Limits...
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.


Related in: MedlinePlus

Stabilizer measurement circuit for the 5-qubit code written in terms of CZ gates (vertical lines with dots).A cycle is moving through this circuit once and performing the measurement step.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4588586&req=5

f1: Stabilizer measurement circuit for the 5-qubit code written in terms of CZ gates (vertical lines with dots).A cycle is moving through this circuit once and performing the measurement step.

Mentions: A logical state is prepared in the computational basis using the first five (data) qubits, as shown in Fig. 1. The next four qubits are used as ancilla qubits to measure the four stabilizers after which four measurement outcomes (x1, x2, x3, x4) are obtained. There are 16 possible measurement outcomes which are in a one to one correspondence with the 16 possible errors that might occur [counting the outcome (0, 0, 0, 0) as a trivial error]. In Table 1 we list all possible measurement outcomes and the corresponding single qubit errors. We call the implementation of the circuit and performing the measurement step a cycle, which is shown in Fig. 1. If one goes through a cycle and a single error occurs on any of the first 5 qubits, this might be reflected in the measurement result and thus detected. But instead suppose that no errors occur on the data qubits but right before the measurement step a bit-flip error occurs on the first syndrome qubit, giving the measurement outcome of (1, 0, 0, 0). An incorrect interpretation of the result would be to conclude that one of the 16 possible errors on the data qubits has occurred, whereas in fact the fault lies with a syndrome qubit. We therefore require a protocol that is tolerant to a single syndrome-qubit (or readout) error. To this end, we note that for errors uncorrelated in time, it is likely that after readout and re-initialization that the syndrome qubit will return to its original “faithful” state at the end of the next cycle. The procedure followed in our simulations is therefore the following:


Logical error rate in the Pauli twirling approximation.

Katabarwa A, Geller MR - Sci Rep (2015)

Stabilizer measurement circuit for the 5-qubit code written in terms of CZ gates (vertical lines with dots).A cycle is moving through this circuit once and performing the measurement step.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Stabilizer measurement circuit for the 5-qubit code written in terms of CZ gates (vertical lines with dots).A cycle is moving through this circuit once and performing the measurement step.
Mentions: A logical state is prepared in the computational basis using the first five (data) qubits, as shown in Fig. 1. The next four qubits are used as ancilla qubits to measure the four stabilizers after which four measurement outcomes (x1, x2, x3, x4) are obtained. There are 16 possible measurement outcomes which are in a one to one correspondence with the 16 possible errors that might occur [counting the outcome (0, 0, 0, 0) as a trivial error]. In Table 1 we list all possible measurement outcomes and the corresponding single qubit errors. We call the implementation of the circuit and performing the measurement step a cycle, which is shown in Fig. 1. If one goes through a cycle and a single error occurs on any of the first 5 qubits, this might be reflected in the measurement result and thus detected. But instead suppose that no errors occur on the data qubits but right before the measurement step a bit-flip error occurs on the first syndrome qubit, giving the measurement outcome of (1, 0, 0, 0). An incorrect interpretation of the result would be to conclude that one of the 16 possible errors on the data qubits has occurred, whereas in fact the fault lies with a syndrome qubit. We therefore require a protocol that is tolerant to a single syndrome-qubit (or readout) error. To this end, we note that for errors uncorrelated in time, it is likely that after readout and re-initialization that the syndrome qubit will return to its original “faithful” state at the end of the next cycle. The procedure followed in our simulations is therefore the following:

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