Preconditioner not working with HHL_solver

[Cmurilochem]

Hey @koenleijnse, @samuelvanbeek-QAL and @NicoRenaud, I was investigating this issue and came up with another.

So, I was testing with Net0.inp and, after applying our preconditioner to the original linear system, I noticed that the HHL shows difficulties to solve the resulting problem. Interestingly, the original problem (without preconditioning) is solved very efficiently, despite A having a condition number of ~36.

Here is an example with the exact matrices I obtain after preconditioning the original system:

import numpy as np
from scipy.sparse import csc_matrix

from qiskit.primitives import Estimator
from quantum_newton_raphson.hhl_solver import HHL_SOLVER


A = csc_matrix([[1., -0.21697899], [-0.21697899, 1.]])
b = np.array([-4.74931887, 146.99031501])

solver = HHL_SOLVER(estimator=Estimator())
results = solver(A, b)

if np.linalg.norm(A.dot(results.solution) - b) > 0.1:
    print("HHL solution innacurate...")
    print("A @ x:", A.dot(results.solution))
    print("b:", b)

The A matrix looks very good with a condition number of ~1.5. Maybe I am foreseeing something. Do you have any hint as for the reason HHL is not being able to solve it accurately ?
Thanks!

[samuelvanbeek-uva]

Hi Carlos, I was still running the HHL solving test with 100 random matrices for several different matrix sizes. After 99 hours, the job was canceled. Therefore, I now built a limit for the condition number of the matrix to be 10.0 at maximum before trying to solve, since the plots we discussed previously showed that a condition number of e.g. 8.0 could already take a long time. If you say that even with a condition number of 36 it is still able to solve in a feasible amount of time, that is very interesting, and it seems that I already get long durations for a condition number of 10. And of course, it is very strange that after preconditioning it is not solved (accurately/inefficiently), even for a relative low condition number. I have not looked into preconditioning yet and I do not have any suggestion for any clarification unfortunately. I hope I have the results from the test using many random matrices to see the patterns with time vs matrix size, qubits and condition number. Maybe it can provide any hint. Please let me know if there is any other test I can do, I will also have a look into the preconditioning. Best, Samuel

…

________________________________ From: Carlos Murilo Romero Rocha ***@***.***> Sent: 23 September 2024 12:10 To: QuantumApplicationLab/QuantumNewtonRaphson ***@***.***> Cc: Samuel van Beek ***@***.***>; Mention ***@***.***> Subject: [QuantumApplicationLab/QuantumNewtonRaphson] Preconditioner not working with HHL_solver (Issue #18) Hey @koenleijnse<https://github.com/koenleijnse>, @samuelvanbeek-QAL<https://github.com/samuelvanbeek-QAL> and @NicoRenaud<https://github.com/NicoRenaud>, I was investigating this issue and came up with another. So, I was testing with Net0.inp and, after applying our preconditioner to the original linear system, I noticed that the HHL shows difficulties to solve the resulting problem. Interestingly, the original problem (without preconditioning) is solved very efficiently, despite A having a condition number of ~36. Here is an example with the exact matrices I obtain after preconditioning the original system: import numpy as np from scipy.sparse import csc_matrix from qiskit.primitives import Estimator from quantum_newton_raphson.hhl_solver import HHL_SOLVER A = csc_matrix([[1., -0.21697899], [-0.21697899, 1.]]) b = np.array([-4.74931887, 146.99031501]) solver = HHL_SOLVER(estimator=Estimator()) results = solver(A, b) if np.linalg.norm(A.dot(results.solution) - b) > 0.1: print("HHL solution innacurate...") print("A @ x:", A.dot(results.solution)) print("b:", b) The A matrix looks very good with a condition number of ~1.5. Maybe I am foreseeing something. Do you have any hint as for the reason HHL is not being able to solve it accurately ? Thanks! — Reply to this email directly, view it on GitHub<#18>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/BJY2WBO4Q2JBAN2BCUFDWWTZX7SK7AVCNFSM6AAAAABLIIJ6DKVHI2DSMVQWIX3LMV43ASLTON2WKOZSGQZDEOBQGQ3DONQ>. You are receiving this because you were mentioned.

[Cmurilochem]

Thanks @samuelvanbeek-QAL. Absolutely! Thanks for putting lots of efforts to it; please, pay attention to the timings as we have a limited budget in snellius. The matrix I am considering is very small 2x2, so the size also play a role here. I will continue on that as implementing the preconditioner may improve a lot the scalability of the algo.