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@@ -25,3 +25,5 @@ Manifest.toml | |
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| # Vi/Vim backup files | ||
| .*.swp | ||
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| .DS_Store | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,52 @@ | ||
| using ITensors, ITensorMPS | ||
| using Zygote | ||
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| s = siteind("Qubit") | ||
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| f(x) = op("Ry", s; θ=x)[1, 1] | ||
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| x = 0.2 | ||
| @show f(x), cos(x / 2) | ||
| @show f'(x), -sin(x / 2) / 2 | ||
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| # Simple gate optimization | ||
| ψ0 = state(s, "0") | ||
| ψp = state(s, "+") | ||
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| function loss(x) | ||
| U = op("Ry", s; θ=x) | ||
| Uψ0 = replaceprime(U * ψ0, 1 => 0) | ||
| return -(dag(ψp) * Uψ0)[] | ||
| end | ||
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| # Extremely simple gradient descent implementation, | ||
| # where gradients are computing with automatic differentiation | ||
| # using Zygote. | ||
| function gradient_descent(f, x0; γ, nsteps, grad_tol) | ||
| @show γ, nsteps | ||
| x = x0 | ||
| f_x = f(x) | ||
| ∇f_x = f'(x) | ||
| step = 0 | ||
| @show step, x, f_x, ∇f_x | ||
| for step in 1:nsteps | ||
| x -= γ * ∇f_x | ||
| f_x = f(x) | ||
| ∇f_x = f'(x) | ||
| @show step, x, f_x, ∇f_x | ||
| if norm(∇f_x) ≤ grad_tol | ||
| break | ||
| end | ||
| end | ||
| return x, f_x, ∇f_x | ||
| end | ||
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| x0 = 0 | ||
| γ = 2.0 # Learning rate | ||
| nsteps = 30 # Number of steps of gradient descent | ||
| grad_tol = 1e-4 # Stop if gradient falls below this value | ||
| x, loss_x, ∇loss_x = gradient_descent(loss, x0; γ=γ, nsteps=nsteps, grad_tol=grad_tol) | ||
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| @show x0, loss(x0) | ||
| @show x, loss(x) | ||
| @show π / 2, loss(π / 2) |
65 changes: 65 additions & 0 deletions
65
examples/autodiff/circuit_optimization/state_preparation.jl
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| using ITensors, ITensorMPS | ||
| using OptimKit | ||
| using Random | ||
| using Zygote | ||
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| nsites = 20 # Number of sites | ||
| nlayers = 3 # Layers of gates in the ansatz | ||
| gradtol = 1e-4 # Tolerance for stopping gradient descent | ||
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| # A layer of the circuit we want to optimize | ||
| function layer(nsites, θ⃗) | ||
| RY_layer = [("Ry", (n,), (θ=θ⃗[n],)) for n in 1:nsites] | ||
| CX_layer = [("CX", (n, n + 1)) for n in 1:2:(nsites - 1)] | ||
| return [RY_layer; CX_layer] | ||
| end | ||
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| # The variational circuit we want to optimize | ||
| function variational_circuit(nsites, nlayers, θ⃗) | ||
| range = 1:nsites | ||
| circuit = layer(nsites, θ⃗[range]) | ||
| for n in 1:(nlayers - 1) | ||
| circuit = [circuit; layer(nsites, θ⃗[range .+ n * nsites])] | ||
| end | ||
| return circuit | ||
| end | ||
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| Random.seed!(1234) | ||
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| θ⃗ᵗᵃʳᵍᵉᵗ = 2π * rand(nsites * nlayers) | ||
| 𝒰ᵗᵃʳᵍᵉᵗ = variational_circuit(nsites, nlayers, θ⃗ᵗᵃʳᵍᵉᵗ) | ||
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| s = siteinds("Qubit", nsites) | ||
| Uᵗᵃʳᵍᵉᵗ = ops(𝒰ᵗᵃʳᵍᵉᵗ, s) | ||
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| ψ0 = MPS(s, "0") | ||
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| # Create the random target state | ||
| ψᵗᵃʳᵍᵉᵗ = apply(Uᵗᵃʳᵍᵉᵗ, ψ0; cutoff=1e-8) | ||
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| # | ||
| # The loss function, a function of the gate parameters | ||
| # and implicitly depending on the target state: | ||
| # | ||
| # loss(θ⃗) = -|⟨θ⃗ᵗᵃʳᵍᵉᵗ|U(θ⃗)|0⟩|² = -|⟨θ⃗ᵗᵃʳᵍᵉᵗ|θ⃗⟩|² | ||
| # | ||
| function loss(θ⃗) | ||
| nsites = length(ψ0) | ||
| s = siteinds(ψ0) | ||
| 𝒰θ⃗ = variational_circuit(nsites, nlayers, θ⃗) | ||
| Uθ⃗ = ops(𝒰θ⃗, s) | ||
| ψθ⃗ = apply(Uθ⃗, ψ0) | ||
| return -abs(inner(ψᵗᵃʳᵍᵉᵗ, ψθ⃗))^2 | ||
| end | ||
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| θ⃗₀ = randn!(copy(θ⃗ᵗᵃʳᵍᵉᵗ)) | ||
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| @show loss(θ⃗₀), loss(θ⃗ᵗᵃʳᵍᵉᵗ) | ||
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| loss_∇loss(x) = (loss(x), convert(Vector, loss'(x))) | ||
| algorithm = LBFGS(; gradtol=gradtol, verbosity=2) | ||
| θ⃗ₒₚₜ, lossₒₚₜ, ∇lossₒₚₜ, numfg, normgradhistory = optimize(loss_∇loss, θ⃗₀, algorithm) | ||
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| @show loss(θ⃗ₒₚₜ), loss(θ⃗ᵗᵃʳᵍᵉᵗ) | ||
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| nothing |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,81 @@ | ||
| using ITensors, ITensorMPS | ||
| using OptimKit | ||
| using Random | ||
| using Zygote | ||
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| nsites = 4 # Number of sites | ||
| nlayers = 2 # Layers of gates in the ansatz | ||
| gradtol = 1e-4 # Tolerance for stopping gradient descent | ||
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| # The Hamiltonian we are minimizing | ||
| function ising_hamiltonian(nsites; h) | ||
| ℋ = OpSum() | ||
| for j in 1:(nsites - 1) | ||
| ℋ -= 1, "Z", j, "Z", j + 1 | ||
| end | ||
| for j in 1:nsites | ||
| ℋ += h, "X", j | ||
| end | ||
| return ℋ | ||
| end | ||
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| # A layer of the circuit we want to optimize | ||
| function layer(nsites, θ⃗) | ||
| RY_layer = [("Ry", (n,), (θ=θ⃗[n],)) for n in 1:nsites] | ||
| CX_layer = [("CX", (n, n + 1)) for n in 1:2:(nsites - 1)] | ||
| return [RY_layer; CX_layer] | ||
| end | ||
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| # The variational circuit we want to optimize | ||
| function variational_circuit(nsites, nlayers, θ⃗) | ||
| range = 1:nsites | ||
| circuit = layer(nsites, θ⃗[range]) | ||
| for n in 1:(nlayers - 1) | ||
| circuit = [circuit; layer(nsites, θ⃗[range .+ n * nsites])] | ||
| end | ||
| return circuit | ||
| end | ||
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| s = siteinds("Qubit", nsites) | ||
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| h = 1.3 | ||
| ℋ = ising_hamiltonian(nsites; h=h) | ||
| H = MPO(ℋ, s) | ||
| ψ0 = MPS(s, "0") | ||
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| # | ||
| # The loss function, a function of the gate parameters | ||
| # and implicitly depending on the Hamiltonian and state: | ||
| # | ||
| # loss(θ⃗) = ⟨0|U(θ⃗)† H U(θ⃗)|0⟩ = ⟨θ⃗|H|θ⃗⟩ | ||
| # | ||
| function loss(θ⃗) | ||
| nsites = length(ψ0) | ||
| s = siteinds(ψ0) | ||
| 𝒰θ⃗ = variational_circuit(nsites, nlayers, θ⃗) | ||
| Uθ⃗ = ops(𝒰θ⃗, s) | ||
| ψθ⃗ = apply(Uθ⃗, ψ0; cutoff=1e-8) | ||
| return inner(ψθ⃗, H, ψθ⃗; cutoff=1e-8) | ||
| end | ||
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| Random.seed!(1234) | ||
| θ⃗₀ = 2π * rand(nsites * nlayers) | ||
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| @show loss(θ⃗₀) | ||
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| println("\nOptimize circuit with gradient optimization") | ||
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| loss_∇loss(x) = (loss(x), convert(Vector, loss'(x))) | ||
| algorithm = LBFGS(; gradtol=1e-3, verbosity=2) | ||
| θ⃗ₒₚₜ, lossₒₚₜ, ∇lossₒₚₜ, numfg, normgradhistory = optimize(loss_∇loss, θ⃗₀, algorithm) | ||
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| @show loss(θ⃗ₒₚₜ) | ||
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| println("\nRun DMRG as a comparison") | ||
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| e_dmrg, ψ_dmrg = dmrg(H, ψ0; nsweeps=5, maxdim=10) | ||
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| println("\nCompare variational circuit energy to DMRG energy") | ||
| @show loss(θ⃗ₒₚₜ), e_dmrg | ||
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| nothing |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,49 @@ | ||
| using ITensors, ITensorMPS | ||
| using OptimKit | ||
| using Zygote | ||
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| function ising(n; J, h) | ||
| os = OpSum() | ||
| for j in 1:(n - 1) | ||
| os -= J, "Z", j, "Z", j + 1 | ||
| end | ||
| for j in 1:n | ||
| os -= h, "X", j | ||
| end | ||
| return os | ||
| end | ||
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| function loss(H, ψ) | ||
| n = length(ψ) | ||
| ψHψ = ITensor(1.0) | ||
| ψψ = ITensor(1.0) | ||
| for j in 1:n | ||
| ψHψ = ψHψ * dag(ψ[j]') * H[j] * ψ[j] | ||
| ψψ = ψψ * replaceinds(dag(ψ[j]'), s[j]' => s[j]) * ψ[j] | ||
| end | ||
| return ψHψ[] / ψψ[] | ||
| end | ||
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| n = 10 | ||
| s = siteinds("S=1/2", n) | ||
| J = 1.0 | ||
| h = 0.5 | ||
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| # Loss function only works with `Vector{ITensor}`, | ||
| # extract with `ITensors.data`. | ||
| ψ0 = ITensors.data(random_mps(s; linkdims=10)) | ||
| H = ITensors.data(MPO(ising(n; J, h), s)) | ||
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| loss(ψ) = loss(H, ψ) | ||
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| optimizer = LBFGS(; maxiter=25, verbosity=2) | ||
| function loss_and_grad(x) | ||
| y, (∇,) = withgradient(loss, x) | ||
| return y, ∇ | ||
| end | ||
| ψ, fs, gs, niter, normgradhistory = optimize(loss_and_grad, ψ0, optimizer) | ||
| Edmrg, ψdmrg = dmrg(MPO(H), MPS(ψ0); nsweeps=10, cutoff=1e-8) | ||
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| @show loss(ψ0), norm(loss'(ψ0)) | ||
| @show loss(ψ), norm(loss'(ψ)) | ||
| @show loss(ITensors.data(ψdmrg)), norm(loss'(ITensors.data(ψdmrg))) |
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