Adiabatic Quantum Computing (AQC) is a model of quantum computing that solves problems by leveraging the natural tendency of physical systems to seek their lowest energy state (the ground state).
Unlike the more common "gate-based" model (used by Google or IBM), which uses a sequence of logical gates like a recipe, AQC is more like a slow, controlled "evolution" of a physical system.
1. How It Works: The Core Principles
The foundation of AQC is the Adiabatic Theorem. In physics, an "adiabatic" process is one that happens slowly enough that the system doesn't gain or lose heat to its surroundings.
In a quantum context, the theorem states:
If you start a quantum system in its lowest energy state (ground state) and change the conditions very slowly, the system will stay in the ground state throughout the entire process.
The 3-Step Process
Start (Initial Hamiltonian): You begin with a simple quantum system where the ground state is easy to find and prepare (e.g., all qubits in a uniform superposition).
Evolve: You slowly "morph" the system by changing its magnetic fields or interactions. This transition is represented by the formula:
$$H(t) = (1 - \frac{t}{T})H_{\text{initial}} + \frac{t}{T}H_{\text{problem}}$$where $t$ is time and $T$ is the total duration.
Finish (Problem Hamiltonian): By the end of the evolution, the system’s configuration matches the specific "landscape" of your problem. Because of the adiabatic theorem, the system is now in the ground state of this new landscape—which is your answer.
2. Real-World Examples
AQC is exceptionally good at Optimization Problems—finding the "best" or "cheapest" solution among millions of possibilities.
Example A: The Logistics "Traveling Salesperson"
Imagine you need to find the shortest route for a delivery truck to visit 20 cities.
The Landscape: Every possible route is like a point on a mountain range. The "height" of the point is the total distance of that route.
The Goal: Find the lowest valley (the shortest route).
AQC Approach: AQC "paints" this mountain range onto the qubits. It starts with the truck "everywhere" at once (superposition) and slowly lets the physics of the qubits settle into the deepest valley.
Example B: Financial Portfolio Optimization
A bank wants to pick a group of 50 stocks that gives the highest return with the lowest risk.
The Landscape: High-risk/low-return combinations are high peaks; low-risk/high-return combinations are deep valleys.
AQC Approach: The quantum system explores all trillions of stock combinations simultaneously and settles into the configuration that represents the "optimal" portfolio.
3. AQC vs. Gate-Based Computing
| Feature | Gate-Based (e.g., IBM, Google) | Adiabatic (e.g., D-Wave) |
| Logic | Discrete steps (Gates) | Continuous evolution |
| Analogy | Following a digital circuit | A marble rolling to the bottom of a bowl |
| Strengths | Universal (Shor's Algorithm, etc.) | Specifically Optimization & Sampling |
| Hardware | Harder to scale (high error rates) | Easier to scale to thousands of qubits |
4. Why it matters: Quantum Tunneling
Classical computers can get "stuck" in a local minimum (a small dip that isn't the lowest point) because they can't climb over the "hills" of the landscape. AQC uses Quantum Tunneling, allowing the system to pass through energy barriers to find the true global minimum.
No comments:
Post a Comment
Note: only a member of this blog may post a comment.