Quantum Computing Is Further Away Than It Seems, And Entropy Is One Of The Main Reasons For This

In this article I will discuss the definition of quantum systems and how entropy limits their high scalability due to the need to keep them isolated in closed systems, at low entropy, since such a condition can currently only be sustained for very short periods of time.

Introduction

In this article, I will delve into quantum computing in a technical yet didactic way. This topic has been making headlines on social media and news outlets, where companies like Microsoft are supposedly very close to developing a quantum supercomputer that could revolutionize everything we know today as computing power. However, sensationalism, coupled with intellectual ignorance, prevents many from seeking to understand what is actually real and what is not in quantum computing. Many written and published news stories have the sole purpose of attracting attention through a catchy headline, often bearing no relation to the actual content.

Before even contextualizing quantum computers, I want to remind you, dear reader, of the concept of classical computing and its ability to perform tasks in our daily lives to truly understand that quantum computers will not come any time soon and even if there is a major advance in the area (which I believe will take at least + 10 years), they probably will not replace the home computers we have in our daily lives.

Classical Computing: A Brief Summary

Classical computing, as I’ve discussed in more detail in my previous articles, encompasses all computing currently in use, from embedded systems and data centers to mobile devices and desktops.

Unlike quantum computing, classical computing is based on classical physics itself (such as Newton’s laws, laws of thermodynamics, etc.) that describe the large-scale world as we know it.

Here are some of the main features of classical computers:

• Classical computing is classified as deterministic because the outcome of mathematical operations, for example, is always fixed and determined to a single result. This is considered one of the biggest differences between a classical and quantum computer, as quantum computers are probabilistic.
• Classical computers are mostly built on transistors, tiny structures that have individually reached sizes approaching those of an atom. A superconductor (transistor) made of silicon can reach 7 nm (nanometers). A silicon atom, on the other hand, has a diameter of 111 pm (picometers), with 1 nm being equivalent to 1,000 pm. This demonstrates how close the smallest component that makes up today’s classical computers is to the size of an atom, thus limiting their long-term scalability.
• While quantum computers have enormous potential to perform complex tasks (which will be discussed in more detail later in this article), they likely won’t replace classical computers for general, everyday use. A cell phone, for example, works perfectly for everyday tasks like searching for information, communicating with others, and accessing social media, and will likely never require the computing power of a quantum computer. Classical computing is and will continue to be the foundation of computing for most everyday technological applications.

How Quantum Computers Work

Quantum computers use the fundamental principles of quantum mechanics to process information, distinguishing themselves profoundly from classical computing, which uses transistors and operates with traditional bits.

Using analogies, I will explain in detail the concepts of quantum computing, comparing them with classical computing for better understanding:

• Bit vs. Qubit: Think of a Bit as a coin that can only be heads (0) and tails (1) up. A Qubit is like a coin flipping in the air: until you observe it, it can be in any combination of heads (0) or tails (1) at the same time (superposition).
• Parallel Processing: On a classical computer, solving a maze involves testing each possible path to the result one at a time, which can be time-consuming and computationally expensive depending on the case. On a quantum computer, however, using the aforementioned superposition, it’s possible to test all possible paths from the maze to the result simultaneously, finding a much faster solution to certain problems.
• Quantum Entanglement: Imagine two qubits represented as magic dice: when you roll one, the result of the other is instantly known, allowing that if one die is numbered 1, the other die will be numbered 1 face down (opposite side), regardless of the distance between them. This allows for correlations impossible in classical computing.

Creation of Electromagnetic Fields and Confinement of Qubits

In a quantum chip, electric fields (Paul traps) or semiconductor structures (Quantum Dot) are created to confine electrons.

After the electrons are confined, an intrinsic property of this atom is used to control the equivalent of the 0s and 1s of classical computing. This property is called spin, which refers to its magnetic orientation, which has two directions: UP and DOWN.

Several more complex concepts will not be covered in this article, because, despite the complexity of the subject, I want to make it a little more abstract for a better understanding of the topic.

Think of magnetic orientation as a representation of arrows indicating the orientation of the electron’s angular momentum, with up arrows representing spin +1/2 and down arrows representing spin −1/2.

Electronic Spin Manipulation and Quantum Entanglement

Once electrons are confined, quantum entanglement occurs, a fundamental concept in quantum physics that describes a connection between particles, often referred to as “spooky action at a distance.”

This connection allows that even if, for example, two electrons are very far from each other, they still have a connection between them. This allows that when an electron has a spin UP (∣↑⟩), its quantum entangled partner automatically has the opposite position to its spin, that is, spin DOWN (∣↓⟩).

It applies to the entangled electrons confined in the quantum computer, where the spin position of one electron will be the opposite position of its other partner electron, and so on.

Considering this, electrons have a state called superposition. In this state, the electron can have its spin directed up and down simultaneously.

In this sense, we can ask ourselves, after all, how does a quantum computer alter the spin of a single electron?

The electron spin change, which can function as a qubit, primarily uses oscillating magnetic fields (like microwaves) at extremely specific frequencies and, in some cases, carefully controlled electric fields.

• Oscillating magnetic fields (microwaves): by applying an alternating magnetic field with an appropriate frequency, it is possible to induce transitions between the “up” (UP) and “down” (DOWN) spin states. This is equivalent to rotating the spin vector in the so-called Bloch Sphere, changing the quantum state of the Qubit.
• Electric fields: Recent research indicates that alternating electric fields can also manipulate electron spin, taking advantage of relativistic effects that cause an electric field to behave like a magnetic field in the electron’s frame of reference.

Qubit and Logic Gate Architecture

The physical design of this entanglement is similar to the physical design of a classical computer chip. However, in a quantum chip, the electrons themselves are the connections, resistors, transistors, and capacitors.

The difference is that on a classical chip, transistors, resistors, and capacitors are several atoms in size. On a quantum chip, these components would be the size of a single electron.

Furthermore, the electrical energy present in a classical chip travels at the speed of light. With a quantum chip, entanglement occurs instantaneously, which in theory may seem faster than the speed of light, but in reality, this is not the case.

What actually happens is that entanglement creates instantaneous correlations between particles, but it doesn’t transmit information. Instantaneous exists only at the level of probabilities, not useful information. Therefore, it doesn’t contradict relativity and doesn’t offer a path for data or energy transmission.

Speed ​​of Operations

The question of speed in quantum vs. classical computing is complex and often misunderstood. The advantage of quantum systems lies not in raw operating speed, but rather in algorithmic efficiency for specific mathematical problems that classical computing cannot solve.

Operating Frequencies

Classical computers operate at significantly higher frequencies than quantum computers:

• Classical Computing: Modern CPUs reach 4–5 GHz, executing billions of operations per second.
• Quantum Computing: Operates at frequencies of only 1–10 MHz, with typical gate times of 100–1000 nanoseconds.

Gross Speed ​​Difference

Comparison in nanoseconds reveals even more striking differences:

• Quantum Operations: 555ns (single gate) and 1,000ns (dual gate) on IBM ; 100ns (single gate) and 12ns (dual gate) on Google Sycamore .
• Classical Operations: 0.2–0.5ns per instruction on the CPU (up to 5,000x faster than quantum operations).

Errors and Quantum Correction

Quantum computers with 50–100 qubits can theoretically outperform classical computers in specific tasks, such as factoring large numbers, simulating complex molecules, TSP (Traveling Salesman Problem) problems, quantum machine learning, and others. However, noise generated by quantum gates severely limits the size of circuits that can be executed without large errors.

Noise occurs because the electron or ion trapped in the quantum circuit is extremely sensitive to any type of external interference, be it thermal fluctuations (temperature variations), electromagnetic fields, interactions with photons (light particles), impurities in materials, imperfections in semiconductors (silicon) and even measurements on the electrons themselves.

All these interferences cause what we call decoherence, where the electron loses all its quantum properties (superposition and entanglement), resulting in the destruction of the quantum system’s ability to exist in multiple states simultaneously.

To illustrate, consider a quantum system of N qubits with 20 possible states. This means that each additional entangled qubit in the system will result in an exponential increase in the number of decoherence errors. This occurs because the chance of a single qubit being affected and resulting in the loss of its superposition increases, and a single qubit can alter the quantum state of the entire system.

The graph above illustrates the exponential growth of the error rate in quantum computers as the number of qubits in the system increases. The red curve indicates that:

• Initially ( 1–10 qubits ): The error rate remains low and controllable.
• Accelerated growth ( 10–40 qubits ): The error rate increases rapidly exponentially.
• Saturation ( 40–50 qubits ): The error rate approaches 100%, making the system practically infeasible without error correction.

Currently, quantum computers still experience interference even at temperatures close to absolute zero and in isolation, as even the slightest noise can cause the entire system to fail. To overcome this challenge, Peter Shor introduced the first concept of quantum error correction (QEC).

QEC protects quantum information by correcting the states of entangled electrons, as a qubit error caused by external noise can decohere its state even before the system’s operations are complete. Although a viable solution, quantum corrections require that one logical qubit (a fault-tolerant electron) have approximately 1,000 physical qubits (physical structures formed by electrons, superconducting circuits, ions, or entangled photons that protect information from errors) for active correction.

Using QEC, logical qubits become nearly immune to failures, as the correction helps prevent the information being processed from being compromised. Furthermore, error rates using correction methods like QEC can be reduced by up to 50x, increasing coherence time by up to 100x in quantum systems.

In the graph above, quantum systems with implemented QEC have the following performance:

• Initial Region (17–49 qubits) : Relatively high logical error rate (~10⁻⁴), but still controllable.
• Improvement Region (49–200 qubits) : Significant error suppression, with rapid reduction.
• Optimized Region (200+ qubits) : Extremely low logical error rate (~10⁻¹⁵), suitable for practical algorithms.

Practical Example: Why Would 2 + 2 Fail?

In classical computing, optimized for deterministic operations, they have error rates around ~10⁻¹⁸, meaning they are immune to decoherence errors. Therefore, the sum of 2 + 2 will never fail in a classical system.

Regarding quantum computing, the sum of 2 + 2 would not fail due to theoretical limitations. What happens in practice is that there are many challenges to quantum control of operations, among them the fact that operations in quantum systems, unlike classical ones, are probabilistic and not deterministic.

Error rates per logic gate reach 1% in systems like those from IBM and Google. A basic circuit for an addition operation might require 10 logic gates. With a 1% error per gate, the probability of success drops to (0.99)¹⁰ ≈ 90%, because with each added gate, the error rate is multiplied, not added. Therefore, errors accumulate exponentially, not linearly.

In experimental tests with IBMQ Lima (7 Qubits), a quantum circuit for 2 + 2 returned “4” in 82% of the executions, while in the other 18% other results were returned, such as “3” and “5”.

To make it easier to understand, imagine rolling a die to calculate 2 + 2. In the classical case, the die always lands on a 4 (deterministic). In the quantum scenario, the die has a 90% chance of landing on a 4 and a 10% chance of showing a 3, 5, or another result (probabilistic).

Scalability challenges of quantum systems

With superconducting circuits, qubit error rates increase as the circuit size increases. Furthermore, because qubits are so small, they require much more electronic control due to the qubits being physically close to each other.

Among the various obstacles to the development of quantum systems, the three most critical are:

1. Manufacturing at scale: One of the main challenges facing quantum systems is the complexity of manufacturing and scalability. Superconducting qubits rely on junctions that require high-resolution lithography (EUV) and exotic materials (niobium), which are incompatible with traditional production lines. Furthermore, silicon qubits require wafers with 99.999% purity and controlled isotopy (silicon-28) to minimize electromagnetic noise that could destabilize the qubits. Finally, manufacturing a 100-qubit quantum chip costs approximately US$10 million, compared to US$50 million for a conventional 7nm chip.
2. Miniaturization: Superconducting qubits are 10,000 times larger than silicon transistors, and can occupy ~100 × 100 μm (including control structures). Furthermore, electron entanglement caused by electromagnetic traps can reach macroscopic levels (~10 cm), making them impractical for portable devices. Finally, magnetic shielding structures increase the quantum system’s volume by over 500%.
3. Cooling: These systems require cooling to extremely low temperatures, sometimes reaching near absolute zero (-273°C). In addition to the isolation required by the quantum chip, cooling is necessary for the electrons to have a longer coherence time (stability) above 1 ms. The major challenge is that a commercial refrigerator costs around $500,000, with annual maintenance costs of over $100,000.

What is Entropy?

The concept of entropy can be quite confusing at first, but as you, dear reader, delve deeper into this text, you will understand the idea behind this force that controls everything in our universe and how it relates to the central theme of this article, quantum computing.

Entropy is simply the thermal measure of a closed system, also commonly defined as a measure of disorder. Furthermore, it is the fundamental basis of the Second Law of Thermodynamics, which describes how all systems tend toward a state of equilibrium in which entropy is at its maximum and there is no energy available to do useful work.

The most popular and intuitive analogy that helps with understanding is that of a messy room. Imagine you’ve just organized your room: clothes folded in the closet, books lined up on the shelf, everything in its proper place. In this state, entropy is low because there’s only one (or a few) ways to keep everything perfectly organized.

Now, without any intervention from you, your room naturally tends to become cluttered over time. A sock might end up on the floor, books might be left on the table, clothes might pile up on the chair. There are thousands of ways for your room to become messy , but only one way for it to be perfectly tidy. Therefore, the probability of clutter is much higher, representing high entropy .

This occurs because there are many more possible options for a disordered state than for an ordered state. It’s a matter of statistical probability. The universe naturally tends to evolve toward states that are more likely to occur, which are the most disordered.

Entropy Causality in Quantum Systems

In quantum computers, entropy arises in several ways: as a measure of quantum uncertainty (Von Neumann entropy), as a physical processing cost (Landauer’s principle), and as a direct indicator of decoherence mechanisms and the efficiency of error-correcting codes.

Unlike classical entropy, which was described in the previous topic, quantum entropy measures the uncertainty about the quantum state, including purely quantum effects such as superposition and entanglement.

In isolated systems (without interaction with the environment), evolution is reversible and the von Neumann entropy of the total system remains constant, that is, low entropy . When there is interaction with the environment ( open systems ), decoherence occurs : quantum superpositions are lost, the system passes from a pure state to a mixed state, that is, high entropy .

The great challenge is that, in practice, it is extremely difficult to maintain a perfectly isolated quantum system; therefore, even though theory predicts constant entropy for isolated systems, any minimal interaction with the environment causes the system to tend toward increased entropy. Maintaining closed and completely isolated systems goes completely against their nature, as they inevitably interact with the surrounding environment. In open systems, there are thousands of possible states in which the system can find itself disordered, making them extremely difficult to maintain isolated and with low entropy for long periods of time. Any noise in the system causes decoherence, and decoherence increases entropy, making it difficult to return to the initial state.

Photonic Computing: A Light at the End of the Tunnel

Photonic computing uses photons (particles of light) instead of electrons to process and transmit information. This technology relies on optical circuits and components such as waveguides, modulators, and interferometers to perform logical and mathematical operations, manipulating light properties such as intensity, phase, and polarization.

Features

• Speed : Photons travel at the speed of light, allowing for much higher processing rates.
• Low energy consumption : Moving light generates less heat and electrical losses.
• Intrinsic parallelism : Ability to perform multiple calculations at the same time, taking advantage of unique physical properties of light.
• Room temperature operations : Unlike many quantum systems, photonic processors can operate without extreme cooling.

Advantages

In addition to these characteristics, photonic computing has specific advantages compared to quantum systems that can help it address entropy and decoherence problems.

The first of these is immunity to external noise, where photons interact very little with the environment, allowing photonic systems to be less susceptible to external disturbances that result in decoherence as occurs in electronic or spin qubit systems.

Another great advantage is room temperature operations, where the need for thermal and magnetic insulation is reduced and the maintenance of quantum states is maintained for longer without suffering decoherence.

Disadvantages

While computing holds great promise, it presents several challenges that must be overcome for its widespread adoption. The main ones are:

• Limited miniaturization: Photonic components still operate, for the most part, at the micrometer scale, while conventional electronics have already reached the nanometer scale. This hinders their scalability to more compact systems that integrate millions of components on a single chip.
• High production costs: Manufacturing photonic circuits requires specialized materials and equipment, increasing unit costs. The lack of a mature infrastructure, such as that already exists for electronic chips, contributes to high costs.
• Optical memory and storage: Storing data efficiently and non-volatilely using light is still very deficient, limiting the adoption of applications that require large memory capacity.
• Signal loss and errors: Manipulating light at the nanoscale can lead to signal loss and calculation errors, requiring the development of robust error correction techniques.
• Identical photons: Photonic computing only works correctly if the photons used are identical. This ensures that they can interfere with each other in optical circuits, enabling reliable quantum operations. Furthermore, generating these identical photons in a controlled and repeated manner is one of the field’s greatest challenges today.

Conclusion

In conclusion, quantum computing is a promising field with the ultimate goal of solving specific real-world problems that classical computing cannot solve, not necessarily completely replacing it. However, the challenges of scalability, high production costs, and especially the high decoherence rate in quantum systems will be a long journey to resolve. Contrary to what many media outlets report in biased news, quantum computing is unlikely to be widely used in homes within the next 20 years.

Useful Links

Potential and challenges of quantum computing hardware technologies

• Entropy: The Invisible Force That Brings Disorder to the Universe
• Thermodynamics | Laws, Definition, & Equations | Britannica
• 4.2: Entropy