Remove mps limit custom mps

[LuisAlfredoNu]

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---

Context:
Currently, LT only accepts MPS with the following bond dimensions:

[ [2,2] [2,2,4] [4,2,8] [8,2,16] .... [16,2,8] [8,2,4] [4,2,2] [2,2]]

Which is a limitation of MPSPrep gate because it is not possible to pass custom MPS from other softwares that works with different MPS layouts

Description of the Change:
Remove the checks regarding MPS bond dimension and define the device argument bond_dim to pass the new bond dimension that will be used in the device initializer to allocate the a custom MPS into the GPU.

An example of how to use it:

wires = 4
bond_dims = [5,7,5]

MPS_example = create_MPS_with_custom_bondDims(wires, bond_dims)

dev = qml.device("lightning.tensor", 
                 wires=wires, 
                 bond_dim=bond_dims # New device argument that only accepts a list of n_qubits-1 element 
                 )

dev_wires = dev.wires.tolist()

@qml.qnode(dev)
def circuit(custom_MPS=MPS_example):
    
    qml.MPSPrep(mps=custom_MPS, wires=dev_wires)
    # circuit content 
    # ...
    
    return qml.expval(qml.PauliZ(0))

Benefits:

Possible Drawbacks:
The MPS shape should be symmetric, i.e. [[2,n] [n,2,m] ... [m,2,n] [n,2]]

Related GitHub Issues:
[sc-83835]

[github-actions]

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[multiphaseCFD]

Thanks @LuisAlfredoNu for the nice work!

[multiphaseCFD]

Suggested change

// print MPS_shape_dest and MPS_shape_source

[multiphaseCFD]

Suggested change

	std::cout << "MPS_shape_dest: " << std::endl;
	for (const auto &shape : MPS_shape_dest) {
	for (const auto &dim : shape) {
	std::cout << dim << " ";
	}
	std::cout << std::endl;
	}
	std::cout << "MPS_shape_source: " << std::endl;
	for (const auto &shape : MPS_shape_source) {
	for (const auto &dim : shape) {
	std::cout << dim << " ";
	}
	std::cout << std::endl;
	}

[multiphaseCFD]

Would you please update the docstr to add the new arg?

[multiphaseCFD]

just wondering how max_bond_dim would work in the background if _bond_dim.

[multiphaseCFD]

looks good as long as it works for algo and product. it would be even better to late initialize TN object util MPSprep is called.

[LuisAlfredoNu]

Nice idea, but I am afraid of the potential risk of skipping multiple safety checks because the only way to update the TN object until the call of qml.MPSPrep should be destroy the current MPS and then create a new one with the new bond dims 😕