peropq.pauli_bitstring¶

Classes¶

PauliString

Class representing efficiently Pauli matrices as bitstrings.

Functions¶

`pauli_from_string`(string, length[, start_qubit, ...])	Get an instance of PauliString from a string.
`_get_non_identity_indices`(bit_string)	Get the non identity indices.
`_get_i_power`(bit_string1, bit_string2)	Get the right power for the multiplication, i.e. (1j)^power.
`_pauli_string_mult`(pauli_string1, pauli_string2)	Multiply two bitstrings.
`bit_string_commutation`(bit_string1, bit_string2)	Return whether two bitstrings representing pauli strings commute.

Module Contents¶

class peropq.pauli_bitstring.PauliString(bit_string, coefficient=1.0)¶

Class representing efficiently Pauli matrices as bitstrings.

Parameters:

bit_string (numpy.typing.NDArray)
coefficient (complex)

bit_string¶

coefficient¶

__mul__(other)¶

Multiply PauliString with a complex number or PauliString.

Parameters:: other (PauliString | complex)
Return type:: PauliString

__rmul__(other)¶

Multiply PauliString with a complex number or PauliString.

Parameters:: other (complex)
Return type:: PauliString

__eq__(other)¶

Equality for PauliStrings.

Two PauliStrings are equal if their coefficients are equal and if their Paulis are equal on all qubits. The underlying qubit_pauli_maps may differ (in the number of Identities).

Parameters:: other (object)
Return type:: bool

commutes_with(other)¶

Return whether this PauliString commutes with given PauliString.

Parameters:: other (PauliString) – The right side of the Commutator
Returns:: True if PauliStrings commute, False otherwise
Return type:: bool

get_pauli(qubit)¶

Return a string indicating the Pauli matrix associated with the input qubit.

Parameters:: qubit (int)
Return type:: str

normalized_trace()¶

Returns 2^(-n)*Tr(self).

The trace is just the coefficient times the product of the traces of the Paulis over all n qubits (including any identities on qubits not explicitly contained in the qubit_pauli_map). Since Tr(Pauli.I) == 2, and Tr(Pauli.X) == Tr(Pauli.Y) == Tr(Pauli.Z) == 0, the result will either be 0 (if any of the Paulis is not the Identity) or self.coefficient (if all paulis are the identity).

Return type:: complex

peropq.pauli_bitstring.pauli_from_string(string, length, start_qubit=0, coefficient=1.0)¶

Get an instance of PauliString from a string.

Parameters:

string (str) – represents the pauli string
length (int) – legnth of the Pauli string (i.e. number of qubits)
start_qubit (int) – first qubit to place the Pauli on
coefficent – of the Pauli string
coefficient (complex)

Returns:

instace of PauliString corresponding to the input string.

Return type:

PauliString

peropq.pauli_bitstring._get_non_identity_indices(bit_string)¶

Get the non identity indices.

Parameters:: bit_string (numpy.typing.NDArray)
Return type:: numpy.typing.NDArray

peropq.pauli_bitstring._get_i_power(bit_string1, bit_string2)¶

Get the right power for the multiplication, i.e. (1j)^power.

Parameters:

bit_string1 (numpy.typing.NDArray)
bit_string2 (numpy.typing.NDArray)

Return type:

int

peropq.pauli_bitstring._pauli_string_mult(pauli_string1, pauli_string2)¶

Multiply two bitstrings.

Parameters:

pauli_string1 (PauliString)
pauli_string2 (PauliString)

Return type:

PauliString

peropq.pauli_bitstring.bit_string_commutation(bit_string1, bit_string2)¶

Return whether two bitstrings representing pauli strings commute.

Parameters:

bit_string1 (numpy.typing.NDArray) – first bit_string
bit_string2 (numpy.typing.NDArray) – second bit_string

Returns:

True if the two bitstrings commute, False otherwise.

Return type:

bool