Quantum Annealing for absolute beginners
Day 14 — Quantum30 Challenge
Today was an active rest day of QuantumComputingIndia’s challenge and I once again revisited the topic of Quantum Annealing which was yesterday’s quota. The reason I didn’t write about it yesterday was I wanted to fill in some voids in my brain regarding the subject, and thus, instead wrote about the DiVincenzo Criteria. The following article is an overview of the subject and covers the following topics:
- What are Quantum Annealers
- The process
- Application
- Differences with other quantum computers
- Are Quantum Annealers Quantum computers?
In the classical world, annealing refers to a process in which a material is heated to a specific temperature (varies based on the material), held at that temperature (soaked), and then gradually cooled down. This process rearranges the electron arrangement within the material, leading to a more stable configuration and resulting in improved properties such as hardness, ductility, conductivity, etc.
(If you have worked with chocolate, it is similar to the process where pure chocolate is made into compound chocolate by heating, soaking, and cooling down which will turn in into something which is easier to work with.) So basically, we have slowly transitioned our state of the system in order to achieve a stable configuration.
This annealing concept translates into quantum annealing in the realm of quantum computing. In quantum annealing, the quantum system (qubits) evolves over time through various quantum operations to reach the lowest energy state of the qubit’s Hamiltonian.
What are Quantum Annealers used for?
Before looking at the process of annealing, we’ll discuss the applications. Quantum Annealers is specifically designed to solve Optimisation and Ising Model problems.
Optimization problems
Optimization problems deal with finding the best solutions out of the large number of options given. For instance, imagine choosing a route to your friend’s house from multiple paths. Each path has its pros and cons, such as time and road conditions. Some take a longer time to reach with good roads while some take a shorter time but with dangerous or bad routes. The objective is to find the path that offers the best compromise.
Some of the famous optimization problems are as follows:
a. Travelling Salesman Problem: A salesman needs to travel to different cities and come back to the starting city, but choosing a route that minimizes his total distance.
b. Quadratic Unconstrained Binary Optimization (QUBO): It is a mathematical framework that represents binary variables as decisions or choices for optimization of an objective function (mostly represented as the sum of terms, each having a coefficient and one or more binary variables). The goal is to minimize the objective function.
c. Max Cut Problem: The maximum cut problem involves partitioning the nodes of a graph into two sets to maximize the number of edges between the sets.
Ising Model Problems
The Ising model is a simplified representation study of a system that has interactions of spins and magnetic moments. The key principle behind the Ising model is spins interact with neighboring spins. So for a lattice, which is a grid of discrete points or sites, each site can have an associated spin, which represents the magnetic orientation of that point. The spin can take one of two values, typically represented as +1 and -1, corresponding to “up” and “down” magnetic orientations. The objective function (here, known as the Energy function) takes into account both the individual spin and the spins due to interaction. The main goal is to find a configuration of the entire spin set in order to achieve the lowest energy function value.
How do Quantum Annealers work?
Quantum Annealers use qubits (which are in a superposition of 2 states).
When the annealing process is done, they will collapse into individual states with specific probabilities. When an external magnetic field a.k.a ‘bias’ is applied, we can tweak the probabilities of the different states. The bias results in the qubit states arranging themselves in such a way that the entire system has the lowest possible energy.
When the bias is not applied, the probability of getting both states at the lowest energy is 50–50.
In analogy to the Ising model problem where we had spins influencing each other, two qubits can influence each other when they are coupled. This is done by a coupler. A coupler can make both the qubits end up either in the same state or in opposite states. So, a coupler is responsible for the interactions between two qubits. Due to coupling, entanglement naturally occurs between both, and now, we have a single wavefunction with 4 distinct states (|00>, |01>, |10>, |11>). So, when these undergo the annealing process, their corresponding energies will be depending upon the biases corresponding to each qubit and the coupling between them.
Analogous to the Gate-based quantum computers where we control the qubit by using different quantum gates, in Quantum Annealing, we can the qubits by influencing the biases and the coupling on the qubits.
So in summary, the annealing process is as follows
Qubits (in superposition) Arrangement→ Undergoes Quantum Annealing Process → Couplers and biases are introduced → Process ends → The arrangement of collapsed qubits with minimal energy is obtained.
What makes Quantum Annealers different from other quantum computers?
In, Quantum Computers like gate-based quantum computers (IBM’s and Google’s Quantum computers), trapped ion quantum computers (developed by IonQ), etc. we explicitly control the transition of the qubits from an initial state to a final state by various computations. In Quantum Annealers, on the other hand, the qubits naturally transition from an initial to the final state in the annealing process in response to the energy landscape defined by the problem, being solved.
Currently, DWAVE is the most famous and significant players in the field of quantum annealing.
Do Quantum Annealers fall under the category of Quantum Computers?
A quantum computer is a device that computes by using and exploiting quantum phenomena like superposition and entanglement.
Apart from that, they should also follow DiVincenzo’s criteria.
Let’s take a look at Quantum Annealers.
- They do have well-defined qubits, long coherence times, and the capability to measure qubits individually.
- However, for the qubit initialization criterion, it may have a different emphasis. The annealers need to make sure that the initialization would ensure the optimization of the state.
- Also, since annealers don’t do quantum algorithms and just focus on optimization problems, they do not need any universal set of gates.
In conclusion, there is still a debate about whether Annealers should be considered Quantum Computers. While some argue that they are because of the superposition and entanglement property being satisfied and that since it is a problem-specific device and can have certain discrepancies with DiVincenzo criteria, some argue that they are not. But for the other party, one can say that quantum annealers do fall under the category of ‘Adiabatic Quantum Computers’ that rely on the slow evolution of the qubits.
So which side are you with?