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| include("yao_types.jl") |
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| using LinearAlgebra |
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| struct StateVector |
| n_qubits::Int |
| amplitudes::Vector{ComplexF64} |
| end |
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| function StateVector(n_qubits::Int) |
| amps = zeros(ComplexF64, 2^n_qubits) |
| amps[1] = 1.0 + 0.0im |
| return StateVector(n_qubits, amps) |
| end |
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| function apply_gate!(sv::StateVector, gate::AbstractBlock, target::Int) |
| mat = gate_matrix(gate) |
| n = sv.n_qubits |
| dim = 2^n |
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| for i in 0:dim-1 |
| if (i >> target) & 1 == 0 |
| j = i | (1 << target) |
| a0 = sv.amplitudes[i+1] |
| a1 = sv.amplitudes[j+1] |
| sv.amplitudes[i+1] = mat[1,1] * a0 + mat[1,2] * a1 |
| sv.amplitudes[j+1] = mat[2,1] * a0 + mat[2,2] * a1 |
| end |
| end |
| end |
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| function apply_controlled!(sv::StateVector, gate::AbstractBlock, control::Int, target::Int) |
| mat = gate_matrix(gate) |
| n = sv.n_qubits |
| dim = 2^n |
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| for i in 0:dim-1 |
| if ((i >> control) & 1 == 1) && ((i >> target) & 1 == 0) |
| j = i | (1 << target) |
| a0 = sv.amplitudes[i+1] |
| a1 = sv.amplitudes[j+1] |
| sv.amplitudes[i+1] = mat[1,1] * a0 + mat[1,2] * a1 |
| sv.amplitudes[j+1] = mat[2,1] * a0 + mat[2,2] * a1 |
| end |
| end |
| end |
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| function gate_matrix(::H) |
| s = 1.0/sqrt(2.0) |
| ComplexF64[s s; s -s] |
| end |
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| function gate_matrix(::X) |
| ComplexF64[0 1; 1 0] |
| end |
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| function gate_matrix(::Y) |
| ComplexF64[0 -im; im 0] |
| end |
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| function gate_matrix(::Z) |
| ComplexF64[1 0; 0 -1] |
| end |
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| function gate_matrix(::S) |
| ComplexF64[1 0; 0 im] |
| end |
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| function gate_matrix(::Sdg) |
| ComplexF64[1 0; 0 -im] |
| end |
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| function gate_matrix(::T) |
| ComplexF64[1 0; 0 exp(im*π/4)] |
| end |
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| function gate_matrix(::Tdg) |
| ComplexF64[1 0; 0 exp(-im*π/4)] |
| end |
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| function gate_matrix(::SX) |
| ComplexF64[(1+im)/2 (1-im)/2; (1-im)/2 (1+im)/2] |
| end |
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| function gate_matrix(g::Rz) |
| θ = g.theta |
| ComplexF64[exp(-im*θ/2) 0; 0 exp(im*θ/2)] |
| end |
|
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| function gate_matrix(g::Ry) |
| θ = g.theta |
| c = cos(θ/2) |
| s = sin(θ/2) |
| ComplexF64[c -s; s c] |
| end |
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| function gate_matrix(g::Rx) |
| θ = g.theta |
| c = cos(θ/2) |
| s = sin(θ/2) |
| ComplexF64[c -im*s; -im*s c] |
| end |
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| function measure_qubit!(sv::StateVector, target::Int)::Int |
| n = sv.n_qubits |
| dim = 2^n |
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| prob_0 = 0.0 |
| for i in 0:dim-1 |
| if (i >> target) & 1 == 0 |
| prob_0 += abs2(sv.amplitudes[i+1]) |
| end |
| end |
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| outcome = rand() < prob_0 ? 0 : 1 |
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| norm_factor = outcome == 0 ? sqrt(prob_0) : sqrt(1.0 - prob_0) |
| for i in 0:dim-1 |
| bit = (i >> target) & 1 |
| if bit == outcome |
| sv.amplitudes[i+1] /= norm_factor |
| else |
| sv.amplitudes[i+1] = 0.0 + 0.0im |
| end |
| end |
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| return outcome |
| end |
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| function fidelity(sv1::StateVector, sv2::StateVector)::Float64 |
| return abs2(dot(sv1.amplitudes, sv2.amplitudes)) |
| end |
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