[Blocks] Block-focus system

[GiggleLiu]

Block

• A block is a function unit, like Arbituary rotation, Entangler, FFT, Grover search et. al.
• A block contains a list of blocks/gates, thus forming a tree that terminates on gates (leaves).
• A block does not have qubit indices to specify which qubits apply. However, a gate has, its indices are relative to its parent block. Block operation space is specified using the focus system described bellow.

Focus

A wave function is a tensor of order-3, psi(f, r, b).

• f: focused dimensions
• r: remaining dimensions
• b: batch dimension.

All blocks must be applied on the first (focused) dimension. Here, benchmark is needed to optimize the memory structure based.

Focus is a special "gate", users use it to change focused qubits to perform operations, like Focus(4, 0, 1) will change operation basis to lines (4, 0, 1) by index unraveling and permuting, i.e. for a 5-bit system, we will have psi((4, 0, 1), (2, 3), b). After this "gate", all blocks must be size 3, until another focus "gate" applied. Uses can use Focus() to restore the state to default all focus mode.

For un-blocked gates, we don't require the alignment of focused bits and gate operation space.

[Roger-luo]

First, for development related issue, please add a tag like: [Your Topic] in the very beginning of the title. And it would be better to use good first issue label for guideline issues.

IMHO, I still insist to have indexes stored in a block rather than gates. This is because the lack of inheriting in Julia, you cannot inherit members like Python, and this will cause multiple definitions of indexes. Try not to think about a Julia program like Python, and it's better to illustrate practical solution with a minimum working example (MWE) then you will find out this problem...

struct GateX
    indexes
end

struct GateY
    indexes
end

But it seems that packing separated indexes together would be a good solution for reduce memory in-contiguous and decrease cache missing.

[Roger-luo]

As was discussed with @GiggleLiu , this is a rewrite of original blueprint folder to make it more trackable and clear. The Python part is removed, mix python and julia up is quite weired... I will write another issue about parameter cache later. The details will be updated during the development.

Wave function & Register

A quantum register is an abstraction of quantum states processed by quantum circuits. It is an object that contains N qubits, and can be reshaped, permuted.

mutable struct Register{T <: AbstractArray, N}
    data::T
end

A register is actually a wave function in the form Psi(f, r, b), where

• f: concentrated dimensions
• r: remaining dimensions
• b: batched dimensions

Interfaces

Since, all types in julia is duck typed, we will firstly define this framework's structure by defining required functions.

Interface of Gate

type with:

• apply!: apply this gate-like object to a quantum register with certain parameters
  -update!: update this gate-like object (may contain parameters, like rotation gates) with some parameters

will be a subtype of AbstractGate. Besides, there will be several properties (some functions with only one input):

• size: get the size of this gate-like object (how many qubits it will apply to)
• TBD.

Interface of Block

The interface of block is the same with the interface of gates, which means blocks are a kind of gates. We will list extra interfaces in the future.

Types

Basic Gates

Basic gates are building material of circuits, e.g X, Y, Z, Rx, Ry, Rz, etc. It only use the interface of Gates.

Blocks

The following types will use the block interface.

Block

Block are linear operators can be expanded on computational basis. It takes Block-List as its member, thus can be viewed as a tree. It can use the interface of Gates. (which means a block can be treated as a gate)

Concentrator

A Concentrator will permute and expose the legs of a quantum register to other blocks/gates. For instance, given a register of 5 qubits and a Toffli gate on No. 1, 3, 5 qubit, by applying a concentrator of 1,3,5 to the register, No, 1, 3, 5 will be permuted and packed to be contiguous and exposed to next block/gate.

This is needs decision: use Focus or Concentrator as this block's name. I will use concentrator at the moment. Let's make this decision afterwards. However, I will list several reasons about why Concentrator:

1. concentrator means to pack a bunch of lines together in classical circuits
2. the meaning of focus as a noun is about optics which is far from what we are doing here

LeafBlock

LeafBlock is an abstract type for all blocks that do not have children. This may include:

• Algorithmic Blocks: Grover search, etc.
• Gate Blocks, e.g X, Y, etc.

Other Special Blocks

• Measure
• Entangler