Superposition, probability and qubits!

Hello and welcome to the world of quantum computing! I was interested in this topic and wanted to learn something about it, but most of the articles I've read were either too technical or not explaining the topic enough so I was still puzzled. So let's go on!

In the last article we've looked at the differences between a classical physics (=everyday behavior of large objects) and quantum physics (= physics of tiny particles like atoms, photons and electrons). Remember the hide-and-seek game we have played? And that our friend could be in multiple places until I discover their location? For tiny particles it works like that. They have properties that can be described by mathematical equations that look like waves. These equations, called wave functions, describe the probabilities of finding the particles in different positions. And this probability is an important aspect of quantum computing.

Secondly, imagine you have a tiny electron, and you don't know exactly where it is. It's as if the electron is a bit of a "blur" or spread out, existing in a range of possible positions at the same time. This is quite different from our everyday experience, where objects are usually in one place at a time. According to the principles of quantum mechanics, when you're not looking at a single electron, it's not confined to being in just one specific position or state. Instead, it can exist in a so-called "superposition" of multiple or positions simultaneously. Additionally, electrons can also exist in a superposition of different energy states. This means that, when not observed, an electron's energy isn't limited to one particular value; it can be in a mix of energy levels.

I repeat this once more because this is important: According to the principles of quantum mechanics electrons can exist in multiple positions and having multiple energy states simultaneously.

This behavior of particles like electrons being in multiple places or states at once is a fundamental aspect of quantum mechanics and is often referred to as the "wave-like" behavior of particles. It's important to note that this behavior becomes more pronounced on the scale of individual particles, and it's not something we notice in our macroscopic world due to the process of quantum decoherence I mentioned in the previous article.

"Why do you called it "wave-like?" Waves also have those "superpositions?" Yes, waves also exhibit the principle of superposition. In fact, the concept of superposition is a fundamental characteristic of waves, whether they're water waves, sound waves, or electromagnetic waves. Superposition in waves means that when multiple waves meet, their effects add together. This can lead to constructive interference (when waves reinforce each other) or destructive interference (when waves cancel each other out). Waves can have different amplitudes (heights) and frequencies (patterns of repetition), and when they overlap, they combine in a way that reflects the superposition principle.

For example, if you throw a pebble into a pond, it creates ripples. If you throw two pebbles at different spots, the ripples they create will eventually overlap. At certain points, the ripples will combine to create larger waves, and at other points, they will cancel each other out, resulting in calm spots. This superposition behavior of waves is similar to how particles in quantum mechanics can exist in multiple states simultaneously, leading to interference patterns. The connection between the behavior of waves and particles in quantum mechanics is a key aspect of the particle-wave duality concept. We use wavelike functions in quantum mechanics, thinking of particles as having possibilities to spread out like ripples, and these possibilities help us figure out where we might find the particle when we measure it.

So, the relation between superposition and probability is that superposition describes a particle's ability to exist in multiple states simultaneously, and probability gives us a way to understand the chances of measuring a particular state when we observe it. The probability amplitudes associated with each possible state help us calculate these probabilities and understand how they can interfere with each other to create unique quantum behavior.

How do we apply this to the world of quantum computing? Qubits! A qubit, short for "quantum bit," is a fundamental unit of quantum information. Unlike classical bits that are either 0 or 1 (meaning the electric signal either exists or doesn't), qubits can exist in a superposition of both 0 and 1 states simultaneously. This means that a qubit can represent a combination of both states with varying probabilities. It's like a blend of 0 and 1, not definitively one or the other.

Besides superposition, qubits also have a second property, called "entanglement." Qubits can be "entangled" with each other. When qubits are entangled, the state of one qubit is dependent on the state of another qubit, even when they are physically separated. This allows for unique correlations and interactions that classical bits can't achieve.

Keep in mind that this is a quantum world! And if you want to "look" at a qubit, it will collapse from its quantum, superposition state, and it becomes either 0 or 1, depending on the probabilistic nature of its quantum state. However, we can sort of manipulate the entanglement and superposition state of qubits using something called "quantum gates." They are similar to "logic gates" in classical computers and its specific functions are beyond the scope of this article.

Last but not least, if we want our quantum computer to actually compute, we need to teach him some operations, algorithms, to leverage the properties of qubits, allowing for faster solutions to certain problems compared to classical computers. Algorithms like Shor's and Grover's are examples of quantum algorithms that can outperform classical counterparts for specific tasks. We'll look at this in the next article!

A small side-step (a bit technical) - you may wonder how does a qubit actually look like? Or a quantum computer? Well it depends on the physical implementation of a qubit - and there are a few options! Qubits can be created using tiny circuits made of superconducting materials. These circuits can have different energy levels, and the qubit states correspond to different energy states. Superconducting qubits are manipulated using microwave pulses. These qubits are the most common implementation these days. We can also have qubits that can be realized using individual ions that are trapped using electromagnetic fields. The internal energy states of these ions can serve as qubit states. The ions are manipulated using laser beams. Qubits can also be encoded in the polarization states of photons (particles of light). Photons can be in horizontal, vertical, or a combination of both polarizations, serving as the qubit states.

In terms of a physical appearance, it's important to note that qubits are not visible to the naked eye because they operate on extremely small scales, often at the level of individual atoms or subatomic particles. They're typically manipulated and measured using specialized equipment like lasers, microwave sources, and other high-tech tools.

When you ask "How large can actually a quantum computer be?" Well, size can vary widely depending on the technology used for implementing qubits and the level of complexity of the system. The size of practical quantum computers is evolving rapidly. Many current quantum computers are relatively small and fit within a laboratory setup. These might consist of a few qubits and the necessary control equipment, which can include cryogenic systems for cooling, microwave sources, and other specialized components. These systems can range from the size of a small table to a larger experimental setup. Quantum computers with a greater number of qubits and improved performance might occupy a larger physical footprint. These systems could be comparable in size to some high-performance computing clusters or server racks. Superconducting qubits are being developed in arrays, where many qubits are interconnected. These arrays can be physically larger due to the necessary cooling and wiring systems. Depending on the desired number of qubits, these arrays could be housed in specially designed cooling units or cabinets. It's important to note that the size of a quantum computer isn't just determined by the number of qubits. Supporting equipment, cooling systems, and control infrastructure also contribute to the overall size. As quantum technologies advance and new methods of qubit implementation are explored, it's possible that more compact and efficient designs will emerge.

And a funny question to the end: When we have 1 qubit, do 8 qubits form a "qubyte?"

Short answer is no :) the concept of grouping qubits together to form larger units of quantum information is still important in quantum computing. However, due to the unique nature of qubits and their quantum properties, the way they are grouped and manipulated can be more complex than in classical computing. In quantum computing, larger units of information are often referred to as "quantum registers" or "quantum words." These are collections of qubits that are manipulated as a single entity to perform quantum operations and computations. Quantum registers can be used to encode more complex information and perform more sophisticated calculations. However, due to the principles of superposition and entanglement, the behavior of a group of qubits is not always straightforward. The state of a quantum register is a combination of all the possible states of its constituent qubits, potentially leading to a much larger set of possibilities than classical bits.

Until next time! Stay tuned!

Further reading: Superposition principle, Quantum logic gate