Solving linear system: Ax = b
This folder solve the below matrix and vector with 12 qubits
1 -1 1
A = -2 3 4 , b = (4, -4, 8)
1 -4 -1
QA_12qubits.ipynb: Original QUBO and Ising models
QA_12qubits_penalty.ipynb: QUBO and Ising models with constraint terms equal to 0
QA_12qubits_penalty.ipynb: QUBO and Ising models with constraint terms equal to 1000
QA_12qubits_rmvd_penalty.ipynb: QUBO and Ising models with removed constraint terms
Original Panelty 0 Panelty 1,000 Panelty removed
QUBO 57 299, 279 67, 278 508, 605
Ising 175 363, 703 176, 114 258, 960
- This folder contains sage & python code for implementing QUBO formulations for system of linear equations using Sylvester's law of inertia.
- Joint work with Sun Woo Park
- The same code can be found in the following link: https://github.com/spark483/Quantum_Computing_sub
- Arxiv preprint link: https://arxiv.org/abs/2111.10084
- This calculator prints out the d-wave quantum annealer command for solving a system of linear equations using the quadratic unconstrained binary optimization formulation.
- The following code implements the following QUBO models which utilize X qubits.
- QUBO formulation utilizing Sylvester's law of inertia & qubit relations (compiles up to 132 qubits)
- QUBO formulation utilizing only the quadratic relation q^2 = q (compiles up to 64 qubits)
- (The error message "no embedding found" shows that the D-wave quantum annealer cannot process the second QUBO formulation.)
- QUBO model utilizing Sylvester's Theorem:
- Empirical maximum number of utilizable qubits: 132 qubits (D-wave 2000Q quantum annealer)
- Models utilizing more than 136 qubits cannot be compiled (D-wave 2000Q quantum annealer)
- QUBO model utilizing only the quadratic relation:
- Empirical maximum number of utilizable qubits: 64 qubits (D-wave 2000Q quantum annealer)