*Khanh Giang*

Here’s an interesting fact for you: the Apollo Guidance Computer (AGC) that was used on Apollo 11 to take humans to the moon had roughly 4 kilobytes (kb) of random accesses memory (RAM) – the memory used to store temporary results from calculations. It also had 72 kb of read only memory (ROM) which cannot be changed, and is used to start the computer. Today, the average smartphone typically has 4 gigabytes (GB) of RAM, and 8GB of ROM. That’s 7 million times more processing power than the AGC.

And that’s not all. The ACG weighs 32kg, whilst the average smartphone weighs less than 200g – a mere 0.6% of the weight of the ACG. Our computer chips are getting smaller with an increasing amount of processing power, which leaves one to wonder what’s the limit? Will we have the processing power of a current supercomputer in a smart watch anytime soon?

**Moore’s Law**

This problem was first considered as early as 1965, when Gordon Moore, the cofounder of Intel, predicted that the number of transistors in an integrated circuit (the building blocks of a computer) will double approximately every two years.

As you can see i the figure above, the prediction has generally held true since then, and as such is now known as Moore’s Law. However, with the the current density of 300 million transistors/mm^{2}, and the size of a processor reaching 5nm (for scale, a typical atom is about 0.1 to 0.5 nanometers in diameter, and the Covid virus is about 60 to 150 nm), scientists are debating when this law will cease to hold.

Moore’s Law is the direct consequence of the physical limits of the circuit – computing devices must communicate within themselves via electric signals that cannot surpass the speed of light. Therefore, to increase communication speed, the distance traveled must be shortened, and so faster computers must be smaller. But once the size of the components becomes *too* small, quantum effects kick in and we can no longer use our classical circuit.

Furthermore, classical computers consume energy which they convert into heat. Our modern computers suffer from excessive energy consumption (low battery – looking at you Apple) and excessive heat output (eg. a burning hot laptop that can’t be put on your lap). These are further reasons as to why Moore’s law is estimated to reach its limit in the next few years: the energy required to cool these densely packed, tiny transistors will surpass the energy supplied.

**Reversibility**

There is, however, a new kid on the block which may be able to help. In fact, both of the problems described above can be solved by a property of quantum computers called *reversibility*. We all know that once our coffee cup falls off the table and breaks, it can’t stick itself together and fly back up onto the table. Isn’t that strange? Both the falling down and flying up follow the same physics, so why even after supplying more energy (eg. heating up the broken pieces), doesn’t the coffee cup merge together and fly back up?

The answer lies in entropy – the measure of how chaotic a system is. The second law of thermodynamics says that the entropy of a closed system (like our universe) should always increase.

But let’s look a little closer. How does the second law come to be? Imagine a box with 100 atoms floating around, starting with all atoms on the right-hand side, which I’m sure you’ll agree is very ordered as far as atoms are concerned. After some time, 100 atoms will be chaotically bouncing around everywhere in the box. The chance that the atoms from this random state bounce their way back to all be on the right-hand side is pretty slim. That’s why we say entropy increases: the system will get more chaotic as time goes on.

However, what if we only have 3 atoms? Clearly it isn’t so hard for all 3 atoms to all be on one side or the other. On a small (microscopic) scale, atoms’ behaviour is essentially reversible, while macroscopic objects like transistors are described by irreversible physical processes.

So how would this “reversibility” solve our energy problems? Isn’t a car going from London to Oxford then back following a reversible process, but still consuming energy in the form of fuel? Indeed this isn’t a reversible process, as once the fuel runs out, the car will no longer be able to “reverse” its state. A truly reversible process like the one required by our quantum computer, is one that can go back and forth between the two cities infinitely, and as such would not consume any fuel (energy)!

Nevertheless, no process can be fully reversible as there will always be some energy lost (we don’t exist in a perfect vacuum, but a chaotic environment with lots of atoms bouncing around and taking away energy), so even though our quantum computer may consume very little energy, it can never reach a true “0 energy consumption” state. For our discussion here, the key thing is that the energy consumption will be much lower for a quantum computer than its classical counterpart.

**Vs classical computer**

While the energy-heat problems are real issues we are trying to fix, they are merely a side benefit of a quantum computer, not the reason why we might want one in the first place. We are working toward a solution for smaller computers with more computing power, and quantum computers meet this need: they are fundamentally superior to classical computers.

In classical computers, information is stored in bits, which can be either (0) – turned off/false or (1) – turned on/true.

By analogy, in quantum computers, we also store information in “qubits”, which can either be in state (0) or (1) like the classical bits (of course we can have 3 state systems but that’s probably not practical!). But the fun thing with quantum bits is that they don’t have to be in either of those states!

To understand why this is the case, let’s look at the classic thought experiment: Schrödinger’s Cat. In a box, we put our cat, a radioactive sample that has a 50% chance of undergoing radioactive decay, and a Geiger counter that releases a poisonous gas if it detects the decay. After some time, we open the box, and we either discover our cat to be dead, or still alive.

The weirdness of this experiment isn’t in our (Schrödinger’s!) questionable decision to harm the cat, but rather what happens before the box is opened. Is the cat dead, or is it alive? We don’t know, and as far as we are concerned, the cat has a 50% chance of being alive, and 50% chance of being dead before we look.

Quantum bits are the same: They can be in state a(0) + b(1), with a^{2} chance of being in state (0) and b^{2} chance of being in state (1), where a and b are complex numbers (why they are squared is a little beyond the scope of this article, but a simple explanation has to do with waves – like how we add the height (amplitude) of two tsunamis merging into a total height).

Already we can see the potential of quantum computers. A single classical bit can be in either 0 or 1, but a qubit can take both values at once with different probabilities. For 2 classical bits, we can have 4 configurations: 00, 01, 10 and 11. Our 2 qubits can also be in 1 of those 4 states, but analogously they can be in a mixture (physicists call this “superposition”) of those states, for example as 50% (00) and 50% (01); or even 2% (00), 87% (01), 8% (10) and 3% (11).

So 1 qubit can pack 2 classical bits of information, 2 qubits can pack 4, and in general, n qubits can take 2^{n}. This means that for the memory space of 1000 qubits, merely 125 bytes, we can store up to 1.1 x 10^{301} bits, or 1.3 x 10^{282} Exabytes. For comparison, the highest capacity of the iPhone 12 is 512GB, and so to store 1.3 x 10^{282} Exabytes we would need about two million iPhones.

The speed (memory) of the quantum computer thus is exponentially faster than its classical counterpart. This exponential growth has many interesting consequences, but isn’t without problems, both of which will be discussed in the third article of the series (COMING SOON).

In this 1st article we have covered why we need a quantum computer, how is it superior to a classical computer, and a key feature it must have: Reversibility. How we actually construct such a computer will be explained in the next article.

[…] the previous article, we looked at why quantum computers are needed and the importance of their ability to be […]

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[…] ground: a(0) + b(1), but the measurement can only return 0 or 1. It’s the same as we saw in the first article with the Schrödinger’s Cat experiment, before the box is opened, the cat is in a […]

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