# 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)`

to get the gradients, simply add an adjoint

`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.

## Forward mode AD engine (Faithful gradient)

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 = 2*Re(∂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_back`

— Method`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_back`

— Method`mat_back([::Type{T}, ]block::AbstractBlock, adjm::AbstractMatrix) -> Vector`

The backward function of `mat`

. Returns the gradients of parameters.

`YaoBlocks.AD.projection`

— Method`projection(y::AbstractMatrix, op::AbstractMatrix) -> typeof(y)`

Project `op`

to sparse matrix with same sparsity as `y`

.

`YaoBlocks.AD.generator`

— Method`generator(rot::Rotor) -> AbstractBlock`

Return the generator of rotation block.

`YaoBlocks.AD.rotgrad`

— MethodThe matrix gradient of a rotation block.