deltakit.explorer.codes.BivariateBicycleCode

class deltakit.explorer.codes.BivariateBicycleCode(param_l: int, param_m: int, m_A_powers: list[int], m_B_powers: list[int], validate: bool = True, check_logical_operators_are_independent: bool = False)

Bases: CSSCode

Class to represent the IBM Bivariate Bicycle qLDPC codes, as specified in arXiv:2308.07915. If validate=True, will check a series of conditions as the code is constructed to validate that the produced code is a valid BB code.

Parameters:

• param_l (int) – The parameter l, used to construct a code of length n = 2lm.

• param_m (int) – The parameter m, used to construct a code of length n = 2lm.

• m_A_powers (List[int]) – The powers of the polynomial terms used to construct the matrix A. Each polynomial is of the form x^a + y^b + y^c so the sequence should specify [a, b, c].

• m_B_powers (List[int]) – The powers of the polynomial terms used to construct the matrix B. Each polynomial is of the form y^a + x^b + x^c so the sequence should specify [a, b, c].

• validate (bool, Optional) – If True, will perform a series of check on the code’s parameters to ensure the constructed code is a valid BB code. By default, True.

• check_logical_operators_are_independent (bool, optional) – Whether to check if logical X-Z operator pairs are independent. If True, then the commuting relations [X_k, Z_l] = 0 (k != l) are checked for the logical operators, ensuring that the logical operators correspond to separate logical qubits. If False, this check is ignored, in which case the logical operators can be dependent, e.g. instead of only accepting X_1, X_2 and Z_1, Z_2, the input X_1, X_1*X_2 and Z_1, Z_1*Z_2 is also accepted. Note this is forced to False if validate is False. By default, False.

n

The parameter n as in the [[n,k,d]] specification of an error-correcting code. E.g, number of physical qubits.

Type:

int

k

The parameter n as in the [[n,k,d]] specification of an error-correcting code. E.g, number of logical qubits.

Type:

int

m_x

A binary matrix representing the matrix x in the paper. Used to construct matrices A and B for constructing the parity check matrices.

Type:

npt.NDArray[np.int_]

m_y

A binary matrix representing the matrix y in the paper. Used to construct matrices A and B for constructing the parity check matrices.

Type:

npt.NDArray[np.int_]

m_A_submatrices

A length-3 tuple containing the submatrices A1, A2 and A3 of A. Used to calculate stabilisers.

Type:

Tuple[npt.NDArray[np.int_], npt.NDArray[np.int_], npt.NDArray[np.int_]]

m_B_submatrices

A length-3 tuple containing the submatrices B1, B2 and B3 of B. Used to calculate stabilisers.

Type:

Tuple[npt.NDArray[np.int_], npt.NDArray[np.int_], npt.NDArray[np.int_]]

m_Hx

Parity check matrix for X checks.

Type:

npt.NDArray[np.int_]

m_Hz

Parity check matrix for Z checks.

Type:

npt.NDArray[np.int_]

Methods

BivariateBicycleCode.calculate_number_of_logical_qubits	Calculate the maximum number of logical qubits that are encoded into the code by subtracting the rank of Hx and Hz parity matrices from the number of (data) qubits.
BivariateBicycleCode.check_logical_operators_are_independent	Check that the logical operators are independent.
BivariateBicycleCode.encode_logical_pluses	Set up the CSSStage which represents the encoding of a logical \(\ket{+}\dots\ket{+}\)
BivariateBicycleCode.encode_logical_zeroes	Set up the CSSStage which represents the encoding of a logical \(\ket{0}\dots\ket{0}\).
BivariateBicycleCode.from_matrix	Return a CSSCode object with stabilisers that have no ancilla qubits.
BivariateBicycleCode.measure_stabilisers	Set up the CSSStage which represents measuring the stabilisers for num_rounds rounds.
BivariateBicycleCode.measure_x_logicals	Set up the CSSStage which represents measuring all logical X operators simultaneously.
BivariateBicycleCode.measure_z_logicals	Set up the CSSStage which represents measuring all logical Z operators simultaneously.
BivariateBicycleCode.overwrite_logicals	Method to allow for updating both X and Z logicals simultaneously.
BivariateBicycleCode.x_and_z_operators_commute	Compute whether an X-type stabiliser commutes with a Z-type stabiliser.