Quantum computing is a revolutionary technology already making waves in many industries, such as drug discovery, cryptography, finance, and logistics. It works by exploiting quantum mechanical phenomena to perform complex computations in a fraction of the time classical computers require. Two main quantum mechanical phenomena drive quantum computers' speed and computational prowess – superposition and entanglement.

Unlike classical computers, which operate on binary bits (0 and 1), quantum computers operate on quantum bits or qubits. Qubits can exist in a state of superposition. This means that any qubit has some probability of existing simultaneously in the 0 and 1 states, exponentially increasing the computational power of quantum computers.

Another unique property that qubits have is their ability to become entangled. This means that two qubits, no matter how physically far, are correlated so that knowing the state of one particle automatically tells us something about its companion, even when they are far apart. This correlation can be harnessed for processing vast amounts of data and solving complex problems that classical computers cannot.

Classical computers only have the power to simulate phenomena based on classical physics, making it more difficult or slower to solve problems that rely on quantum phenomena. This is where the true importance of quantum computers lies.

Since quantum computers are based on qubits, they can solve challenging problems using classical computers and revolutionise many industries. For example, quantum computers can rapidly simulate molecules and chemical reactions, discovering new drugs and materials with exceptional properties.

Although significant breakthroughs have been made in quantum computing, we are still in the nascent stages of its development.

### Breakthrough #1: Quantum supremacy

The objective of quantum supremacy is to demonstrate that a quantum computer can solve a problem that no classical computer can solve in any reasonable length of time, despite the usefulness of the problem. Achieving this goal demonstrates the power of a quantum computer over a classical computer in complex problem-solving.

In October 2019, Google confirmed that it had achieved quantum supremacy using its fully programmable 54-qubit processor called Sycamore. They solved a sampling problem in 200 seconds which would take a supercomputer nearly 10,000 years to solve. This marked a significant achievement in the development of quantum computing.

*Richard Feynman first theorised the idea of using quantum mechanics to perform calculations impossible for classical computers. Image: Unknown/Wikimedia Commons*

Since then, many researchers have demonstrated quantum supremacy by solving various sampling problems. The impact of achieving quantum supremacy cannot be overstated. It validates the potential of quantum computing to solve problems beyond the capabilities of classical computers, as first theorised by Richard Feynman in the 1980s.

Apart from sampling problems, other applications have been proposed for demonstrating quantum supremacy, such as Shor's algorithm for factoring integers which are extremely important in encryption. However, implementing Shor's algorithm for large numbers is not feasible with existing technology and is hence not the preferred oversampling algorithm for demonstrating supremacy.

### Breakthrough #2: Quantum error correction

The most pressing concern with quantum computers is their sensitivity to errors induced by environmental noise and imperfect control. This hinders their practical usability, as data stored on a quantum computer can become corrupted.

Classical error correction relies on redundancy, ie, repetition. However, quantum information cannot be cloned or copied due to the no-cloning theorem (which states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state). Therefore, a new error correction method is required for quantum computing systems.

*QEC for a single qubit. Image: Self/Wikimedia Commons*

Quantum error correction (QEC) is a way to mitigate these errors and ensure that the data stored on a quantum computer is error-free, thus improving the reliability and accuracy of quantum computers.

The principle of QEC is to encode the data stored on a quantum computer such that the errors can be detected and corrected without disrupting the computation being performed on it.

This is done using quantum error-correction codes (QECCs). QECCs work by encoding the information onto a larger state space. They further correct the error without measuring the quantum state, thereby preventing the collapse of the quantum state.

The first experimental demonstration of QEC was done in 1998 with nuclear magnetic resonance qubits. Since then, several experiments to demonstrate QEC have been performed using, for example, linear optics and trapped ions, among others.

A significant breakthrough came in 2016 when researchers extended the lifespan of a quantum bit using QEC. Their research showed the advantage of using hardware-efficient qubit encoding over traditional QEC methods for improving the lifetime of a qubit.

### Breakthrough #3: Fault-tolerant quantum computing

The detection and elimination of errors is critical to developing realistic quantum computers. QEC handles errors in the stored quantum information, but what about the errors after performing operations? Is there a way to correct those errors and ensure that the computations are not useless?

Fault-tolerant quantum computing is a method to ensure that these errors are detected and corrected using a combination of QECCs and fault-tolerant gates. This ensures that errors arising during the computations don't accumulate and render them worthless.

*Quantum computing features. Image: Akash Sain/iStock*

The biggest challenge in achieving fault-tolerant quantum computing is the need for many qubits. QECCs themselves require a lot of qubits to detect and correct errors.

Additionally, fault-tolerant gates also require a large number of qubits. However, two independent theoretical studies published in 1998 and 2008 proved that fault-tolerant quantum computers can be built. This has come to be known as the threshold theorem, which states that if the physical error rates of a quantum computer are below a certain threshold, the logical error rate can be suppressed to arbitrarily low values.

No experimental findings have proven fault-tolerant quantum computing due to the high number of qubits needed. The closest we've come to an experimental realisation is a 2022 study published in Nature, demonstrating fault-tolerant universal quantum gate operations.

### Breakthrough #4: Quantum Teleportation

We have seen teleportation one too many times in science fiction movies and TV shows. But are any researchers close to making it a reality? Well, yes and no. Quantum teleportation allows for transferring one quantum state from one physical location to another without physically moving the quantum state itself. It has a wide range of applications, from secure quantum communication to distributed quantum computing.

Quantum teleportation was first investigated in 1993 by scientists who were using it as a way to send and receive quantum information. It was experimentally realised only four years later, in 1997, by two independent research groups. The basic principle behind quantum teleportation is entanglement (when two particles remain connected even when separated by vast distances).

Since 1997, many research groups have demonstrated the quantum teleportation of photons, atoms, and other quantum particles. It is the only real form of teleportation that exists.

In fact, the 2022 Nobel Prize in Physics was awarded to three scientists – Alain Aspect, John Clauser, and Anton Zeilinger – for experiments with entangled photons. The work demonstrated that teleportation between photons was possible. Their work demonstrated quantum entanglement and showed it could be used to teleport quantum information from one photon to another.

Quantum teleportation is the cornerstone for building a quantum internet. This is because it enables the distribution of entanglement over long distances.

Another important application of quantum teleportation is enabling remote quantum operations, meaning that a quantum computation can be performed on a distant processor without transmitting the qubits. This could be useful for secure communication and for performing quantum computations in inaccessible or hostile environments.

### Breakthrough #5: Topological Quantum Computing

Topology is a branch of mathematics concerned with studying the properties of shapes and spaces preserved when deformed. But what does it have to do with quantum computing?

In essence, topological quantum computing is a theoretical model that uses quasiparticles called anyons (quasiparticles in two-dimensional space) for encoding and manipulating qubits.

The method is founded on the topological properties of matter, and in the case of anyons, the world lines (the path that an object traces in four-dimensional spacetime) of these particles form braids. These braids then make up the logic gates which are the building blocks of computers.

*No experimental studies demonstrate topological quantum computing. Image: FMNLab/Wikimedia Commons*

Topological qubits are protected against local perturbations and can be manipulated with high precision, making them less susceptible to decoherence. Additionally, topological quantum computing is more resistant to errors due to its inherent redundancy and topological protection, making it a promising candidate for fault-tolerant quantum computing.

Most topological quantum computing research is theoretical; currently, no studies provide substantial experimental support for the same. But, developments in this area of research are vital for building practical and scalable quantum computers.

### Conclusion

With a mix of theoretical and experimental demonstrations, quantum computing is still in the early stages of research and development. These developments can potentially revolutionise several industries and academic disciplines, including financial services, materials science, cryptography, and artificial intelligence.

Even if there is still more study, the implications for quantum computing's future are promising. We may anticipate further developments and innovations in the years to come.

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