physics

Quantum annealing

Quantum annealing is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Quantum annealing rather than just read about it. In short: Quantum annealing (QA) is an optimization process 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 spin glass or solving QUBO…

Key takeaways

Quantum annealing belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Quantum annealing to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Quantum annealing from memory before moving on to harder problems.

Reference excerpt

Quantum annealing (QA) is an optimization process 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 spin glass or solving QUBO problems, which can encode a wide range of problems like Max-Cut, graph coloring, SAT or the traveling salesman problem. The term "quantum annealing" was first proposed in 1988 by B. Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori (ja) in 1998, though an imaginary-time variant without quantum coherence had been discussed by A. B. Finnila, M. A. Gomez, C. Sebenik and J. D. Doll in 1994. Quantum annealing starts from a quantum-mechanical superposition of all possible states (candidate states) with equal weights. Then the system evolves following the time-dependent Schrödinger equation, a natural quantum-mechanical evolution of physical systems. 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 or essentially tunneling through peaks. If the rate of change of the transverse field is slow enough, the system stays close to the ground state of the instantaneous Hamiltonian (also see adiabatic quantum computation). If the rate of change of the transverse field is accelerated, the system may leave the ground state temporarily but produce a higher likelihood of concluding in the ground state of the final problem Hamiltonian, i.e., Diabatic quantum computation. The transverse field is finally switched off, and the system is expected to have reached the ground state of the classical Ising model of spin glass that corresponds to the solution to the original optimization problem. A foundational study of the transverse Ising spin glass model was made by B. K. Chakrabarti in 1981. An experimental demonstration of the success of quantum annealing for random magnets was reported immediately after the initial theoretical proposal. Quantum annealing has also been proven to provide a fast Grover oracle for the square-root speedup in solving many NP-complete problems.

Comparison to simulated annealing Quantum annealing can be compared to simulated annealing, whose "temperature" parameter plays a similar role to quantum annealing's tunneling field strength. In simulated annealing, the temperature determines the probability of moving to a state of higher "energy" from a single current state. In quantum annealing, the strength of transverse field determines the quantum-mechanical probability to change the amplitudes of all states in parallel. Analytical and numerical evidence suggests that quantum annealing outperforms simulated annealing under certain conditions (see Heim et al and see Yan and Sinitsyn for a fully solvable model of quantum annealing to arbitrary target Hamiltonian and comparison of different computation approaches).

Quantum mechanics: analogy and advantage

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Quantum annealing

Start with the simplest possible case. Write down what Quantum annealing claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Quantum annealing before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Quantum annealing ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Quantum annealing

In research: Quantum annealing appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Quantum annealing in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Quantum annealing is common in secondary-school and first-year university syllabi. It links to neighbouring topics Optimization algorithms and methods, Quantum algorithms, Stochastic optimization, so understanding it makes those chapters shorter.
In everyday life: Look for Quantum annealing outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Quantum annealing in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Quantum annealing means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Quantum annealing out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Quantum annealing in simple terms?

Why does Quantum annealing matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Quantum annealing?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Quantum annealing.