lcu implementation

[JamesB-1qbit]

This implements the Linear Combination of Unitaries algorithm.
Both the standard form for any operator and the truncated taylor series form are included.

[alexfleury-sb]

I am good with the most of it. Here are some general questions:

• Could get_truncated_taylor_series be in a different file as it seems different vs the LCU?
• Is there any justification for the use of vec = (vecs[:, 0] + vecs[:, 1])/np.sqrt(2) as the initial state in the tests?

[ValentinS4t1qbit]

A few things. Good work, you make solid use of the tangelo objects and numpy, your documentation and flow looks great as well.

[JamesB-1qbit]

I am good with the most of it. Here are some general questions:

• Could get_truncated_taylor_series be in a different file as it seems different vs the LCU?
• Is there any justification for the use of vec = (vecs[:, 0] + vecs[:, 1])/np.sqrt(2) as the initial state in the tests?

• They are both LCU based algorithms. They just use a different encoding for the ancilla qubits.
• No, just something that is not an eigenvector of the Hamiltonian.

[ValentinS4t1qbit]

Good stuff !