Quantum annealing
Introduction
Quantum annealing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions (candidate states), by a process using quantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems) with many local minima; such as finding the ground state of a physical system.
Quantum Mechanics and Quantum Annealing
Quantum annealing relies on the principles of quantum mechanics, the branch of physics that deals with phenomena on a very small scale, such as molecules, atoms, and subatomic particles. Quantum mechanics introduces the concept of quantum states, superposition, and entanglement, which are key to understanding quantum annealing.
Quantum annealing starts from a quantum-mechanical superposition of all possible states (configurations) with equal weights. Then the system evolves following the time-dependent Schrödinger equation, a fundamental equation in quantum mechanics. The amplitudes of all candidate states keep changing, realizing a quantum parallelism, according to the time-dependent strength of the transverse field, which causes quantum tunneling between states.
Quantum Tunneling
Quantum tunneling is a quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays a crucial role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the Sun. It has important applications to modern devices such as the tunnel diode, quantum computing, and the scanning tunneling microscope.
In the context of quantum annealing, quantum tunneling is used to escape local minima in the energy landscape. This is a significant advantage over classical annealing and other classical optimization methods which lack this feature.
Quantum Annealing Process
The process of quantum annealing involves initializing the system into a quantum superposition of all states, then gradually changing the system Hamiltonian from a simple form whose ground state is easy to prepare to a final form whose ground state represents the solution to the problem of interest. This gradual change is done in such a way that the system stays close to its ground state, hence increasing the probability of ending in the ground state.
Quantum Annealing vs Classical Annealing
Quantum annealing differs from classical annealing in the way it escapes local minima in the solution space. While classical annealing can get stuck in a local minimum, quantum annealing uses quantum tunneling to escape these local minima and has a higher probability of finding the global minimum.
Quantum Annealing Machines
There are several companies, such as D-Wave Systems, that manufacture quantum annealing machines. These machines use superconducting circuits that can generate a quantum-mechanical superposition of different magnetic states, and can be used to solve optimization problems.
Applications of Quantum Annealing
Quantum annealing has been used in various fields such as machine learning, finance, and drug discovery. It has been used to solve complex optimization problems that are difficult to solve using classical methods.
Challenges and Future Directions
Despite its potential, quantum annealing faces several challenges. These include issues related to quantum coherence, error correction, and scalability. However, ongoing research and technological advances are expected to address these challenges in the future.