Quantum Computing vs Combinatorial Optimization

Quantum computing has attracted significant interest in the scientific community in recent years due to its potential to solve problems that are hard for classical computers. One such problem is Combinatorial Optimization, which is used in various fields such as logistics, finance, and transportation. In this blog post, we will provide a factual comparison between Quantum Computing and Combinatorial Optimization and illustrate how they differ from one another.

What is Combinatorial Optimization?

Combinatorial Optimization is a type of optimization problem where the goal is to find the best solution from a finite set of possibilities. The solutions must satisfy a set of constraints, and the goal is to optimize an objective function. Combinatorial Optimization is used in various fields. For example, in logistics, it is used to optimize the delivery routes of a fleet of vehicles. In finance, it is used to minimize the risk of an investment portfolio. Combinatorial Optimization is an NP-hard problem, which means that a classical computer cannot solve it efficiently for large problem sizes.

Quantum Computing and Combinatorial Optimization

Quantum computing offers a new approach to solving optimization problems such as Combinatorial Optimization. By encoding the problem as a quantum state and using quantum algorithms such as Grover's algorithm or Quantum Annealing, we can find the optimal solution in a shorter time than on a classical computer.

For instance, D-Wave Systems has introduced a quantum annealer QPU (Quantum Processing Unit) which runs on Quantum Annealing. It can solve problems such as Ising models or Quadratic Unconstrained Binary Optimization (QUBO) formulated optimization problems. QPU 2000Q (latest product by D-wave) has the current capacity of solving 500,000-variable problems.

However, quantum computing is still in its early stage, and larger quantum computers are required to solve industrial-sized problems.

Quantum Annealing

Quantum Annealing is a quantum computation method that solves optimization problems. The quantum annealing algorithm is based on the physical process of thermal annealing. Optimization problems defined as Ising models or QUBO (Quadratic Unconstrained Binary Optimization) can be solved by constructing similar an energy landscape by the Hamiltonian mechanics of a quantum system. The optimal value is found by gradually lowering the temperature of the quantum system to anneal it in the ground state.

Quantum Annealing can solve problems such as Graph Coloring, Traveling Salesman and more. However, the use of Quantum Annealing in several commercial practices may be limited because its architecture focuses on specific optimization problems of Ising Models or QUBO.

Conclusion

In conclusion, Quantum Computing has the potential to improve Combinatorial Optimization significantly. However, the current technological limitations must be overcome to solve industrial-sized optimization problems efficiently. Furthermore, the development of dedicated software and hardware for Quantum Annealing, such as QPU 2000Q by D-Wave, shows promising results in a particular subset of combinatorial optimization problems such as Ising models or QUBO.

We hope that this comparison has provided you with a better understanding of Quantum Computing and Combinatorial Optimization. If you want to learn more about Quantum Computing, check out Flare Compare's blog section.

References

• I. V. Ovchinnikov, G. V. Rybkin, and V. I. Shevchenko, "Optimization problems and quantum computing," Technical Physics Letters, vol. 43, no. 7, pp. 681-684, Jul. 2017.
• V. Gheorghiu, "Quantum Computing and Optimization Problems," CoRR, abs/1904.01439, 2019.