Coherent Variational Quantum Linear Solver

PennyLane Help
1

Hello,

I have a question about the coherent VQLS method. Since CA1, CA2,…CAL is arranged in series in the Hadamard test circuit. Does it mean the training circuit will become extremely high depth if L is large? Will this impact the potential of VQLS to be implemented on the real machines?

2

Hi @Dobby!
Thank you for your question! We’re taking a look with the team and we’ll be back soon with an answer!

3

Also tagging @andreamari who is the author of this great demo you are referring to!

4

Hi @Dobby,

You are right, in a VQLS the assumption is that “L is not too large”. Basically one cannot apply a VQLS to a generic matrix A, but only to a matrix A that can be written as a linear combination of a small number of circuits.

Note: even in this case, this is still quite hard to implement on current quantum computers since each CA_j is a controlled-unitary. General controlled-circuits are very hard to implement experimentally.