Qubits, cats, and computers: understanding the quantum basics

Until now, we've looked at how classical computers work, from bits and logic gates to CPUs and cloud computing. If you missed my post about classical computing, you can catch up in my earlier post. Now it’s time to explore quantum computing and why it catalyzes the next technological revolution.

Is a qubit the same as a bit?

As you already know, in classical computing, a bit is a basic unit with two states, 0 or 1. This simple unit powered the 3rd Industrial Revolution, the Digital Revolution, and continues to fuel the current Industry 4.0 era, which merges AI, the Internet of Things, cloud computing, and digital-physical systems.

In quantum mechanics, the basic unit of information is called a quantum bit, or simply, a "qubit". What makes qubits so different is that they aren’t limited to just 0 or 1. Instead, a qubit is a state vector that uses probability amplitudes to describe the likelihood of being in either state. We will review amplitudes in more detail very soon.

Some people describe a qubit as being simultaneously in a 0 or 1 state. It is pretty challenging to wrap your mind around how it can be both 0 and 1 at the same time. Andy Matuschak and Michael Nielsen, in their essay "Quantum computing for the very curious" challenge that interpretation in a humorous way. I slightly paraphrased, as we aren't familiar with quantum notation yet:

"...saying it is simultaneously in the 0 state and the 1 state seems like word salad, and makes about as much sense as Lewis Carroll’s nonsense poem Jabberwocky: ’Twas brillig, and the slithy toves Did gyre and gimble in the wabe: All mimsy were the borogoves, And the mome raths outgrabe.' …"

Quantum mechanics uses a special Dirac notation, where |0⟩ and |1⟩ represent quantum states. This vertical bar and angle bracket don’t carry meaning alone; they simply indicate that we’re working in the quantum domain. This is also known as ket notation.

A general qubit state can be expressed as a linear combination of the basis states |0⟩ and |1⟩. This means the qubit can be written as:

∣ψ⟩ = α|0⟩ + β|1⟩ 

Where ∣ψ⟩ (pronounced as "psi")  is the qubit’s state. So, where do probabilities come in? In quantum mechanics, the amplitudes (α "alpha" and β "beta") are special coefficients that encode how likely the qubit is to be measured either |0⟩ or |1⟩. The squared modulus (|α|² and |β|²) of these amplitudes represents the probability of measuring the qubit in a particular state.

Unlike classical probabilities, which can be only real numbers, these amplitudes can be complex numbers. This allows qubits to occupy a continuous space of states. If you recall from probability theory, the sum of all possible outcomes must equal 1. In quantum mechanics, this rule still applies, but we apply it to the squared magnitudes of the amplitudes:

|α|² + |β|² = 1

For example, if we want to represent an equal probability of the qubit becoming |0⟩ or |1⟩, we would set amplitudes (α and β) to 1 divided by the square root of 2, and if both amplitudes are squared, it would be equal to 1/2. Hence, 1/2 + 1/2 = 1.

We can also express the |0⟩ and |1⟩ states as column vectors:

These vectors represent definite states. The first one means there is a 100% probability of the qubit being in the |0⟩ state and a 0% chance of it being in the |1⟩ state. Conversely, the second represents a 100% chance of measuring |1⟩ and 0% for |0⟩.

Source: Smite-Meister, own work

Now, imagine a qubit like a basketball — a fully 3D object with x, y, and z axes. Any possible quantum state of a qubit corresponds to a vector pointing from the center of the ball to a point on its surface.

This ball is called the Bloch sphere. Unlike classical bits, which are either 0 or 1, a qubit can be anywhere on this sphere, thanks to a mathematical property called superposition.

The direction of the vector, where it points on the sphere, is determined by the amplitudes α and β.

• If the qubit is |0⟩, the vector points straight up;

• If it’s |1⟩, it points straight down.

• If it's in superposition, it points somewhere in between, and the direction depends on both: the ratio of α to β, and the phase (if α or β has imaginary parts, it rotates the vector around the sphere).

The qubit lives on the sphere, but when we measure it, the state collapses to either |0⟩ or |1⟩ based on those amplitudes. Even if the qubit was pointing diagonally, like somewhere between |0⟩ and |1⟩ (say, at 45°), measurement forces it to make a choice. Which one it collapses to depends on how close the vector was to each pole, and that’s defined by the amplitudes α and β.

These ideas lead us to two of the most important concepts in quantum computing: superposition and measurement. Superposition means a qubit exists in a combination of |0⟩ and |1⟩ rather than just one or the other. We can’t see this state directly; we only know the result after measuring the qubit, meaning we observe its state. Only qubits can do this. The strange part? We have no way of knowing the exact amplitudes before the measurement. We can’t look inside a superposition. We can only see the outcome: 0 or 1.

What a radioactive cat can teach us about superposition

One of the most famous cats, after Garfield and Tom, is Schrödinger's cat, named after physicist Erwin Schrödinger. He came up with a thought experiment to illustrate what superposition really means in quantum mechanics.

Imagine a sealed box containing a cat, a flask of poison, and a radioactive atom. Yes, it’s rather an evil setup, but thankfully, it’s only hypothetical. A sensor monitors the radioactive atom. If it decays and emits radiation, the sensor triggers a mechanism that breaks the flask, releasing the poison and killing the cat. If the atom doesn’t decay, the flask remains intact, and the cat survives.

Since we can’t see inside the box, we can't know whether the cat is alive or dead until we open it. In the quantum world, this uncertainty is described as superposition: the system exists in a combination of both possibilities until it is observed. If we map this to our earlier qubit example, we could say |0⟩ represents “cat is dead” and |1⟩ represents “cat is alive.” We don’t have access to the underlying probabilities; we only know that once we measure (open the box), the superposition collapses into a single, definite outcome.

No cats were harmed in this (purely theoretical) experiment. But the paradox illustrates one of the strangest and most fundamental concepts in quantum mechanics.

What superposition enables that classical bits can’t

So, what can these unique properties of a qubit offer compared to a classical bit? To answer this, let’s look back at classical computers. Remember when I explained how billions of transistors are constantly flipping states across the CPU, ALU, and GPU to execute programs and operations? Classical computers execute tasks linearly, meaning one step at a time. While they can have multiple cores and break work into parallel threads, at the fundamental level, tasks are still processed sequentially. No doubt, modern computers are incredibly fast, and supercomputers are even more capable of processing vast amounts of data. But classical computers struggle with a specific class of problems, those where adding just one more variable exponentially increases the number of possible outcomes.

Imagine building a portfolio from five stocks: AAPL, MSFT, GOOGL, AMZN, and META. You make a binary decision for each stock: include it or not. This results in 2⁵ = 32 possible combinations, including the empty portfolio. We require at least one stock, so we exclude the empty option, leaving us with 31 valid combinations. That number might not seem significant, and a classical computer can certainly crunch through it in seconds.

Now, if you add one more stock, say NVDA, the number of combinations doubles: 2⁶ = 64, minus the empty portfolio = 63. With 10 stocks, it grows to 1,023; with 20 stocks, over a million. And that’s before adding constraints like budget, risk, or industry diversification. This type of growth is called exponential, and as I mentioned earlier, classical computers must evaluate these combinations one by one, making the problem increasingly difficult.

This is where quantum computers come in. Thanks to the unique properties of qubits, specifically superposition. A quantum computer can, in theory, evaluate all possible states (in this case, portfolio combinations) simultaneously, allowing it to find the most likely or optimal solution faster than a classical computer.

Here’s another way to think about it. Imagine a giant labyrinth with only one correct path to the exit. A classical computer enters and must try each possible path step by step: left, right, forward, or back — one decision at a time. A quantum computer, on the other hand, thanks to superposition, could explore all possible paths at once and instantly return the correct one. Quantum computers don’t operate with just one qubit but many. So you can imagine the scale of parallelism we’re talking about.

Once we understand more core concepts, we’ll explore real-world use cases for quantum computing in a separate post. For now, just remember that quantum computers are especially powerful when dealing with problems that scale exponentially, the kind of problems that become unmanageable for classical machines.

Inside the quantum computer

You may wonder why we haven’t built or started using these ultra-powerful machines. Here’s the twist: nothing powerful comes without limits. The very thing that gives a quantum computer its superpower, the qubit, is also its biggest weakness. Qubits are highly vulnerable, and external interference can easily change their state, making results inaccurate. To understand this better, we’ll need to look inside the structure of a quantum computer.

Source: John D via iStock

If you've never seen a quantum computer, it looks like a giant golden chandelier, just like the one in the picture above. But what you're seeing isn’t the computer itself; it’s the cooling system. The actual quantum chip is at the very bottom of all those layers. Everything above it is mostly tubes, wiring, and shielding, designed to do one thing: keep the chip super cold.

As I mentioned earlier, qubits are extremely vulnerable to the outside environment. Qubits can take various physical forms, depending on the type of quantum computer. For example, they can take the form of trapped ions, individual atoms suspended in an electromagnetic field, individual photons, or neutral atoms manipulated with lasers. I can hardly picture all these forms, but on the Motley Fool Money podcast “Quantum Is the New Silicon,” Tim White gave a great metaphor: qubits are like kids running wild on a hill; you can’t control them. Qubits in superposition are like those kids, and to measure them and get an accurate result, you first need to slow them down.

To "slow them down", the quantum processor is cooled to just above absolute zero:

• around –273°C (or –459°F)

• That’s colder than outer space.

• This is done using a dilution refrigerator. The tubes in the quantum chandelier are part of a carefully staged cooling system that lowers the temperature layer by layer.

  
  

This extreme cold does more than just quiet the qubits. It also helps shield them from interference, like heat, electrical noise, or stray magnetic fields that could nudge them out of their quantum state. In a way, the chip sits inside a kind of artificial vacuum, isolated from the chaos of the outside world so it can behave purely according to the rules of quantum physics.

However, slowing them down isn’t enough to match the processing speed of a classical computer. You need a significant number of qubits, and the more qubits you have, the harder they are to stabilize them. Just like with the kids running wild, the more kids on the hill, the harder it is to keep them under control. The true power of quantum computing lies in the interaction between qubits, a phenomenon called entanglement. We’ll explore this in more detail in my next post. Things get even more complicated when the distance between individual qubits increases, and stabilizing and coordinating them becomes even harder.

Several companies have already built quantum computers. For example, IBM recently unveiled its largest chip, Condor, with 1,121 qubits. Google has its 105-qubit Willow chip, and Rigetti has built one with 84 qubits. While the number of qubits is important, comparing quantum computers by qubit count alone is not accurate. Different providers use different technologies, each suited to other types of problems. But it’s worth mentioning that these companies are working toward building logical qubits, fault-tolerant qubits that represent a higher-level abstraction, where all the noise and interference have essentially been mitigated. Physicists estimate you may need 100 to 1,000 physical qubits to create just one logical qubit. Today, IBM and Google have only physical qubits.

However, Microsoft and Atom Computing recently announced they've achieved 24 logically connected qubits. For comparison and to understand how far we still are from a "real" fault-tolerant quantum computer, physicists estimate that we’ll need around 1,000 logical qubits to reach a true technological breakthrough. That’s the scale at which quantum computers could begin solving real-world problems far beyond the reach of classical machines, many of which we’ll explore in future posts.

What’s Next: How Quantum Computers Compute

In this post, we explored what a qubit is and how it differs from a classical bit. You may have noticed we introduced a bit of math and linear algebra along the way. It seems that, to truly understand how quantum computing works at its core, I’ll need to dig a little deeper into the math.

That said, I’ve found a helpful resource for revisiting some of those key concepts you probably learned in school but haven’t thought about in a while: 3Blue1Brown’s excellent series of YouTube videos on linear algebra.

Believe me, there will be more math ahead, but I’ll keep it to a minimum. Just enough to give you a strong grasp of the core quantum concepts without overwhelming you or me.

In the next post, I’ll walk through some foundational ideas: quantum gates and entanglement and show how quantum computers actually compute.