Known restrictions

Expectation values of higher order observables

So far, FLOYao only supports expectation values of observables that are sums of squares of Majorana operators. But in general, one can use Wick's theorem to calculate the expectation values of expressions of the form

\[ ⟨O⟩ = ⟨Ω|U^† O U|Ω⟩\]

where $|Ω⟩ = |0 ⋯ 0⟩$ is the all zero state, $O$ a string of Majorana operators and $U$ a FLO unitary. Thus, using linearity of the expectation value, it is possible to efficiently calculate the expectation value of any observable that can be expanded in a sum of polynomially (in the number of qubits) many products of Majorana operators. (See also Classical simulation of noninteracting-fermion quantum circuits again for details). If you need expectation values of higher order (in the number of Majorana operators involved) observables, feel free to open a pull request!

"Hidden" FLO circuits

Yao.jl allows to express the same circuit in different forms. E.g. 

chain(nq, put(1 => X), put(2 => X))

and

kron(nq, 1 => X, 2 => X)

represent the same FLO circuit, but only the latter will be recognised as such. Similarly 

kron(nq, 1 => X, 2 => X, 3 => X, 4 => X)

and

chain(nq, kron(1 => X, 2 => X), kron(3 => X, 4 => X))

represent the same FLO circuit but only the latter will be recognised as such. This is because

  • We don't check if a whole ChainBlock is a FLO circuit, even if its single gates are not. Instead a ChainBlock is applied gate by gate, each of which has to be a FLO gate.
  • For KronBlocks we first try if each factor is a FLO gate and then if the whole block altogether is of the form kron(nq, i => σ1, i+1 => Z, ⋯, i-1 => Z, j => σ2) with σ1, σ2 ∈ [X, Y].

If you run into a case that is a FLO circuit / gate but not recognised as such please open an issue or even pull request.