INTRODUCTION TO QUANTUM COMPUTING PART 2

Welcome to our second article of our blog on quantum computing, where we will take a deeper view into the basic concepts of quantum computing, specifically about algorithms, quantum superposition and quantum entanglement, that were mentioned in the last article

According to the previous post, an algorithm is “a set of well-defined instructions to solve a particular problem” and the three main stages of an algorithm are Input, Processing and Output.

For example, if a person wants to make a cup of instant coffee, it has to follow the following steps:

1. Set its ingredientes (Input):

2. Set the cook process (Processing)

3. Get a cup of instant coffee (Output)

In general, programmers and computing scientists apply the concept of algorithm previously explained for generating video games, internet communications, simulations, mathematical operations, Apps and all current computation, including quantum computing in which the same process of Input, Processing and Output is applied with complex and powerful operations available in this new technology as Quantum Superposition and Entanglement.

How does Quantum Superposition work?

According to the previous post, this phenomenon is caused by very little (at atomic level) physical systems, such as electrons, that can exist in all their theoretically possible states, but these possible states collapse in a unique state when this physical system is observed or measured.

One example where quantum superposition produces observable effects is the Wave-particle duality in the double-slit experiment performed by Thomas Young, where light could behave as a wave and as a particle at the same time. In modern quantum mechanics, this duality expands to any particle or quantum entity.

Double slits experiment [1]

When measuring with particle detectors, a particle is found, but when measuring with wave detectors, a wave pattern is found. This is known as the Measurement Problem in Quantum Mechanics, and is a good example of quantum superposition (State – Wave or Particle – is unknown until measurement).

Subatomic states are related with a property of particles named Spin which can be changed by means of Electromagnetic fields with states as Spin Up and Spin Down, and the mix of these results in a Superposition of quantum states. Quantum computing uses these superposition states to perform “Quantum Parallelism”, that allows the Quantum Algorithms to evaluate multiple states at the same time, and subsequently increasing processing speed.

Superposition of Spin up and down [2]

In the following example, we can see a case where measuring a qubit multiple times gives as a result a probability distribution. The lightbulb was measured 50 times and the results were 35 (70%) OFF lectures and 15 (30%) ON lectures.

It can be said that qubits not only can have all possible values, but also can have probabilities associated to those values, and this means the probabilities are really important to describe a qubit state and manipulate it.

Spooky action at a distance

In the last century, when Quantum Theory was in its early age, the “spooky action at a distance” phenomenon, as Albert Einstein named it, was discovered. Some subatomic interactions make pairs of particles that fly in different directions and, even when they are separated, their relationship remains [3].

This phenomenon, named Quantum Entanglement, can be explained as an invisible bond between these particles, where any change in any of the particles causes changes in the other particles instantly, even if they are light-years away from each other, an also makes impossible to describe the quantum state of one particle independent of the other, they can just be seen as a unique entity [4].

In the case of quantum computing, quantum entanglement can be used to link two or more qubits. The effect this causes in qubits is similar to the effect of connecting two lightbulbs to the same switch.

When you want to change the state (ON/OFF) of one of the lightbulbs, the other lightbulb will inevitably change its state too. This also applies when a lightbulb is ON and the other is OFF and they are entangled.

This ability to bind qubits expands the possible algorithms quantum computing is able to perform, adding “restrictions” to qubit’s possible output depending on other qubits states.

References 

1. Abyss.uoregon.edu. 2022. Two-Slit Experiments. [online] Available at: <http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html> [Accessed 20 June 2022].

2. Abyss.uoregon.edu. 2022. Uncertainty Principle. [online] Available at: <http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec14.html> [Accessed 20 June 2022].

3. The Economist Explains. 2022. What is spooky action at a distance? [online] Available at <https://www.economist.com/the-economist-explains/2017/03/16/what-is-spooky-action-at-a-distance> [Accessed 20 June 2022] 

4. LiveScience. 2022. What is quantum entanglement [online] Available at: <https://www.livescience.com/what-is-quantum-entanglement.html> [Accessed 20 June 2022]

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