# Automatic Differentiation

Yao currently contains builtin automatic differentiation engine (an operator overloading based) especially for quantum circuits. It uses the reversible context of quantum computation to optimize the performance during simulation, thus you may find this is way faster than any other AD engine at the moment.

## Builtin Reverse mode AD engine for simulation

As for expectation, the usage is pretty simple, since the evluation of expectations are just

expect(H, rand_state(10)=>circuit)

expect'(H, rand_state(10)=>circuit)

which will return the pair of gradients, one is the gradient of input register and the other is the gradient of circuit parameters.

The faithful gradient is supported via an external package YaoExtensions, this packages contains some useful extensions to make things work out of the box.

## Integration with General purpose AD engine

The builtin AD engine for Yao only provides the differentiation of quantum circuits, but you can plug it into a general AD engine, such as Zygote by defining your own adjoints, or include this patch.

## APIs

YaoBlocks.AD.apply_back!Method
apply_back!((ψ, ∂L/∂ψ*), circuit::AbstractBlock, collector) -> AbstractRegister

back propagate and calculate the gradient ∂L/∂θ = 2Re(∂L/∂ψ⋅∂ψ/∂θ), given ∂L/∂ψ. ψ is the output register, ∂L/∂ψ* should also be register type.

Note: gradients are stored in Diff blocks, it can be access by either diffblock.grad or gradient(circuit). Note2: now apply_back! returns the inversed gradient!

YaoBlocks.AD.apply_backMethod
apply_back(st::Tuple{<:ArrayReg, <:ArrayReg}, block::AbstractBlock; kwargs...) -> (out, outδ), paramsδ

The backward function of apply!. Returns a tuple of ((input register, gradient of input register), parameter gradients)

YaoBlocks.AD.mat_backMethod
mat_back([::Type{T}, ]block::AbstractBlock, adjm::AbstractMatrix) -> Vector

The backward function of mat. Returns the gradients of parameters.

YaoBlocks.AD.projectionMethod
projection(y::AbstractMatrix, op::AbstractMatrix) -> typeof(y)

Project op to sparse matrix with same sparsity as y.