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Logical error rate in the Pauli twirling approximation.

Katabarwa A, Geller MR - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA.

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.

No MeSH data available.


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Logical error rate for the /0〉L state with T1 = T2 100 μs.
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f2: Logical error rate for the /0〉L state with T1 = T2 100 μs.

Mentions: Figures 2,3 and 4 give the logical error rate PL versus intrinsic error for three values of T1, with T2 = T1. We find in these cases that the PTA overestimates the logical error rate by about a factor of 2 to 3. In Fig. 5, we fix the total intrinsic error to E = 10−3 and test the PTA for five different states on the logical Bloch sphere: the eigenstates of σz, σx, and the +1 eigenstate of σy.


Logical error rate in the Pauli twirling approximation.

Katabarwa A, Geller MR - Sci Rep (2015)

Logical error rate for the /0〉L state with T1 = T2 100 μs.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4588586&req=5

f2: Logical error rate for the /0〉L state with T1 = T2 100 μs.
Mentions: Figures 2,3 and 4 give the logical error rate PL versus intrinsic error for three values of T1, with T2 = T1. We find in these cases that the PTA overestimates the logical error rate by about a factor of 2 to 3. In Fig. 5, we fix the total intrinsic error to E = 10−3 and test the PTA for five different states on the logical Bloch sphere: the eigenstates of σz, σx, and the +1 eigenstate of σy.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA.

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.

No MeSH data available.


Related in: MedlinePlus