Kyungtaek Jun: ktfriends@gmail.com
Hyunju Lee: hyunjulee0824@gmail.com
Solving linear system: Ax = b
We make several QUBO models for matrices and compare the results.
From the results, we propose a new method for constrained problems.
Solving eigenvalue and eigenvector problem: Ax = kx
To solve Ax = kx, we use the two norm square of Ax - kx.
If any k and x satisfies Ax = kx, then the absolute value Ax - kx satisfies the minimum value 0.
Paper: https://www.sciencedirect.com/science/article/pii/S2666720723000243?via%3Dihub
Solving linear system: Ax = b
To solve Ax = b, we use the two norm square of Ax - b.
If any x satisfies Ax = b, then the absolute value of Ax - b satisfies the minimum value 0.
Related preprint (with Eigenvalue problem): https://arxiv.org/abs/2106.10819
Solving RSA cryptosystem: N = pq
To solve N = pq, we use the norm square of N - qp.
If p and q satisfies N = pq, then the absolute value of N - pq satisfies the minimum value 0.
Paper: https://www.nature.com/articles/s41598-023-36813-x
It is an algorithm that finds the maximum value of the energy Hemiltonian used in quantum annealers in the gate model quantum computer.
We generally do QUBO modeling to use q^2 = q when creating an energy Hemiltonian.
We introduce an algorithm that can be used by dividing the size of the entire domain according to the number of qubits.
We also form a QUBO model related to each subregion.
Related preprint: https://arxiv.org/abs/2202.07692