QECScheme

qualtran.surface_code.QECScheme

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A model of the error-correction scheme used to suppress errors

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Main aliases

`qualtran.surface_code.qec_scheme.QECScheme`

qualtran.surface_code.QECScheme(
    error_rate_scaler, error_rate_threshold
)

This class primarily provides a formula for estimating the logical error rate given code parameters (i.e. the distance) and a physical error rate. The class attributes parameterize this formula.

This class also provides the formula for computing the number of physical qubits required to store one logical qubit.

The logical error rate as a function of code distance \(d\) and physical error rate \(p\) is given by

\[ a \left ( \frac{p}{p^*} \right )^\frac{d + 1}{2} \]

Where \(a\) is the error_rate_scaler and \(p^*\) is the error_rate_threshold.

Note: The logical error-suppression factor \(\Lambda = \frac{p^*}{p}\)

Attributes

error_rate_scaler

Logical error rate coefficient.

error_rate_threshold

Logical error rate threshold.

Methods

logical_error_rate

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logical_error_rate(
    code_distance: int, physical_error: float
) -> float

Logical error suppressed with code distance for this physical error rate.

This is an estimate, see the references section.

The formula was originally expressed as \(p_l = a (b * p_p)^((d+1)/2)\) physical error rate \(p_p\) and parameters \(a\) and \(b\). This can alternatively be expressed with \(p_th = (1/b)\) roughly corresponding to the code threshold. This is sometimes also expressed with \(lambda = p_th / p_p\). A lambda of 10, for example, would be p_p = 1e-3 and p_th = 0.01. The pre-factor \(a\) has no clear provenance.

References

Note

this doesn’t actually contain the formula from the above reference.

code_distance_from_budget

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code_distance_from_budget(
    physical_error: float, budget: float
) -> int

Get the code distance that keeps one below the logical error budget.

physical_qubits

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@abc.abstractmethod
physical_qubits(
    code_distance: int
) -> int

The number of physical qubits per logical qubit used by the error detection circuit.

make_gidney_fowler

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@classmethod
make_gidney_fowler()

The qec scheme parameters considered in the Gidney/Fowler set of references.

References

make_beverland_et_al

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@classmethod
make_beverland_et_al()

The qec scheme parameters considered in Beverland et al. reference.

References

__ne__

__ne__(
    other
)

Check equality and either forward a NotImplemented or return the result negated.

__eq__

__eq__(
    other
)

Method generated by attrs for class QECScheme.