# A Complete Guide to Quantum Computing

Table of Contents

## What’s Quantum Computing

Computing is an activity that creates, requires or derives benefits from computers. It also means to build and design hardware and software systems, which in turn serve a range of applications, including making computer systems behave intelligently, do scientific studies, process and structure bulk data and a lot more. Quantum computing is that area of computing where the focus lies in establishing and developing a computer technology that is based on the principles of quantum theory, a modern physics explaining the behavior of matter and energy on an atomic and subatomic level. In a layman’s language, it means that its physics that explains how everything works. Thus, understanding quantum mechanics to concoct new ways of computing.

Fundamentally, quantum computers are designed to perform quantum computations. These computers extract some of the observations and happenings of quantum mechanics to provide a milestone in processing power. To make this possible, these computers make use of qubits (quantum bits). This is different from the traditional computers, which use only bits, represented by binary numbers 0 and 1. Every app, website, emails etc., that we use are ultimately made up of these millions of bits in some combination of 0s and 1s. These have numerous benefits as we enjoy them in our daily lives. However, this doesn’t reflect the way how things actually work. Things in the actual world are not so simple and also quite uncertain. As an analogy, let’s consider a problem where we need to find an exit inside a maze with ‘n’ number of different pathways inside of it. Classical computers will go through each path to find an exit one at a time. This can be a very time-consuming process if the maze is very large. Now, if additionally it is also given that after a very short time interval ‘t’ the pattern of pathways changes. In such a scenario wherein the problem is morphing faster than the computer can solve it, the uncertainty and complexity are too high. Quantum computers can easily tackle such problems since they can compute multidimensionally i.e. they can navigate multiple paths in a single moment of time. This is because these computers have an astounding ability to generate as well as manipulate qubits. Qubits are quantum versions of bits, typically particles such as electrons or photons. They can hold as well as handle the uncertainty because, rather than just being 0 and 1, they can be both simultaneously or even somewhere on the spectrum between the two states. This achieved state is referred to as coherent superposition.

Another amazing thing that qubits make possible is entanglement. Here, two particles are linked together even if physically they are separate entities, i.e. if one behaves in a certain manner, the other will instantaneously change its behavior in a predictable way. For the time being, we call this magic since no one really understands or knows how this actually works. In the language of quantum computing, it means that you can move information around even if it contains uncertainty.

## Parallels Between Classical and Quantum Computers

In drawing parallels between traditional computers and quantum computers, the major difference between the two is that the latter is much faster than the former in computation techniques and way more sophisticated. Since we have established earlier that quantum computers have the ability to encode information in qubits, this ability makes it operate at an exponentially higher rate than the conventional computer that too by consuming much lesser energy in doing the same. Classical computers are very good at calculus, whereas quantum computers are even better at optimization, simulating molecules, sorting etc. Quantum algorithms make it possible to deal with certain computational problems more accurately and efficiently. In fact, quantum computers can solve complex problems that many conventional computers and supercomputers won’t be able to solve ever, e.g., combinatorial optimization problems. In such problems, we need to explore a wide range of combinations to find an optimal setting. They have applications in management science, industries, finance, engineering etc. Classical or even supercomputers do not have such a memory to hold such a massive number of combinations of problems in the real world. Also, they have to go through the analysis of each combination one by one. Now, that can take forever. Let us go through one simple illustration:

Let us suppose you need 1 item from an unsorted list of *n* items. On classical computers, you will need to check at least *n/2 *items on an average, or else all the *n *items. In comparison, quantum computers using Grover’s algorithm will find the item by going through roughly √*n *of them. This means in order to find a unique item from the list of 1 trillion items where each item takes 1 microsecond to check, whereas the classical computer will take one week and the quantum computer just one second! This ability can be a game-changer in various industries.

It is inevitable that quantum computers will be the future; however, there are certain drawbacks to it with respect to classical computers.

Quantum computers are pretty hard to design, build and program. Classical computers can store data, while quantum computers cannot. The memory of a quantum computer only lasts a few microseconds. Quantum computers are also way more erroneous than classical computers. This is because of decoherence, which corrupts the information received. Decoherence is a phenomenon where the quantum behavior of qubits decays and disappears when they interact with their environments. Qubits lose their quantum states on the slightest vibration or change in temperature. They need to be kept at a colder temperature and cannot operate at room temperature. Therefore, one cannot use them at home or any business place where they can’t be kept in supercooled fridges. Competing technologies and architectures are doing their best; still, the breakthrough is probably several years away.

Quantum computers also cannot give straightforward answers as classical computers do. Instead, through quantum computers, one usually gets an estimation of the probability of different answers.

In conclusion, what we derive is that quantum computers are still years away from replacing classical computers. It’s apparent that both have their pros and cons. What will basically matter will be what problems are better suited for one and what for the other. Quantum computers are better suited for tasks like optimization problems, hyper-complex data analysis and simulations, while most of the everyday processing is easily handled by classical computers.

## The Math of Quantum Computing

The mathematics one needs to study for quantum computing is probability theory, quantum calculus and linear algebra. Let’s work out briefly the representation of qubits mathematically.

Ignoring the abstract form so that even people from non-mathematical backgrounds can understand, let’s say vectors are a list of numbers and let dimension be a component of those numbers in that list. Let us now see how one qubit is represented in 2-dimensional vectors.

Qubits take values 0 and 1. In 2D vector, it will be as following:

This is what we call a superposition. To understand it properly, visualize the vector on a unit circle. The square root values here signify the probability of the qubit being in 0 and 1 state.

Each point in the unit circle is a qubit state. Classical computation can be in only two states, while quantum computation is directed to all the points in 2D space.

Similarly, to present two qubits, we take vectors in 4D as following:

These 4D vectors point in all the directions of a sphere in 4D space. In general, N qubits will have 2^{N} basic states and will point in all the directions of the sphere in the 2^{N} dimensional space. To change the states of the system, quantum gates are used. Quantum gates are Unitary matrices and, when multiplied with any state, can change it to another. Unitary matrices can be thought of as a block of vectors that describes how the vectors move around the sphere. They are used to preserve probability amplitudes. Each quantum gate is a different unitary matrix that changes the vector representation of the states of qubits. Ex:

Let the same quantum gate be applied to the different basic state and then let’s observe the 2nd state achieved:

The presence of negative entry is totally acceptable since, in order to get the probability that each qubit turns back into the basic state, we take absolute values. As a matter of fact, not only can these numbers be negative, they can also be complex numbers. What does that imply? It follows that the state of N qubits is actually represented on the sphere in the 2^{N} complex dimension. This has twice the dimensionality of the sphere in 2^{N} real dimensions. Imagine the enormous amount of superposition one can process. For example, if we have to perform a 6 qubit computation like <010001> (say), it is performing calculation using a sphere in a 64 dimensional complex sphere (since 2^{6} = 64), which is quite complicated and too lengthy. It took only four steps with a quantum computer to find this state which could take as many as thousands of steps using classical computation.

## The Potential of Quantum Computing

Quantum Computing holds great potential to revolutionize computation altogether as there are several amazing and useful applications for it. For example, it has applications in traffic optimization, finance, batteries, weather forecast, climate change, cybersecurity, cryptography, drug development, artificial intelligence, etc. Let’s take a look at a few of its applications.

### Cyber Security

Quantum computers are efficient in solving many complex problems. They can be used in random number generation (RNG) and in factoring large numbers. These categories of problems have profound implications for cybersecurity. For instance, random number generation is intrinsically associated with cryptography. To create true randomness using conventional computation techniques is highly difficult as traditional computers do not work on chance. Therefore, traditional RNG works on an algorithm known as a pseudo-random number generator, which isn’t truly random. They are provided with certain sets of instructions to execute tasks. In this manner, randomness is deterministic, and hence the security is compromised. For someone with the appropriate knowledge of RNG, decryption will be very much possible. Quantum random generators, however, make use of quantum optics which serves as a source to generate true randomness. Companies such as Quantum Dice and IDQuantique are developing this technology currently.

### Finance Modeling

Financial problems, specifically dealing with uncertainty and constrained optimizations, have a requisition for the ability to compute and assess the possible outcomes. The algorithms or models which banks use to compute potential outcomes are those which calculate statistical probabilities. These methodologies are quite effective. However, when seemingly low probable events occur more frequently, these fall into the fallible domain. The efficacy of machine learning to solve specific financial services problems is often hindered by conventional computers, whereas quantum computers assure quality solutions. Furthermore, risk analysis is hard to calculate for conventional computers since it’s challenging to analyze a large number of outcomes. The complex data structure poses challenges in finding patterns, doing classifications in targeting and prediction models, but with quantum computer’s data modelling capabilities, we might witness a game-changing revolution. Quantum computers provide quadratic speedups for such kinds of simulations. The complexity of trading and business could also be handled with quantum technology due to its combinatorial optimization capabilities.

In fact, the Covid-19 pandemic has shown that for financial institutions, punctual and precise risk assessment is still a challenge. The economic crises in the past two decades led to several changes in the policies of financial institutions. This introduced real-time risk models, which are highly complex but powered with artificial intelligence. But they are still powered by classical computers, thereby limiting their abilities. The arrival of quantum computers is most probably going to be revolutionary. However, it will take time until the necessary quantum algorithms are developed, and other required necessitations are met.

### Drug Development With Quantum Computing

The pharmaceutical industry is believed to enjoy promising benefits from quantum computers as they will transform and drive efficiencies for the pharma industry. Its prime aid would be in accelerating the discovery as well as research and development (R&D) of new drugs. Even though classical computers are widely used in drug development and discovery, with quantum computers and improved accelerated molecular comparison, enhanced quality of drugs in a comparatively lesser amount of time is possible, and thus, better predictions and know-how on the efficacy of the drug can be made. Quantum Computing can also reduce the costs of data-rich R&D procedures.

The current challenge in biopharma R&D procedure – from drug discovery to development is:

- Costly
- Lengthy
- Risky

It is estimated that it takes about 12-15 years to progress from the discovery of a drug to its launch. The cost for the same exceeds $2 billion with a success rate of less than than 10%. To study the interaction between a drug and its target in the human system, chemistry algorithms work on predicting how drug molecules will bind to particular target proteins by modelling the binding energy on such interaction. Quantum computers reduce the computation time for such simulations. For instance, modelling for some basic molecular structures of penicillin on the classical computer will take 10^{86} bits, whereas it would use as few as 286 qubits on a quantum computer.

### Quantum Computing in Weather forecast & Climate Change

Prediction of extreme weather conditions like heat waves, hurricanes etc., is quite necessary in order to prevent human fatalities and property damages. Prior insights into the same with increased accuracy can help in better preparation for the same and reduction in the losses.

Over the years, a lot of work is done in developing advanced computational models to enhance and improve forecasting with observable progress. However, when it comes to the development of numerical weather and climate prediction models, classical as well as supercomputers fail to meet the requirements. In fact, analyzing a huge amount of data with several dynamic variables such as temperature, pressure, and density in real-time is a challenging puzzle for conventional computers.

Quantum computers can improve the conventional numerical methods to boost predictions of weather conditions by handling a bulk amount of data containing several variables quickly and efficiently by harnessing the power of qubits and quantum optimization algorithms. Thus in the future, quantum computers will be capable of providing high precision weather forecasting at local as well as global level.

Quantum computing can also aid in fighting climate changes. As Richard Feynman (one of the fathers of quantum computing) put it, “Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical”.

Quantum computing can greatly aid humanity’s fight against global warming. So far, the earliest applications of it can predict emissions and facilitate emission reduction. Even though its full potential is decades away, the coming decade, referred to as NISQ (Noisy intermediate-scale quantum), will improve machines that are prone to errors and have limited computational capabilities. Progresses in hardware and software can enable these machines to model molecular interactions, involving as much as 150 atoms, accurately, and thus, can lead to the development of better and more efficient catalysts which can create breakthroughs in number of carbon-intensive processes by substantial emission reduction, including:

- Green Ammonia (Haber-Bosch process)
- Green hydrogen power
- Carbon Capture

With the help of quantum computing, chemical industries can discover new fertilization production chemicals, and thus, lower CO2 emissions. New quantum generated chemicals used to synthesize fertilizers will cut 3%-5% of the world’s natural gas consumption since quantum computer modelling can develop energy-efficient catalysts that will have promising potential to reduce CO2.

### Artificial Intelligence and Quantum Computing

Artificial Intelligence is also a transformational technology like quantum computing. AI has made rapid progress since the previous decade; however, it is likely to need quantum computing to achieve significant progress. With quantum computing, AI’s computational limitations can be worked out, and it can also tackle more complex problems. The development of quantum algorithms in AI will allow for massive improvisations in learning, reasoning and understanding of AI.

As per Ilyas Khan, CEO of Cambridge quantum computing, for the first time, Natural language processing (NLP) algorithm has achieved ‘meaning awareness’ on a quantum computer. This means the AI can understand the whole sentence rather than just individual words. Over time, this meaning awareness can be expanded to phrases and finally to an entire speech. Hence, AI and machine learning can greatly benefit from quantum computers due to the fascinating computational capabilities which will have applications in robotics, computer vision and NLP. Quantum computers can help to train machine learning models and create optimized algorithms, and thus one can complete years of analysis within days. When quantum computing and AI merge fully, it will be a mind-blowing breakthrough in the world of technology.

## Immediate Threats of Quantum Computing

When the time arrives that quantum computers become a part of our everyday life and solve the problems that a classical computer cannot, we say our civilization has achieved quantum supremacy. For now, quantum supremacy exists in pockets around the world, with only a few players to have achieved it. In 2019, Google announced that it has reached quantum supremacy and that its quantum computer is 100 million times faster than the classical computer. While we have already kind of understood how the quantum world will revolutionize the computation era in several fields, there is another side to look at as well.

There is a possibility that the powerful computational capabilities of quantum computers can pose serious threats to IT security, finance, communication, businesses, health records, research projects, government intelligence, and even national security. Quantum computing has the potential to disrupt modern cryptography, thus leading to what is being termed as ‘encryption chaos’. Some researchers believe that a universal 2000-qubit system could be just 5-10 years away. Now, we know sensitive information is passed across the internet. Take for instance, credit card numbers which are secured via public-key cryptography. A 2000-qubit system would easily be capable of breaking public-key crypto algorithms. In this regard, no one can really assume that their data will be safe anymore once a select few entities reach quantum supremacy.

Quantum computers do not only possess the potential to break public-key cryptographic systems, but they can also break symmetric and asymmetric cryptosystems. If that happens then, the integrity of Internet protocols like HTTPS will be dramatically compromised. This means secure browsing, online banking, online shopping, and other activities on the internet are not safe. Some malicious players can actually meddle with cybersecurity if they achieve quantum supremacy.

Take an example of end to end encryption used in messaging platforms such as WhatsApp. Currently, it is not at all easy for any hacker who tries to intercept coded messages sent to decrypt them. It would take approximately a thousand years to find all the possible combinations to break the cryptographic key even with the most sophisticated computers in the market. However, with quantum computers, these encryptions can be cracked in a matter of a few moments. How does that happen? Well, encryption algorithms are typically mathematical problems comprising large numbers. Encryption keys contain thousands of bits, and therefore, it is difficult to determine the correct combination. For example, WhatsApp uses a 256-bit version of the AES. This means to crack the encryption, one needs to encode the data into ciphertext that has 2256 possible key combinations (a number 78 digits long). For traditional computers, it is highly improbable to brute-force through every combination to arrive at the right one. Even one of the fastest supercomputers, China’s Tianhe-2 (Milky-Way-2), would take millions of years to crack 256-bit AES encryption. One can understand how safe our data is with cryptography. But, quantum computers will take minutes to crack these encryptions. Imagine how jeopardizing it is for modern cryptography. Quantum computers can factor large prime numbers. This ability will aid in breaking the RSA (Rivest-Shamir-Adleman) encryption system (an asymmetric algorithm for public-key crypto).

Among countries, China has already achieved quantum supremacy after developing a quantum computer that is 10 billion times faster than Google’s quantum computer. Since China invests billions of dollars in quantum technology, it wouldn’t be a surprise if it becomes the first nation to achieve quantum supremacy. While the quantum computer built by Google is using super cold superconducting metal, China has used a technology that manipulates photons to achieve the same results. This implies that there can be different ways in which quantum computers can be built with improvisations. In this manner, some players can be a step ahead and also take advantage of that position. It’s no wonder why rivals of Google such as IBM, Microsoft, Amazon and Intel have spent heavily on developing quantum hardware.

## Envisioning a Post-Quantum World

According to most experts, quantum supremacy is still 9 to 10 years away. Presently, quantum computers are not error-free and do not exercise their complete potential as well. This is because the procedure from its design to its maintenance is highly complex and also quite expensive. It means that there is time to think through the prevention of quantum attacks which will eventually become prominent in the future. That is where post-quantum cryptography dives in. While certain cryptography algorithms are quantum-safe, others are not. For example, public-key cryptographic algorithms like RSA, Elliptic Curve Cryptography and DLP (discrete logarithm problems) are unsafe. In contrast, Cryptographic hashes, MAC algorithms and symmetric key cyphers will be safe from quantum attacks.

The quest for quantum-resistant algorithms has already begun. The National Institute of Standards and Technology (NIST) has already initiated a process to develop post-quantum cryptographic algorithms. In addition, several mathematicians and programmers have started to find a replacement for integer factorization used in Public-key crypto and digital signatures.

Google, on the other hand, is trying a strategy to couple an elliptic curve crypto (ECC) algorithm with a post-quantum algorithm. ECC is stronger than RSA to break. Hence it can be used against quantum attack as well; even if quantum cryptography is broken somehow, the addition of ECC can still provide a certain level of security.

Other plans include the use of lattice scheme, code-based and multivariate scheme. Among these, lattice appears most promising. Imagine how hard it is to calculate the shortest vector (which is a quantum) of a large lattice. This is because it exists in more than one dimension.

The Quantum era is not far away anymore. The world has also started preparations for it. The challenge in this whole scenario is information asymmetry and disproportionate access to resources. In order to develop quantum algorithms, one needs knowledge of quantum mechanics and the necessary resources for the same. Quantum mechanics is an emerging field, and hence this process is going to be quite challenging. Quantum technology will change the shape of everything from business, and finance to health and the environment. The coming decades are going to be revolutionary in the techno world.

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