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State Overlap

Base.filter! — Method
filter!(filterfunc::Function, psum::PauliSum)

Filter a PauliSum in-place by removing all Pauli strings for which filterfunc(pstr, coeff) returns false.

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Base.filter — Method
filter(filterfunc::Function, psum::PauliSum)

Return a filtered PauliSum by removing all Pauli strings for which filterfunc(pstr, coeff) returns false.

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PauliPropagation.overlapwithcomputational — Method
overlapwithcomputational(psum::PauliSum, onebitinds::Vector{Integer})
overlapwithcomputational(pstr::PauliString, onebitinds::Vector{Integer})

Calculates the overlap of a Pauli sum or Pauli string with the computational basis state which has one-bits at all specified indices and zero-bits elsewhere. If |x><x| is a computational basis state, it we compute Tr[psum * |x><x|] = <x|psum|x> or Tr[pstr * |x><x|] = <x|pstr|x>. For example, overlapwithcomputational(psum, [1,2,4]) returns the overlap with |1101000...>.

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PauliPropagation.overlapwithpaulisum — Method
overlapwithpaulisum(rho::PauliSum, psum::PauliSum)

Calculate the overlap of a Pauli sum psum and a quantum state rho represented in the Pauli basis via another PauliSum. This is equivalent to the trace Tr[rho * psum]. Calls scalarproduct(rho, psum) * (2^rho.nqubits) to calculate the overlap.

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PauliPropagation.overlapwithplus — Method
overlapwithplus(psum::PauliSum) 
overlapwithplus(pstr::PauliString)

Calculates the overlap of a Pauli sum or Pauli string with the plus state |+><+|, i.e. Tr[psum * |+><+|] = <+|psum|+> or Tr[pstr * |+><+|] = <+|pstr|+>.

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PauliPropagation.overlapwithzero — Method
overlapwithzero(psum::PauliSum) 
overlapwithzero(pstr::PauliString)

Calculates the overlap of a Pauli sum with the zero state |0><0|, i.e., Tr[psum * |0><0|] = <0|psum|0> or Tr[pstr * |0><0|] = <0|pstr|0>.

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PauliPropagation.scalarproduct — Method
scalarproduct(pobj1::Union{PauliSum,PauliString}, pobj2::Union{PauliSum,PauliString})

Calculates the scalar product between any combination of PauliSum and PauliString. This calculates the sum of the products of their coefficients for all Pauli strings that are present . Important: This is not equivalent to the trace Tr[psum1 * psum2] but instead Tr[psum1 * psum2]/2^n, and equivalently for Pauli strings.

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