paulie.common.pauli_string_linear.PauliStringLinear#

class paulie.common.pauli_string_linear.PauliStringLinear(combinations)#

Bases: PauliString

Representation of a linear combination of Pauli string.

adjoint_map(other)#

Compute the adjoint map \(ad_{A}(B) = [A,B]\).

Parameters:

other – Linear combinations for the adjoint map.

Returns:

None if the commutator is zero (i.e., if A and B commute). Otherwise, returns a PauliString proportional to the commutator.

Raises:

PauliStringLinearException – Not implemented

commutes_with(other)#

Check if this Pauli string commutes with another.

Parameters:

other – Linear combinations for checking commutes.

Returns:

True if they commute, False if they anticommute.

copy()#

Copy Linear combination of Pauli strings.

Returns:

Copy of self.

expand(n)#

Increasing the size of the Pauli string by taking the tensor product with identities in the end.

Parameters:

n (int) – New Pauli string length.

Returns:

Pauli string of extend length.

Raises:

PauliStringLinearException – Not implemented

exponential()#

Get the exponential of a linear combination of Pauli strings.

Returns:

Exponential of a linear combination of Pauli strings.

gen_all_pauli_strings()#

Generate a list of Pauli strings that commute with this string.

Yields:

Commutant of the Pauli string

Raises:

PauliStringLinearException – Not implemented

get_anti_commutants(generators=None)#

Get a list of Pauli strings that no-commute with this string.

Parameters:

  • generators – Collection of Pauli strings on which commutant is searched.

  • specified (If not)

  • size. (then the search area is all Pauli strings of the same)

Returns:

List of Pauli strings that no-commute with this string.

Raises:

PauliStringLinearException – Not implemented

get_commutants(generators=None)#

Get a list of linear combinations that commute with this string.

Parameters:

  • generators – Collection of Pauli strings on which commutant is searched.

  • specified (If not)

  • size. (then the search area is all Pauli strings of the same)

Returns:

List of linear combinations that commute with this string.

Raises:

PauliStringLinearException – Not implemented

get_matrix()#

Get matrix representation for Pauli string.

Returns:

Matrix representation for the Pauli string.

get_nested(generators=None)#

Get nested of Pauli string

Parameters:

  • generators – Collection of Pauli strings on which nested is searched.

  • specified (If not)

  • size. (then the search area is all Pauli strings of the same)

Returns:

Nested of Pauli string.

Raises:

PauliStringLinearException – Not implemented

get_size()#

Get the length of the Pauli Strings in this linear combination.

Returns:

Length of the Pauli Strings in this linear combination.

get_substring(start, length=1)#

Get a substring of Paulis inside the Pauli string.

Parameters:

  • start – Index to begin extracting the string.

  • length – Length of each substring.

Returns:

substring of the Pauli string.

Raises:

PauliStringLinearException – Not implemented

property h#

Get the Hermitian conjugate of this linear combination. This is found by taking the complex conjugate of all coefficients, as the Pauli matrices themselves are Hermitian.

Returns:

Hermitian conjugate of this linear combination.

inc()#

Pauli string increment operator.

Returns:

Pauli string whose bit representation is greater than 1.

Raises:

PauliStringLinearException – Not implemented

is_identity()#

Check if this Pauli string is the identity.

Returns:

True if self is the identity.

Raises:

PauliStringLinearException – Not implemented

is_zero()#

Check if the linear combination is effectively zero. This can be done by checking if all coefficients are close to zero.

Returns:

True if the linear combination is zero, False otherwise.

kron(other)#

Kroniker multiplication pauli string on linear combination of Pauli strings.

Parameters:

other – Linear combinations for Kroniker multiplication.

Returns:

Linera combination of PauliString.

multiply(other)#

Multiplication operator of two linear combination of Pauli strings.

Parameters:

other – Linear combinations for multiplication.

Returns:

PauliString proportional to the multiplication.

norm()#

Calculates the Frobenius norm of the coefficient vector. The norm is \(sqrt(∑ |cᵢ|²)\), where cᵢ are the coefficients of the Pauli strings in the linear combination.

Returns:

Frobenius norm of the coefficient vector.

quadratic(basis)#

Computes the quadratic form \(Q_{j} = \sum_{S \in \mathrm{self}} S \otimes (L_{j} * S)\) where self represents the component \(C_{k} = \sum S\), and basis is the linear symmetry \(L_{j}\).

Parameters:

basis – Linear symmetry \(L_{j}\).

Returns:

Linear combination of PauliString.

rkron(other)#

Right Kroniker multiplication pauli string on linear combination of Pauli strings.

Parameters:

other – Linear combinations for right Kroniker multiplication.

Returns:

Linera comination of PauliString.

set_substring(start, pauli_string)#

Set substring starting at position start.

Parameters:

  • start – Index to begin the string.

  • pauli_string – Substring of PauliString.

Returns:

None

Raises:

PauliStringLinearException – Not implemented

simplify()#

Combines terms with the same Pauli string by summing their coefficients. Removes terms with coefficients close to zero. This version assumes the PauliStringLinear object is directly iterable.

Returns:

Linear combination.

tensor(other)#

Tensor product of this linear combination with another.

Parameters:

other – Linear combinations to tensor product.

Returns:

Result of the tensor product self on others.

Raises:

PauliStringLinearException – Not implemented

trace()#

Computes the trace of the operator represented by this linear combination.

The trace is non-zero only if the Identity operator is present in the sum. \(Tr(self) = (\textit{coefficient of Identity}) * 2^{n}\).

Returns:

Complex value of the trace.