Quantum Computing Fundamentals

1. Introduction

Quantum computing is set to revolutionize our world, much like classical computers have over the past few decades. Classical computers, which include devices like computers, servers, and phones, have transformed how we work, communicate, and live. However, they have limitations in the types of calculations they can perform and the ability to increase the number of transistors on a chip.

To overcome these limitations, we need quantum computers. Quantum computers use qubits that can exist in multiple states simultaneously, thanks to principles like superposition and entanglement. This allows them to process vast numbers of possibilities at once, giving them immense processing power and enabling them to solve complex problems much faster than classical computers.

Despite their potential, quantum computing faces several challenges, including computational errors, lack of development environments, and sensitivity to environmental factors. However, as the technology matures, it is expected to become more accessible and widely used, offering opportunities to revolutionize fields such as chemistry, telecommunications, city planning, logistics and cybersecurity.

2. The importance of Quantum Computing

Computers have dramatically changed the way how we work, communicate, and live over the past few years. Every year, new innovations emerge, including newer phones, computers, and apps that make work and life easier. Medicines are invented, spacecraft are exploring Mars, robots are taking over simple or hazardous tasks from humans, and the way we fight wars has changed due to AI and drones. Every year, more people are connected to the internet, and computers are transforming societies, both positively and negatively.

This category of devices, which includes computers, servers, phones, cars, and all kinds of gadgets, is now referred to as classical computers. Classical computers are based on electronic switches (transistors) that can perform simple calculations. By combining billions of transistors on a chip, these simple calculations are aggregated. The more transistors on a chip, the more calculations can be performed, resulting in faster computations and the ability to handle more complex calculations. Not every chip needs to have billions or even trillions of transistors; chips with lower counts are easier to produce and cheaper. These affordable chips have found their way into almost every device we know and use.

However, classical computers have two main limitations: the type of calculations they can perform and the ability to increase the number of transistors on a chip.

The first limitation is the type of calculations we can perform. Problems that require exponential calculations are very difficult to solve because transistors are very basic and can only switch on and off. An example given by Stone (2023) illustrates this with arranging guests at a dinner party, which becomes exponentially more difficult as the number of guests increases. With four guests, there are 24 possible seating arrangements, but with five guests, this increases to 120. If the number of guests reaches 10, there are 3.628.800 possible combinations. The text highlights that even with strategies to reduce the number of combinations or using parallel processing, this problem can quickly become unmanageable (Stone, 2023).

The second limitation is that we can't continue adding transistors to a chip indefinitely. Currently, an average transistor is 7 nanometers. A human hair has a diameter of 86 micrometers, so we can fit 6,000 transistors in the diameter of a human hair. At some point, we can't produce smaller chips because of quantum tunneling. According to Veerasingam (2023), quantum tunneling is a quantum mechanical phenomenon where particles pass through a barrier that they classically shouldn't be able to cross. This effect becomes significant at very small scales, such as in semiconductor devices. As we try to make smaller and smaller chips, the insulating barriers between transistors also become thinner. When these barriers are thin enough, electrons can tunnel through them, leading to leakage currents. This leakage reduces the efficiency and reliability of the chips, making it increasingly difficult to continue miniaturizing semiconductor components (Veerasingam, 2023).

To keep reinventing ourselves as humans, to find cures for diseases, solve traffic and logistics issues, discover new materials, and explore space, we need a different kind of computer. A computer that is unimaginably more powerful, capable of performing very complex calculations in short times, and free from scalability issues. That new type of computer is the quantum computer.

It should be noted that we don't need to replace every computer or device with a quantum computer. There will still be a need in the far future for simple calculations that can be done very cheaply with classical computers. This can be compared to the use of GPUs nowadays. We use classical CPUs for simple tasks and offload more difficult tasks, such as video rendering, cryptography, and machine learning, to GPUs. In the future, we'll probably still use classical processors alongside quantum processors.

3. Classical bits and Quantum bits (Qubits)

A classical bit can be compared to a light switch. You can switch a light switch off and on, putting it in one state or the other. Similarly, a bit can be switched off (0) or on (1). The state of a classical bit is always determined and is either zero (0) or one (1).

A quantum bit (qubit) can also be set to zero or one. The notation for zero is |0⟩ and for one is |1⟩ because a qubit is represented as a vector: [1 0] for zero and [0 1] for one. For more information about vectors, visit my blog about linear algebra.

It's important to note that we don't know the state of a qubit until we measure it. When we measure a qubit, it collapses into either |0⟩ or |1⟩. Once a qubit has collapsed into |0⟩ or |1⟩, it remains in that state, just like a classical bit doesn't change its state (Stone, 2023).

3.1 Superposition

A qubit that has not been measured is in superposition. A qubit in superposition is both zero and one at the same time. Although it is both zero and one simultaneously, we only know its state after it collapses. It has a probability of becoming either zero or one. The closer it is in superposition to zero, the higher the probability it will collapse to zero. The same applies to one; the closer it is to one, the higher the probability it will collapse to one. Note that this is a probability, not a certainty. The probabilities always add up to 100%, or 1. For example, if the probability of collapsing to zero is 0.9, then the probability of collapsing to one is 0.1. A qubit in superposition is denoted as |ψ⟩. To visualize the state of a qubit, we use the Bloch sphere, which is a three-dimensional vector space. For more information about three-dimensional vector spaces, visit my blog about linear algebra.

The importance of having a qubit in superposition can be illustrated with the double-slit experiment. The double-slit experiment, first conducted by Thomas Young in the early 19th century, demonstrates the wave-like properties of light. In this experiment, a beam of light is directed at a barrier with two narrow slits. As the light passes through these slits, it spreads out and overlaps, creating an interference pattern on a screen behind the barrier. This pattern consists of alternating bright and dark bands, indicating areas where the light waves reinforce each other (constructive interference) and cancel each other out (destructive interference). This result shows that light behaves as a wave, not just as particles, providing crucial insights into the nature of light and electromagnetic radiation (Radboud University Nijmegen, 2010).

Double Slit Experiment. Radboud University Nijmegen (2010)

Understanding the double-slit experiment is crucial for grasping qubit superposition because it illustrates the fundamental principle of wave-particle duality. Just as light can exist in multiple states (waves) simultaneously and create an interference pattern, qubits in quantum computing can exist in multiple states at once (superposition). This ability to be in multiple states simultaneously allows quantum computers to process a vast number of possibilities at once, rather than sequentially like classical computers. This is what gives quantum computers their immense processing power, enabling them to solve complex problems much faster than classical computers.
Interference can be used to enhance the probability of measuring the correct solution while suppressing the probability of measuring incorrect solutions, leading to a speedup in computation (Microsoft, 2025).

3.2 Entanglement

Quantum entanglement is a phenomenon where two qubits become interconnected in such a way that the state of one qubit instantly determines the state of the other, no matter the distance between them. When one qubit is measured and collapses to a state, the other qubit will instantly collapse to a corresponding state. This happens without any information exchange between the qubits, even if they are light-years apart. How this works is still not fully understood (Reichental, 2019).
Quantum entanglement is crucial for quantum computing as it enhances processing power by allowing qubits to be interconnected, enabling faster complex calculations. In quantum cryptography, entanglement ensures secure communication through quantum key distribution. Additionally, superdense coding uses entanglement to transmit more information than classical bits, and quantum teleportation leverages it to transfer quantum states without moving particles, forming the basis of quantum communication networks (Stone, 2023).

4. Quantum Logic Gates

Quantum algorithms are visualized with the Quantum Circuit Model, which looks like a sheet of music paper (Stone, 2023). The order of operations is from left to right, and each qubit has one line. In the example from TU Delft (n.d.), there are three qubits: the first qubit (q0) goes into superposition, q2 is switched, q0 entangles with q1, and q2 rotates. At the end, all qubits are measured. In this example, each measurement is at the end of the line; in other models, the measurements are returned to a separate line below the last qubit line. The measurements are stored in classical bits.

Quantum Circuit Model (TU Delft, n.d.)

In the visualization, we see the use of logic operators, specifically H, X, and P. There are four main gates that are used most frequently: the Pauli-X gate, Pauli-Y gate, Pauli-Z gate, and the Hadamard gate.
The three Pauli gates each rotate the Bloch sphere by 180 degrees around one of the axes of the three-dimensional vector space (Stone, 2023). The Hadamard gate puts the qubit into superposition. For more information about the Bloch sphere and three-dimensional vector spaces, visit my blog about linear algebra.

4.1 Pauli-X gate

The X gate rotates 180 degrees around the X-axis. When we start at |0⟩ and rotate 180 degrees, we end up at |1⟩, and vice versa (Stone, 2023). In classical computing, this is comparable to the NOT gate, which inverts a 0 to a 1 and vice versa, and is called an inverter.

When the qubit is in superposition, it still rotates 180 degrees around the X-axis. If the qubit has a higher probability of collapsing to 1 and is inverted, the qubit will then have a higher probability of collapsing to 0.

To calculate the X gate operation with Python, we use a 1x2 vector for the qubit state in |0⟩ or [0 1] (q in the example) and a 2x2 matrix for the X gate (x in the example). We multiply x with q, and the result is the inverse of q, which is [1 0], representing the qubit state in |1⟩.

For more information about vectors, matrices and multiplying matrices with python, visit my blog about linear algebra .

4.2 Pauli-Y gate

The Y gate rotates 180 degrees around the Y-axis. Similar to the X gate, it inverts |0⟩ to |1⟩, or in superposition, changes the probability from closer to 0 to closer to 1. The difference is that the Y gate also changes the amplitude of the qubit from positive to negative, or from negative to positive.
To calculate the Y gate operation with Python, we use the imaginary number expressed as 1j in Python and start with the position |1⟩. We also observe the phase shift in the result, which still results in |0⟩.

For more information about vectors, matrices and multiplying matrices with python, visit my blog about linear algebra .

4.3 Pauli-Z gate

The Z gate rotates 180 degrees around the Z-axis. This doesn't change the probability or convert |0⟩ to |1⟩. The rotation only changes the amplitude, from positive to negative and vice versa.
To calculate the Z gate operation with Python, we see no change in the state; |1⟩ is now -|1⟩ due to the change in amplitude. However, there is no difference between -|1⟩ and |1⟩, so it remains |1⟩.

For more information about vectors, matrices and multiplying matrices with python, visit my blog about linear algebra .

4.4 Hadamard gate

5. Problems that need to be solved

Quantum computing seems to be the future, and in many ways, we need this technology now. Unfortunately, there are several major problems that need to be solved first.

One of the problems is that quantum computers make computational errors. These errors have various causes, such as radiation, temperature changes, vibrations, etc. While it is possible to identify and correct these errors with algorithms, it often takes more time to correct the errors than to actually run the desired code (Reichental, 2019). Quantum error correction is a major research area at the moment.
A second problem is the lack of quantum computer operating systems and development environments for software development. It is not possible to create and use apps on a quantum computer in the way we are accustomed to with classical computers

A third problem is the lack of investments in quantum programs and start-ups. Additionally, there are job shortages in general, but especially in quantum computing. There is a need not only for scientists but also for strategists, analysts, consultants, and developers.

A fourth problem is the sensitivity of quantum computers and their cooling needs. Qubits need to be cooled to -273 degrees Celsius. Besides cooling, a quantum computer is very sensitive, so a special room is required for the quantum computer. This is very expensive. In a way, quantum computing is at a level where classical computing was in the 1950s.

There are numerous other problems, such as the number of qubits available, the time a qubit can hold information, limitations on how qubits can interact, quantum architectures, quantum storage, etc.. It is reasonable to expect that quantum computing needs 10 to 15 years to mature enough for mainstream use.

6. Current and future opportunities

Everyone can access and learn more about quantum computing. IBM offers the IBM Quantum Platform, where you can learn how to code using Qiskit and run that code on a quantum computer. Microsoft has Azure Quantum, which is available on a limited basis. Microsoft developed Q#, which is integrated with Visual Studio, and they also provide learning resources. D-Wave systems is one of the first commercial providers of a quantum computing platform, including an SDK and several commercial applications.

Quantum computers could be used for research in chemistry, enhancing mobile telecom performance, production scheduling, optimizing power grids, cybersecurity, medical research, and financial analysis.
At this moment, quantum computers are mostly used for scientific research and by large industrial companies for airplane modeling, chemistry research, and traffic optimization (Reichental, 2019). Most businesses won't use quantum computing in the near future because classical computing offers enough capacity for most applications.

For you, as a reader of this blog, the most important opportunity is to learn more about quantum computing and find business and social opportunities to solve complex problems on quantum computers today or in the near future.

7. Conclusion

Quantum computing holds the promise of transforming our world in ways we are only beginning to understand. While classical computers have brought about significant advancements in technology and society, they have inherent limitations that quantum computers can overcome. By leveraging principles like superposition and entanglement, quantum computers can perform complex calculations at unprecedented speeds, opening up new possibilities in fields such as chemistry, telecommunications, and cybersecurity.

Despite the challenges that quantum computing faces, including computational errors, the need for specialized development environments, and sensitivity to environmental factors, ongoing research and development are paving the way for its broader adoption. As the technology matures, it will become more accessible, offering exciting opportunities for businesses and individuals to solve complex problems and drive innovation.

For those interested in the future of computing, now is the time to learn about quantum computing and explore its potential applications. By staying informed and engaged, we can be part of the journey toward a new era of technological advancement.

Sources

Microsoft (2025). Explore quantum. https://quantum.microsoft.com/en-us/insights/education/concepts/interference

Radboud University Nijmegen (2010, 11 December). Double-slit experiment. https://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Double-slit_experiment.html

Reichental, J. (2019, 5 August). A new era of computing is emerging - Introduction to Quantum Computing [Video]. LinkedIn. https://www.linkedin.com/learning/introduction-to-quantum-computing/a-new-era-of-computing-is-emerging?u=46118444

Stone, O. C. (2023, 17 April). Learn quantum computing - Quantum Computing Fundamentals [Video]. LinkedIn. https://www.linkedin.com/learning/quantum-computing-fundamentals/learn-quantum-computing?contextUrn=urn%3Ali%3AlearningCollection%3A7013770329806249984&u=46118444

TU Delft (n.d.). Quantum circuits. https://www.tudelft.nl/over-tu-delft/strategie/vision-teams/quantum-computing/what-is-quantum/quantum-circuits

Veerasingam, M. (2023, 3 June). Quantum Tunneling And The Semiconductors’ Struggle in the Miniaturization Race. Medium. https://medium.com/@markveerasingam/quantum-tunneling-the-semiconductors-struggle-in-the-miniaturization-race-7ef2df8f9e48

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