# Abstract Registers

Quantum circuits process quantum states. A quantum state being processing by a quantum circuit will be stored on a quantum register. In **Yao** we provide several types for registers. The default type for registers is the `ArrayReg`

which is defined in YaoArrayRegister.jl.

The registers can be extended by subtyping `AbstractRegister`

and define correspinding **register interfaces** defined in YaoBase.jl, which includes:

## Minimal Required Interfaces

The following interfaces are the minial required interfaces to make a register's printing work and be able to accept certain gates/blocks.

But if you don't want to work with our default printing, you could define your custom printing with `Base.show`

.

Missing docstring for `YaoBase.nqubits`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.nactive`

. Check Documenter's build log for details.

you can define `instruct!`

, to provide specialized instructions for the registers from plain storage types.

## Qubit Management Interfaces

Missing docstring for `YaoBase.addbits!`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.reorder!`

. Check Documenter's build log for details.

## Qubit Scope Management Interfaces

### LDT format

Concepturely, a wave function $|\psi\rangle$ can be represented in a low dimentional tensor (LDT) format of order-3, L(f, r, b).

- f: focused (i.e. operational) dimensions
- r: remaining dimensions
- b: batch dimension.

For simplicity, let's ignore batch dimension for the now, we have

\[|\psi\rangle = \sum\limits_{x,y} L(x, y, .) |j\rangle|i\rangle\]

Given a configuration `x`

(in operational space), we want get the i-th bit using `(x<<i) & 0x1`

, which means putting the small end the qubit with smaller index. In this representation `L(x)`

will get return $\langle x|\psi\rangle$.

**Why not the other convension**: Using the convention of putting 1st bit on the big end will need to know the total number of qubits `n`

in order to know such positional information.

### HDT format

Julia storage is column major, if we reshape the wave function to a shape of $2\times2\times ... \times2$ and get the HDT (high dimensional tensor) format representation H, we can use H($x_1, x_2, ..., x_3$) to get $\langle x|\psi\rangle$.

`YaoAPI.focus!`

— Function`focus(f, register, locs...)`

Call a callable `f`

under the context of `focus`

. See also `focus!`

.

**Example**

print the focused register

```
julia> r = ArrayReg(bit"101100")
ArrayReg{1,Complex{Float64},Array...}
active qubits: 6/6
julia> focus(x->(println(x);x), r, 1, 2);
ArrayReg{1,Complex{Float64},Array...}
active qubits: 2/6
```

`focus!(locs...) -> f(register) -> register`

Lazy version of `focus!`

, this returns a lambda which requires a register.

`YaoAPI.relax!`

— Function`relax!(locs::Int...; to_nactive=nqubits(register)) -> f(register) -> register`

Lazy version of `relax!`

, it will be evaluated once you feed a register to its output lambda.

## Measurement Interfaces

Missing docstring for `YaoBase.measure`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.measure!`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.measure_remove!`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.measure_collapseto!`

. Check Documenter's build log for details.

`YaoAPI.select!`

— Function## Others

`YaoAPI.fidelity`

— Function`fidelity(r1::ArrayReg, r2::ArrayReg)`

Calcuate the fidelity between `r1`

and `r2`

, if `r1`

or `r2`

is not pure state (`nactive(r) != nqubits(r)`

), the fidelity is calcuated by purification. See also `pure_state_fidelity`

, `purification_fidelity`

.

`fidelity'(pair_or_reg1, pair_or_reg2) -> (g1, g2)`

Obtain the gradient with respect to registers and circuit parameters. For pair input `ψ=>circuit`

, the returned gradient is a pair of `gψ=>gparams`

, with `gψ`

the gradient of input state and `gparams`

the gradients of circuit parameters. For register input, the return value is a register.

Missing docstring for `YaoBase.tracedist`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.density_matrix`

. Check Documenter's build log for details.

Missing docstring for `YaoBase.viewbatch`

. Check Documenter's build log for details.