Welcome to another exciting episode of "Quantum Computing for Everyone"! Today, we're going to compare two methods used in quantum computing: quantum annealing and quantum adiabatic computing. Both of them share a similar purpose, which is solving optimization problems. However, they have different approaches and implementations that can make one more suitable for a given problem than the other.
Quantum Annealing
Quantum annealing is a method that uses the principles of quantum mechanics to fine-tune the solution to a given problem. It is based on the Ising model, which is a simple mathematical model that represents a set of interacting objects that can have only two states: up or down. The goal is to find the ground state, which is the lowest energy configuration for a given set of objects.
Quantum annealing uses qubits to represent the objects and their interactions. The qubits are initialized in a superposition of states, which means they can have a probability of being up or down at the same time. Then, the system is subjected to a series of perturbations that cause it to evolve towards the ground state. The process is controlled by a programmable parameter called annealing time, which determines the duration of the evolution.
One of the main advantages of quantum annealing is that it can be implemented using a special-purpose device called a quantum annealer, which is designed to perform this task efficiently. One of the most well-known quantum annealers is the D-Wave machine, which has been used to solve a variety of optimization problems in industries such as finance, transportation, and materials science.
Quantum Adiabatic Computing
Quantum adiabatic computing is a method that also uses the principles of quantum mechanics to solve optimization problems. However, its approach is based on a different principle called adiabatic theorem. This theorem states that a system can remain in its ground state if the evolution is slow enough, even if the system is subjected to external perturbations.
Quantum adiabatic computing starts with a Hamiltonian that is easy to prepare, and gradually transforms it into a Hamiltonian that represents the optimization problem. The transformation is controlled by a programmable parameter called switching time, which determines the duration of the evolution. If the switching time is slow enough, the system will remain in its ground state at the end of the process, which represents the optimal solution.
One of the advantages of quantum adiabatic computing is that it is a more general-purpose method than quantum annealing, as it can be used to solve a wider range of problems. However, it can also be more challenging to implement, as it requires precise control of the switching time and the system's energy levels.
Comparison
So, which one is better, quantum annealing or quantum adiabatic computing? Well, it depends on the problem you're trying to solve. According to a study published in 2016 by researchers at the California Institute of Technology, there are situations where quantum annealing outperforms quantum adiabatic computing, and vice versa.
For example, the study found that quantum annealing was more efficient for solving Boolean satisfiability problems, while quantum adiabatic computing was more efficient for solving maximum clique problems. The results also showed that the performance of both methods improved with the size of the problem, but quantum annealing had an advantage over quantum adiabatic computing for larger problems.
Another study published in 2020 by researchers at the University of Bologna compared the performance of quantum annealing and quantum adiabatic computing for solving the traveling salesman problem. The results showed that both methods produced good solutions, but quantum annealing was faster and more reliable than quantum adiabatic computing.
In summary, both quantum annealing and quantum adiabatic computing are powerful methods for solving optimization problems using quantum mechanics. The choice between one or the other depends on the specific requirements of the problem, such as its size and complexity. It's also worth noting that these methods are still in the early stages of development, and new improvements and innovations are expected to emerge in the coming years.
References
- Farhi, E., Goldstone, J., & Gutmann, S. (2014). A Quantum Approximate Optimization Algorithm. arXiv preprint arXiv:1411.4028.
- Bian, Z., Chudak, F., Macready, W.G. (2010). Ising formulations of many NP problems. Front. Phys. China, 5(3), 1-47.
- King, A.D., Yarkoni, S., Nevisi, M.M., Hilton, J.M., & McGeoch, C.C. (2020). Benchmarking Adiabatic Quantum Optimization for the Traveling Salesman Problem. arXiv preprint arXiv:2005.05206.
- Albash, T., & Lidar, D.A. (2016). Adiabatic Quantum Computing. Reviews of Modern Physics, 90(1), 015002.