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NLESC-quantum / quantum_comp

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HHL for calibration #31

Closed NicoRenaud closed 2 years ago

NicoRenaud commented 2 years ago

There is a generic HHL algo implemented in Qiskit. We could use it to see if it could be useful for calibration

NicoRenaud commented 2 years ago

https://github.com/Qiskit/qiskit-terra/blob/main/qiskit/algorithms/linear_solvers/hhl.py

PabRod commented 2 years ago

Some preliminary conclusions:

The more I work on HHL, the more convinced I am that it is not what we need. The qiskit implementation of HHL only allows extracting either <x|x>, the arithmetic average of |x>'s coefficients or <x|B|x>. The last one looks promising, but unfortunately B is not a generic matrix: it has to be a Toeplitz tridiagonal matrix. Other subcases than those seem to be deliberately not implemented, probably because they don't offer any computational advantage compared to other methods.

Furthermore, the whole method is known for not returning a complete solution.

PabRod commented 2 years ago

Task for me: document my conclusions on the HHL readme.

PabRod commented 2 years ago

Managed to run it successfully on the IBMq servers.