### What Quantum Annealing is using quantum physics to find minimum energy states Mapping the Optimization Problem (math) to the Energy Minimization Problem (physics) #### Why Exponential increase in computational capabilities to solve combinatorial optimization problems ##### Technicals Hamiltonian is a function that maps a state to an energy For Quantum Annealers, - The coefficient of the linear term is a bias - Positive --> Pull the bit to be equal to zero - Negative --> Pull the bit to be equal to one - The coefficient of the quadratic term is a coupling - Positive --> Penalizes the 2 bits from both being equal to 1 at the same time Programming a Quantum Annealer is all about providing the biases and couplings that represent your optimisation problem Given theses values the Quantum Annealer defines the given energy landscape using couplers and magnetic fields and finds the lowest energy state through an annealing process ![[Pasted image 20210412093900.png]] At the end of the process, the energy landscape will equal to the problem hamiltonian that was provided aka. the solution Under the right conditions the final state of our system should correspond to the lowest energy state of the problem Hamiltonian ![[Pasted image 20210412093214.png]] #### Challenges - Difficult to maintain a quantum state - Limits in connection and expansion - Still in research ---- Tags: #quantum Links: [[Quantum Tech MOC]] [[QUBO]]