spark483 / Quantum_Computing_sub

This is an identical github repository to "Quantum_Computing" github page: https://github.com/ktfriends/Quantum_Comupting

<Sylvester_Theorem Folder>

Summary

• This folder contains sage & python code for implementing QUBO formulations for system of linear equations using Sylvester's law of inertia.
• Joint work with Dr. Kyungtaek Jun.
• The same code can be found in the following link: https://github.com/ktfriends/Quantum_Comupting/tree/main/Sylvester_Theorem
• Arxiv preprint link: https://arxiv.org/abs/2111.10084

Matrix_congruence_update.ipynb

• This calculator prints out the d-wave quantum annealer command for solving a system of linear equations using the quadratic unconstrained binary optimization formulation.

QA_X-qubits.ipynb

• 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)