Symbolic Computation

The symbolic engine of Yao is based on SymEngine.jl. It allows one to define quantum circuits with symbolic parameters and perform symbolic computation on them. Two macro/functions play a key role in the symbolic computation:

• @vars for defining symbolic variables
• subs for substituting symbolic variables with concrete values

julia> using Yao
julia> @vars θ(θ,)
julia> circuit = chain(2, put(1=>H), put(2=>Ry(θ)))nqubits: 2
chain
├─ put on (1)
│  └─ H
└─ put on (2)
   └─ rot(Y, θ)
julia> mat(circuit)4×4 SparseMatrixCSC{Basic, Int64} with 16 stored entries:
 (1/2)*sqrt(2)*cos((1/2)*θ)  …  (-1/2)*sqrt(2)*sin((1/2)*θ)
 (1/2)*sqrt(2)*cos((1/2)*θ)      (1/2)*sqrt(2)*sin((1/2)*θ)
 (1/2)*sqrt(2)*sin((1/2)*θ)      (1/2)*sqrt(2)*cos((1/2)*θ)
 (1/2)*sqrt(2)*sin((1/2)*θ)     (-1/2)*sqrt(2)*cos((1/2)*θ)
julia> new_circuit = subs(circuit, θ=>π/2)nqubits: 2
chain
├─ put on (1)
│  └─ H
└─ put on (2)
   └─ rot(Y, 1.5707963267949)
julia> mat(new_circuit)4×4 SparseMatrixCSC{Basic, Int64} with 16 stored entries:
             0.353553390593274*sqrt(2)  …  (-0.353553390593274 + -0.0*im)*sqrt(2)
             0.353553390593274*sqrt(2)       (0.353553390593274 + 0.0*im)*sqrt(2)
 (0.353553390593274 + -0.0*im)*sqrt(2)                  0.353553390593274*sqrt(2)
 (0.353553390593274 + -0.0*im)*sqrt(2)                 -0.353553390593274*sqrt(2)

API

The following functions are for working with symbolic states.

@ket_str

julia> ket"110" + 2ket"111"
|110⟩ + 2.0|111⟩

julia> ket"100" + ket"111" |> focus!(1:2)
|100⟩ + |111⟩

@bra_str

julia> bra"111" + 2bra"101"
2.0⟨101| + ⟨111|

julia> bra"111" * (ket"101" + ket"111")
1

szero_state(n; nbatch=1)