# The challenge of quantum annealing in a nutshell

20 Jun 2017 Frankfurt - The Tuesday morning session at ISC17 on Quantum Annealing and its Applications for Simulation in Science and Industry was chaired by Kristel Michielsen from the Jülich Supercomputing Centre. She also gave the first presentation of this session in which she provided an introduction to quantum annealing. The problems of interest for new computing technologies are optimization problems. They include scheduling, trading, flight and train scheduling, production planning, image processing, and so on. The challenge is to find the best option among a finite set of feasible solutions and to minimize the cost function. Kristel Michielsen explained to the audience how to find the minimum energy state of a physical system.

Traditionally, scientists used simulated annealing in the past but simulated annealing has to be replaced with quantum annealing. Instead of a thermal jump, in quantum annealing there is quantum tunneling, Kristel Michielsen explained.

The question is how to solve an optimization problem by quantum annealing. First, you have to write the cost function as an Hamiltonian of the Ising model such that its lowest-energy state represents the solution to the optimization problem, using a quadratic unconstrained binary optimization (QUBO). Then, you have to add a term H1representing the quantum fluctuations.

Quantum annealing is a continuous time evolution of a quantum system described by the Hamiltonian. The total Hamiltonian changes as a function of time from H1at t=0 to Hpat t=ta, Kristel Michielsen showed.

If A(0) is much larger than all other energy scales, then the system will start in the ground state of H1with a probability of 1. If the time evolution is adiabatic, then at t=ta the system is in the lowest-energy state.

The quantum theoretical description of the quantum annealing process is a Landau-Zender theory. The probability has to remain in the lowest energy state during annealing, as Kristel Michielsen explained.

In theory, the quantum annealing hardness ofthe problem is determined by the minimal spectral gap between the lowest-energy state and the first excited state during the annealing process. The minimal gap is determined by Hp.

Using the D-Wave implementation, the system of superconducting flux provides qubits. Not all qubits are connected with each other, Kristel Michielsen explained.

The characteristics are as follows:

• the number of qubits defines the size of problems that can be studied;
• problems cannot always be mapped efficiently on the Chimera graph;
• the type of qubit-qubit interaction depends on the case: for optimization problems it is good but for simulating quantum models it is not enough;
• the precision of model parameters is important

In the Juelich Supercomputing Centre, the researchers simulate quantum computer devices on supercomputers to shed light on the physical processes involved. This helps in the design of new processors.

Kristel Michielsen concluded that the Jülich Supercomputing Centre is moving towards a quantum computer user facility with a three-fold platform: an Open TelekomCloud, a Unified Quantum Computing Platform, and a Modular HPC Center for experimental qubit devices to enhance approximate quantum computing and to support the D-Wave 2000Q annealer.