efficiently with classical computers
We have studied the Pauli twirling approximation (PTA) logical error rate compared to an exact calculation that includes both decoherence and unitary gate errors
In the language of Megasan et al.[5], we find that the PTA is always honest for the parameter regimes considered
Summary
Geller and Zhou[7] took a different approach and asked how well the Pauli twirling approximation (PTA), obtained by twirling the exact error channel over the Pauli basis, performed on a 4-qubit Bell-state. Two other related investigations have recently appeared: Puzzuoli et al.[9] discussed the construction of efficient (Pauli and Clifford) error channels obtained by minimizing the diamond norm subject to the constraint that the approximate channel always upper bounds the error (an honest representation in the terminology of refs 5,9) and tested their accuracy when applied to error-correcting circuits. The results of refs 7,8,10, together with the results reported below, suggest that the PTA is a reliable (and honest) predictor of the logical error rate, at least for low-distance codes
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