*The following article is an abridged version of a paper written by Ranveer Riyat as part of his degree course.*

Quantum computing will change our world. It is an endeavour that has promised to transform drug development, codebreaking, and revolutionise everything from telecommunications to machine learning [1]. With so much hype, it is easy to get lost marvelling at the endless possibilities, without grasping what quantum computing is.

Since the development of the first conventional computer, the benefits of computing have been profound. While computers aid us with an infinite array of everyday tasks, such as finding the fastest route to a destination, surfing the internet, streaming movies, or even enabling safe air travel, there are challenges that today's systems will never be able to solve.

Despite the billions invested in quantum technologies, quantum computers are notoriously difficult to engineer, build, and program [1]. As a result, they are hampered by errors from noise, faults, and loss of quantum coherence, the latter being critical to their dysfunction.

This article will begin by focusing on how quantum computing exploits the laws of quantum mechanics to find solutions to intricate problems. We will then present some significant uses of quantum computers and the current challenges the industry is facing.

#### Fundamentals of quantum computing

An ordinary computer processor performs logical operations using the definite positions of a physical state or ‘bit’ [3]. You may have referred to these definite positions as the ‘on’ one or ‘off’ zero states of a transistor. A computer can simultaneously operate on billions of bits that store information on websites, applications, photographs, and pretty much anything which remotely involves a computer chip.

Although this is adequate for regular everyday tasks, it does not reflect how the universe intrinsically behaves in a quantum mechanical way [4]. Quantum mechanics forgoes deterministic results and instead embraces the concept of probability [5], which means quantum computers have the potential to process exponentially more data compared to classical computers.

In a quantum computer, the rules are different. To realise why, it is crucial to understand three fundamental quantum mechanics principles: superposition, interference, and entanglement.

** **

Superposition

Imagine spinning a coin. While spinning, the coin has an equal probability of landing on heads or tails, but we cannot say for sure which side the coin will land on until the coin falls.

The spinning coin principle gives us some intuition of superposition; it is the ability for a quantum object, i.e., an electron, to exist in multiple states at the same time. For example, an electron could be in either a spin-up or spin-down state. If an electron is in a superposition of both, it has some probability of being in either one simultaneously. A measurement will collapse this superposition, and only then can it be said with certainty which state the electron is in [5].

Understanding superposition makes it possible to comprehend the primary component of information in quantum computing, the qubit. As mentioned, a conventional ‘bit,’ can hold a zero or a one, which could correspond to states such as spin up and spin down. However, qubits can reside in a single basis state, zero or one, and be in a superposition of both states with varying probabilities.

Subsequently, quantum computers with several qubits in superposition can be manipulated by quantum operations to process a vast number of potential outcomes concurrently. The result of a calculation emerges only once the qubits are measured, which immediately causes their quantum state to ‘collapse’ to either 1 or 0. We will not delve into specifically how researchers set qubits into superposition, but currently, precision lasers or microwave beams are used [6].

** **

Interference

Now, when two or more qubits interact with each other, something really fascinating happens. Just like water waves, when two qubits combine, their states can either add up (constructive interference) or cancel each other out (destructive interference). This is like two people jumping on a trampoline - they can make it bounce higher together or cancel each other out.

But why is this useful? Put simply, interference in quantum computers lets us do things faster and more efficiently than classical computers. It is like having two people work together to solve a puzzle, and they finish it faster than one person working alone.

** **

Entanglement

As the name implies, entanglement is a property of quantum systems that reveals itself when states begin interacting and is closely tied to the interference property discussed above. More specifically, entanglement is a special relationship between two qubits in which they become entwined and share a connection that cannot be broken. This means changing the state of one qubit will affect the other qubit instantly, no matter how far apart they are, making it appear that information can travel faster than the speed of light. This also means that once two qubits are entangled, we can no longer describe either qubit individually - they become indistinguishable and can only be described as a single entity.

Researchers do not quite understand why entanglement works, and the phenomena even baffled Einstein, who famously described it as 'spooky action at a distance' [8]. However, it is key to the power of quantum computers. In a conventional computer, doubling the number of bits will double its processing power. However, adding an additional qubit will produce an exponential increase in its computational power due to entanglement. This is because each qubit cannot be decomposed into its constituent states, so adding an extra qubit effectively doubles the number of parallel operations performed [7].

To gauge how powerful entanglement is, consider applying an arbitrary quantum operation on combined qubits. The operation must be applied to all possible states simultaneously, so 64 qubits have the potential to represent more than 18 billion billion states. In theory**, **300 perfectly entangled qubits in superposition could map all the information in the universe, starting from the Big Bang [9].

** **

Presently, the most advanced quantum computer consists of 433 qubits, but going beyond this number is proving to be challenging.

#### Quantum Algorithms

Quantum algorithms provide the bridge between the hardware and the final computation. They answer our question of how we use interference to increase the probability of achieving a correct answer when the answer is not remotely conceivable. Fundamentally, it comes down to knowing the properties a correct answer will have, which is why quantum computers are only advantageous for certain kinds of problems.

An ideal problem for a quantum computer is one is one where it is difficult to obtain an answer but easy to verify the result. A universal example is factoring, which involves finding two numbers that multiply together to construct a larger number. Since there is no inherent process in which this can be done efficiently, a conventional computer will continue to trial combinations of numbers until it finds a solution [11]. However, for immense 2048-bit numbers, trialling in this way means it is practically impossible for a classical computer to find the factors [10]. As a result, nearly every online transaction today relies on the protection of RSA cryptosystems, which hinges on the difficulty of finding factors of large numbers that will break the encryption [10].

However, in 1997, Peter Shor (MIT mathematician) developed a quantum algorithm that uses interference effects to efficiently find the prime factors of large numbers [11]. Here is how it works: first, you use a quantum computer to create a superposition of all the possible factors. This means that the computer is in a state where it is trying all the possible factors at once. Then, using interference, you can make the correct factors "add up" and constructively interfere, while the incorrect factors "cancel out" and destructively interfere. This means that the correct factors become much more likely than the incorrect ones. Finally, you use a quantum measurement to collapse the superposition and find the correct factors.

The downside… it requires a quantum computer with approximately 5 million qubits to work - a scale that is currently beyond our technology [7].

So, what types of problems can a quantum computing currently solve?

We may not be able to perform Shor’s algorithm just yet, but the Volkswagen group are currently attempting to use quantum computers to simulate traffic congestion in cities and compute the optimal route for buses and taxies to minimise congestion [12]. A conventional computer would look at every path, in turn, ruling them out individually until the optimal route is found. Whereas a quantum computer can utilise its superposition and entanglement properties along with an algorithm to simulate traffic, most importantly, in real-time [12]. Solving this problem will massively decrease journey times for everyone, and who knows, you may even receive your deliveries at the promised time.

In general, quantum computers would help immensely with optimisation problems, such as the one above, which play critical roles in everything from defence to financial trading [2].

Current challenges

Although the potential of quantum computing is enormous, the performance is crippled by the fragility of qubits. Recall the gyrating coin. The smallest perturbation, vibration, or sound will cause the coin to topple.

Similarly, the predominant source of error in quantum computing is decoherence, which arises when qubits interact with their environment in ways that causes a collapse of the state function [13]. When this occurs, the quantum nature of the computation is lost, and the system effectively becomes obsolete. Decoherence can happen in many different ways, including changing electromagnetic fields and the interaction between nearby qubits and radiation from warm objects [14].

The current solution to suppress decoherence is to isolate the quantum system at temperatures approaching 0 kelvin (-275.15 Celsius) [14], which impedes any outside disturbances. However, to read processed data, the system must be loosely connected to the outside world, making decoherence somewhat inevitable. Researchers are studying novel forms of quantum error correction to increase coherence times (time before state collapses) while decreasing decoherence [13], but we are far from the oodles of qubits that we desire.

Other less bizarre errors arise from the sheer complexity of quantum computers, including faults while setting qubits into their entangled states [14].

#### Conclusion

The immense potential of a quantum computer is unparalleled, but it requires sophisticated solutions to suppress decoherence in order to maintain its power. Fortunately, quantum computing researchers are making significant strides every year in subduing decoherence, paving the way for even more impressive advances in the field. If these mysterious new computing machines live up to their promise, quantum computers will one day fill a niche in computing, solving certain types of problems that are classically intractable - and transform entire industries along the way.

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[14] C. Almudever et al, *The engineering challenges in quantum computing*, 3, (2017)