qermit.zero_noise_extrapolation

zne.gen_ZNE_MitEx(rebase_pass: pytket._tket.passes.BasePass, noise_scaling_list: List[float], **kwargs)qermit.taskgraph.mitex.MitEx

Generates MitEx object which mitigates for noise using Zero Noise Extrapolation. This is the process by which noise is amplified incrementally, and the zero noise case arrived at by extrapolating backwards. For further explanantion see https://arxiv.org/abs/2005.10921.

Parameters
  • backend (Backend) – Backend on which the circuits are to be run.

  • rebase_pass (BasePass) – BasePass rebasing to the gateset of the backend.

  • noise_scaling_list (List[float]) – A list of the amounts by which the noise should be scaled.

Returns

MitEx object performing noise mitigation by ZNE.

Return type

MitEx

class qermit.zero_noise_extrapolation.zne.Folding(value)

Folding techniques used to increase the noise levels.

Returns

Circuit with gate count increased to scale noise. The unitary implemented by the circuit has not changed.

Return type

Circuit

circuit(noise_scaling: int, **kwargs)pytket._tket.circuit.Circuit

Noise scaling by circuit folding. In this case the folded circuit is of the form \(CC^{-1}CC^{-1}...C\) where \(C\) is the original circuit. As such noise may be scaled by odd integers. The Unitary implemented is unchanged by this process.

Parameters
  • circ (Circuit) – Original circuit to be folded.

  • noise_scaling (int) – Factor by which to scale the noise. This must be an odd integer.

Raises

ValueError – Raised if the amount by which the noise should be scaled is not an odd integer.

Returns

Folded circuit implementing identical unitary to the initial circuit.

Return type

Circuit

gate(noise_scaling: float, **kwargs)pytket._tket.circuit.Circuit

Noise scaling by gate folding. In this case gates \(G\) are replaced at random with \(GG^{-1}G\) until the number of gates is sufficiently scaled.

Parameters
  • circ (Circuit) – Original circuit to be folded.

  • noise_scaling (float) – Factor by which to increase the noise.

Key _allow_approx_fold

Allows for the noise to be increased by an amount close to that requested, as opposed to by exactly the amount requested. This is necessary as there are cases where the exact noise scaling cannot be achieved. This occurs due to the discrete amounts by which the noise can be increased (i.e. the discrete amount by which one gate increases the noise).

Raises

ValueError – Raised if the requested noise scaling cannot be exactly achieved. This can be avoided by appropriately setting _allow_approx_fold.

Returns

Folded circuit implementing identical unitary to the initial circuit.

Return type

Circuit

odd_gate(noise_scaling: int, **kwargs)pytket._tket.circuit.Circuit

Noise scaling by gate folding. In this case odd gates \(G\) are replaced \(GG^{-1}G\) until the number of gates is sufficiently scaled.

Parameters
  • circ (Circuit) – Original circuit to be folded.

  • noise_scaling (float) – Factor by which to increase the noise.

Returns

Folded circuit implementing identical unitary to the initial circuit.

Return type

Circuit

class qermit.zero_noise_extrapolation.zne.Fit(value)

Functions to fit to expectation values as they change with noise.

Returns

Extrapolation of expectation values to the zero noise limit.

Return type

float

cube_root(x: List[float], y: List[float], _show_fit: bool, *args)float

Fit data to a cube root function. This is to say a function of the form \(a + b(x+c)^{1/3}\).

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitted function.

Returns

Extrapolation of data to zero noise limit using the best fitting cube root function.

Return type

float

exponential(x: List[float], y: List[float], _show_fit: bool, *args)float

Fit data to an exponential function. This is to say a function of the form \(a+e^{(b+x)}\). Note that this is a special case of the poly-exponential function.

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitting function.

Returns

Extrapolation to zero noise limit using the best fitting exponential function.

Return type

float

linear(x: List[float], y: List[float], _show_fit: bool, *args)float

Fit data to a linear function. This is to say a function of the form \(ax+b\). Note that this is a special case of the polynomial fitting function.

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitted function.

Returns

Extrapolation to zero noise limit using the best fitting linear function.

Return type

float

poly_exponential(x: List[float], y: List[float], _show_fit: bool, deg: int)float

Fit data to a poly-exponential, which is to say a function of the form \(a+e^{z}\), where \(z\) is a polynomial.

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitted function.

  • deg (int) – The degree of the polynomial in the exponential.

Raises

ValueError – Raised if the degree of the polynomial inputted is negative, or too high to fit to the data.

Returns

Extrapolation of data to the zero noise limit using the best fitting poly-exponential function of the specified degree.

Return type

float

polynomial(x: List[float], y: List[float], _show_fit: bool, deg: int)float

Fit data to a polynomial function.

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitting function.

  • deg (int) – The degree of the function to fit to.

Raises

ValueError – Raised if the degree of the polynomial is negative, or too high to fit the data to.

Returns

Extrapolation to zero noise limit using the best fitting polynomial function of the specified degree.

Return type

float

richardson(x: List[float], y: List[float], _show_fit: bool, *args)float

Use richardson extrapolation. This amounts to fitting to a polynomial of degree one less than the number of data points.

Parameters
  • x (List[float]) – Noise scaling values.

  • y (List[float]) – Expectation values.

  • _show_fit (bool) – Plot data and resulting fitted function.

Returns

Extrapolation to zero noise limit using Richardson extrapolation.

Return type

float

zne.digital_folding_task_gen(rebase_pass: pytket._tket.passes.BasePass, noise_scaling: float, _folding_type: qermit.zero_noise_extrapolation.zne.Folding, _allow_approx_fold: bool)qermit.taskgraph.mittask.MitTask

Generates task transforming a circuit in order to amplify the noise. The noise is increased by a factor noise_scaling using the inputted folding method.

Parameters
  • backend (Backend) – This will be used to compile the circuit after folding to ensure that the gate set matches those available on the backend.

  • rebase_pass (BasePass) – BasePass to rebase circuits to the native gates of backend

  • noise_scaling (float) – The factor by which the noise is increased.

  • _folding_type (Folding) – The means by which the noise should be increased.

  • _allow_approx_fold (bool) – Allows for the noise to be increased by an amount close to that requested, as opposed to by exactly the amount requested. This is necessary as there are cases where the exact noise scaling cannot be achieved. This occurs due to the discrete amounts by which the noise can be increased (i.e. the discrete amount by which one gate increases the noise).

zne.extrapolation_task_gen(_fit_type: qermit.zero_noise_extrapolation.zne.Fit, _show_fit: bool, deg: int)qermit.taskgraph.mittask.MitTask

Generates task extrapolating to the zero noise limit using results from many folded circuits.

Parameters
  • noise_scaling_list (List[float]) – A list of the values by which the noise has been folded.

  • _fit_type (Fit) – The function used to fit to the resulting data.

  • _show_fit (bool) – Plot data and resulting fitted function.

  • deg (int) – The degree of polynomials used.