Error Correction

The fault-tolerant engine lowers a logical circuit onto a surface-code lattice and estimates its logical error rate under a physical noise model. A typical workflow runs in four stages: initialize a logical noise model from physical noise, route a transpiled Clifford+T circuit onto the lattice, visualize the routed program, and estimate its total error across code distances.

Initialize Logical Noise

LogicalNoise

Logical noise parameters retrieved from the backend, with utility methods to analyze and visualize the noise. Methods:

Name	Description
get_clifford_logical_error	Evaluate the fitted 1-qubit Clifford logical error rate at a code distance.
get_cnot_logical_error	Evaluate the fitted CNOT logical error rate at a code distance.
get_s_logical_error	Evaluate the fitted S gate logical error rate at a code distance.
plot_clifford	Plot the 1-qubit Clifford logical error rates as a function of code distance.
plot_cnot	Plot the CNOT logical error rates as a function of code distance.
plot_s	Plot the S gate logical error rate as a function of code distance.

Attributes:

Name	Type	Description
`params`	`LogicalNoiseParameters`	The stored logical error-rate fits, as returned by the logical noise simulation.

get_clifford_logical_error

get_clifford_logical_error(
self: ,
code_distance: int,
error_type: Literal[‘X’, ‘Z’]
) -> float

Evaluate the fitted 1-qubit Clifford logical error rate at a code distance. The stored fit is p_L(d) = 10 ** (a * cd + b), where (a, b) are the coefficients returned by the simulation for the requested error type. Parameters:

Name	Type	Description	Default
`self`	“		required
`code_distance`	`int`	Code distance `cd` at which to evaluate the fit.	required
`error_type`	`Literal['X', 'Z']`	Which Clifford error curve to evaluate; `"X"` or `"Z"` (case-insensitive).	required

Returns:

Type: float
The logical error rate p_L(d).

get_cnot_logical_error

get_cnot_logical_error(
self: ,
code_distance: int,
error_type: Literal[‘IX’, ‘XI’, ‘XX’, ‘IZ’, ‘ZI’, ‘ZZ’]
) -> float

Evaluate the fitted CNOT logical error rate at a code distance. The stored fit is p_L(d) = 10 ** (a * cd + b), where (a, b) are the coefficients returned by the simulation for the requested Pauli term. Parameters:

Name	Type	Description	Default
`self`	“		required
`code_distance`	`int`	Code distance `cd` at which to evaluate the fit.	required
`error_type`	`Literal['IX', 'XI', 'XX', 'IZ', 'ZI', 'ZZ']`	Which CNOT Pauli-error curve to evaluate; one of `"IX"`, `"XI"`, `"XX"`, `"IZ"`, `"ZI"`, `"ZZ"` (case-insensitive). The first character is the Pauli error on the control qubit and the second is the Pauli error on the target qubit, where `I` denotes no error. For example, `"IX"` is an X error on the target qubit, and `"ZI"` is a Z error on the control qubit.	required

Returns:

Type: float
The logical error rate p_L(d).

get_s_logical_error

get_s_logical_error(
self: ,
code_distance: int
) -> float

Evaluate the fitted S gate logical error rate at a code distance. The stored fit is p_L(d) = 10 ** (a * cd + b), where (a, b) are the coefficients returned by the S gate simulation. Parameters:

Name	Type	Description	Default
`self`	“		required
`code_distance`	`int`	Code distance `cd` at which to evaluate the fit.	required

Returns:

Type: float
The logical error rate p_L(d).

plot_clifford

plot_clifford(
self: ,
start: int = 5,
end: int = 31,
show: bool = True
) -> None

Plot the 1-qubit Clifford logical error rates as a function of code distance. Parameters:

Name	Type	Description	Default
`self`	“		required
`start`	`int`	Lower bound of the code-distance axis.	5
`end`	`int`	Upper bound of the code-distance axis.	31
`show`	`bool`	Whether to call `plt.show()` after building the figure. Set to `False` to keep the figure open for further customization or when rendering in a non-interactive context.	True

plot_cnot

plot_cnot(
self: ,
start: int = 5,
end: int = 31,
show: bool = True
) -> None

Plot the CNOT logical error rates as a function of code distance. Parameters:

Name	Type	Description	Default
`self`	“		required
`start`	`int`	Lower bound of the code-distance axis.	5
`end`	`int`	Upper bound of the code-distance axis.	31
`show`	`bool`	Whether to call `plt.show()` after building the figure. Set to `False` to keep the figure open for further customization or when rendering in a non-interactive context.	True

plot_s

plot_s(
self: ,
start: int = 5,
end: int = 31,
show: bool = True
) -> None

Plot the S gate logical error rate as a function of code distance. Parameters:

Name	Type	Description	Default
`self`	“		required
`start`	`int`	Lower bound of the code-distance axis.	5
`end`	`int`	Upper bound of the code-distance axis.	31
`show`	`bool`	Whether to call `plt.show()` after building the figure. Set to `False` to keep the figure open for further customization or when rendering in a non-interactive context.	True

PhysicalNoiseModel

A description of physical noise on a quantum device. Each list field composes the rules it contains: for example, a clifford_1q field with both a DepolarizeRule and a PauliRule(X) applies both channels after every 1-qubit Clifford operation. Attributes:

Name	Type	Description
`idle`	`list[PhysicalNoiseRule]`
`long_idle`	`list[PhysicalNoiseRule]`
`clifford_1q`	`list[PhysicalNoiseRule]`
`clifford_2q`	`list[PhysicalNoiseRule]`
`measure`	`dict[str, Probability]`
`gates`	`dict[str, list[PhysicalNoiseRule]]`

DepolarizeRule

Applies a uniformly random Pauli error with total probability p. p is the probability that some error occurs; with probability 1-p the identity is applied (no error). For a 1-qubit operation, each of the 3 Pauli errors (X, Y, Z) has probability p/3 of being applied. For a 2-qubit operation, each of the 15 non-identity two-qubit Pauli errors has probability p/15 of being applied. Attributes:

Name	Type	Description
`kind`	`Literal['depolarize']`
`p`	`Probability`

PauliRule

Applies a specific Pauli error selected by pauli with probability p. With probability 1-p the identity is applied (no error). Attributes:

Name	Type	Description
`kind`	`Literal['pauli']`
`pauli`	`Literal['X', 'Y', 'Z']`
`p`	`Probability`

LogicalNoiseParameters

Representation for logical error rates of different gates. Attributes:

Name	Type	Description
`clifford`	`CliffordErrors`
`cnot`	`CnotErrors`
`s`	`LogLinear \| None`
`t`	`dict[int, float]`

Route a Program

TopologicalProgram

A circuit lowered to a 3-D surface-code lattice routing. Attributes:

Name	Type	Description
`layout`	`Layout`
`circuit`	`list[RoutedGate]`
`pipes`	`list[Pipe]`
`stats`	`RoutingStats`

Visualize

Estimate Total Error

Functions

initialize_logical_noise

initialize_logical_noise(
name: str,
noise_model: PhysicalNoiseModel
) -> None

Simulate logical error rates for a physical noise model and store them under name. Runs the logical noise simulation on the backend and persists the resulting LogicalNoiseParameters so they can later be retrieved with get_logical_noise or used by subsequent stages of the engine. This is a long-running operation (interrupting this SDK function will not interrupt the initialization in the backend). Parameters:

Name	Type	Description	Default
`name`	`str`	Identifier to store the resulting logical noise under. Must not already exist for the current user.	required
`noise_model`	PhysicalNoiseModel	Physical noise description to simulate.	required

get_logical_noise

get_logical_noise(
name: str
) -> LogicalNoise

Retrieve previously initialized logical noise parameters. Parameters:

Name	Type	Description	Default
`name`	`str`	Identifier used when calling `initialize_logical_noise`.	required

Returns:

Type: LogicalNoise
The stored parameters wrapped in a LogicalNoise for plotting and
analyzing.

remove_logical_noise

remove_logical_noise(
name: str
) -> None

Delete logical noise parameters stored under name. Parameters:

Name	Type	Description	Default
`name`	`str`	Identifier used when calling `initialize_logical_noise`.	required

route_circuit

route_circuit(
qasm: str
) -> TopologicalProgram

Route a transpiled Clifford+T QASM circuit onto a 3-D surface-code lattice. Parameters:

Name	Type	Description	Default
`qasm`	`str`	Transpiled OpenQASM 2 or 3 source (single-qubit Clifford+T and CX).	required

Returns:

Type: TopologicalProgram
A TopologicalProgram describing the routed lattice: per-gate cube
placements, pipes, and aggregate stats.

view_program

view_program(
program: TopologicalProgram,
output_path: str | Path | None = None,
show: bool = False,
start_cycle: int = 0,
end_cycle: int | None = None
) -> str

Render a routed TopologicalProgram as an interactive HTML visualization. The returned HTML is a self-contained page that can be opened directly in a web browser. Parameters:

Name	Type	Description	Default
`program`	TopologicalProgram	The routed program to visualise.	required
`output_path`	`str \| Path \| None`	If given, also write the HTML to this file.	None
`show`	`bool`	If `True`, display the visualization. In a Jupyter notebook the HTML is embedded inline; otherwise it is opened in a web browser, which requires `output_path` to be set.	False
`start_cycle`	`int`	First cycle (z-layer) to include; cubes below it are hidden. Defaults to 0.	0
`end_cycle`	`int \| None`	Cycle (z-layer) to stop before; cubes at or above it are hidden. Defaults to the program’s total cycle count (show all), but is capped to cycles from `start_cycle` when left unspecified.	None

Returns:

Type: str
The HTML document as a string.

estimate_total_errors

estimate_total_errors(
program: TopologicalProgram,
logical_noise: LogicalNoiseParameters | LogicalNoise | str,
code_distances: Iterable[int]
) -> dict[int, float]

Estimate the routed program’s total error (1 - fidelity) at multiple code distances. Parameters:

Name	Type	Description	Default
`program`	TopologicalProgram	The routed program to evaluate.	required
`logical_noise`	LogicalNoiseParameters \| LogicalNoise \| str	Logical-noise fits to evaluate the per-gate fidelities against. Accepts a `LogicalNoiseParameters` directly, a `LogicalNoise` wrapper (its `params` are used), or a `str` name looked up via `get_logical_noise`.	required
`code_distances`	`Iterable[int]`	Surface-code distances at which to estimate the total error.	required

Returns:

Type: dict[int, float]
A mapping from each requested code distance to the estimated total error.

Providers

Applications

Qmod

Initialize Logical Noise

LogicalNoise

get_clifford_logical_error

get_cnot_logical_error

get_s_logical_error

plot_clifford

plot_cnot

plot_s

PhysicalNoiseModel

DepolarizeRule

PauliRule

LogicalNoiseParameters

Route a Program

TopologicalProgram

Visualize

Estimate Total Error

Functions

initialize_logical_noise

get_logical_noise

remove_logical_noise

route_circuit

view_program

estimate_total_errors

​Initialize Logical Noise

​LogicalNoise

​get_clifford_logical_error

​get_cnot_logical_error

​get_s_logical_error

​plot_clifford

​plot_cnot

​plot_s

​PhysicalNoiseModel

​DepolarizeRule

​PauliRule

​LogicalNoiseParameters

​Route a Program

​TopologicalProgram

​Visualize

​Estimate Total Error

​Functions

​initialize_logical_noise

​get_logical_noise

​remove_logical_noise

​route_circuit

​view_program

​estimate_total_errors

Initialize Logical Noise

LogicalNoise

get_clifford_logical_error

get_cnot_logical_error

get_s_logical_error

plot_clifford

plot_cnot

plot_s

PhysicalNoiseModel

DepolarizeRule

PauliRule

LogicalNoiseParameters

Route a Program

TopologicalProgram

Visualize

Estimate Total Error

Functions

initialize_logical_noise

get_logical_noise

remove_logical_noise

route_circuit

view_program

estimate_total_errors