mm.lab_dev.wires.Wires

class mrmustard.lab_dev.wires.Wires(modes_out_bra=None, modes_in_bra=None, modes_out_ket=None, modes_in_ket=None)

Bases: object

A class with wire functionality for tensor network applications.

In MrMustard, instances of CircuitComponent have a Wires attribute. The wires describe how they connect with the surrounding components in a tensor network picture, where states flow from left to right. CircuitComponents can have wires on the bra and/or on the ket side. Here are some examples for the types of components available on mrmustard.lab_dev:

A channel acting on mode ``1`` has input and output wires on both ket and bra sides:

┌──────┐   1  ╔═════════╗   1  ┌───────┐
│Bra in│─────▶║         ║─────▶│Bra out│
└──────┘      ║ Channel ║      └───────┘
┌──────┐   1  ║         ║   1  ┌───────┐
│Ket in│─────▶║         ║─────▶│Ket out│
└──────┘      ╚═════════╝      └───────┘


A unitary acting on mode ``2`` has input and output wires on the ket side:

┌──────┐   2  ╔═════════╗   2  ┌───────┐
│Ket in│─────▶║ Unitary ║─────▶│Ket out│
└──────┘      ╚═════════╝      └───────┘


A density matrix representing the state of mode ``0`` has only output wires:

                ╔═════════╗   0  ┌───────┐
                ║         ║─────▶│Bra out│
                ║ Density ║      └───────┘
                ║ Matrix  ║   0  ┌───────┐
                ║         ║─────▶│Ket out│
                ╚═════════╝      └───────┘


Also a ket representing the state of mode ``1`` has only output wires:

                ╔═════════╗   1  ┌───────┐
                ║   Ket   ║─────▶│Ket out│
                ╚═════════╝      └───────┘

The Wires class can then be used to create subsets of wires:

>>> from mrmustard.lab_dev.wires import Wires

>>> modes_out_bra={0, 1}
>>> modes_in_bra={1, 2}
>>> modes_out_ket={0, 13}
>>> modes_in_ket={1, 2, 13}
>>> w = Wires(modes_out_bra, modes_in_bra, modes_out_ket, modes_in_ket)

>>> # all the modes
>>> modes = w.modes
>>> assert w.modes == {0, 1, 2, 13}

>>> # input/output modes
>>> assert w.input.modes == {1, 2, 13}
>>> assert w.output.modes == {0, 1, 13}

>>> # get ket/bra modes
>>> assert w.ket.modes == {0, 1, 2, 13}
>>> assert w.bra.modes == {0, 1, 2}

>>> # combined subsets
>>> assert w.output.ket.modes == {0, 13}
>>> assert w.input.bra.modes == {1, 2}

Here’s a diagram of the original Wires object in the example above, with the indices of the wires (the number in parenthesis) given in the “standard” order (bra_out, bra_in, ket_out, ket_in, and the modes in sorted increasing order):

              ╔═════════╗
 1 (2) ─────▶ ║         ║─────▶ 0 (0)
 2 (3) ─────▶ ║         ║─────▶ 1 (1)
              ║         ║
              ║  ``Wires``  ║
 1 (6) ─────▶ ║         ║
 2 (7) ─────▶ ║         ║─────▶ 0 (4)
13 (8) ─────▶ ║         ║─────▶ 13 (5)
              ╚═════════╝

To access the index of a subset of wires in standard order we can use the indices property:

>>> assert w.indices == (0,1,2,3,4,5,6,7,8)
>>> assert w.input.indices == (2,3,6,7,8)

Another important application of the Wires class is to contract the wires of two components. This is done using the @ operator. The result is a new Wires object that combines the wires of the two components. Here’s an example of a contraction of a single-mode density matrix going into a single-mode channel:

>>> rho = Wires(modes_out_bra={0}, modes_in_bra={0})
>>> Phi = Wires(modes_out_bra={0}, modes_in_bra={0}, modes_out_ket={0}, modes_in_ket={0})
>>> rho_out, perm = rho @ Phi
>>> assert rho_out.modes == {0}

Here’s a diagram of the result of the contraction:

╔═══════╗      ╔═══════╗
║       ║─────▶║       ║─────▶ 0
║  rho  ║      ║  Phi  ║
║       ║─────▶║       ║─────▶ 0
╚═══════╝      ╚═══════╝

The permutation that takes the contracted representations to the standard order is also returned.

Parameters:

• modes_out_bra (Optional[set[int]]) – The output modes on the bra side.

• modes_in_bra (Optional[set[int]]) – The input modes on the bra side.

• modes_out_ket (Optional[set[int]]) – The output modes on the ket side.

• modes_in_ket (Optional[set[int]]) – The input modes on the ket side.

Attributes

adjoint	New Wires object obtained by swapping ket and bra wires.
bra	New Wires object without ket wires.
dual	New Wires object obtained by swapping input and output wires.
id	A numerical identifier for this Wires object.
ids	A list of numerical identifier for the wires in this Wires object, in the standard order.
ids_dicts	A list of dictionary mapping modes to ids, one for each of the subsets (output.bra, input.bra, output.ket, and input.ket).
index_dicts	A list of dictionary mapping modes to indices, one for each of the subsets (output.bra, input.bra, output.ket, and input.ket).
indices	The array of indices of this Wires in the standard order.
input	New Wires object without output wires.
ket	New Wires object without bra wires.
modes	The modes spanned by the wires.
original	The parent wire, if any.
output	New Wires object without input wires.
sorted_args	The sorted arguments.

adjoint

New Wires object obtained by swapping ket and bra wires.

bra

New Wires object without ket wires.

dual

New Wires object obtained by swapping input and output wires.

id

A numerical identifier for this Wires object.

The id are random and unique, and are preserved when taking subsets.

ids

A list of numerical identifier for the wires in this Wires object, in the standard order.

The ids are derived incrementally from the id and are unique.

>>> w = Wires(modes_in_ket = {0,1}, modes_out_ket = {0,1})
>>> id = w.id
>>> ids = w.ids
>>> assert ids == [id, id+1, id+2, id+3]

ids_dicts

A list of dictionary mapping modes to ids, one for each of the subsets (output.bra, input.bra, output.ket, and input.ket).

If subsets are taken, ids_dicts refers to the parent object rather than to the child.

index_dicts

A list of dictionary mapping modes to indices, one for each of the subsets (output.bra, input.bra, output.ket, and input.ket).

If subsets are taken, index_dicts refers to the parent object rather than to the child.

indices

The array of indices of this Wires in the standard order. When a subset is selected (e.g. .ket), it doesn’t include wires that do not belong to the subset, but it still counts them because indices refer to the original modes.

>>> w = Wires(modes_in_ket = {0,1}, modes_out_ket = {0,1})
>>> assert w.indices == (0,1,2,3)
>>> assert w.input.indices == (2,3)

input

New Wires object without output wires.

ket

New Wires object without bra wires.

modes

The modes spanned by the wires.

original

The parent wire, if any.

output

New Wires object without input wires.

sorted_args

The sorted arguments. Allows to sort them only once.

code/api/mrmustard.lab_dev.wires.Wires

 

Download Python script

 

Download Notebook

 

View on GitHub