# Quantum Computing Basics

# Quantum computing harnesses the rules of quantum physics to perform computation.

Farai Mazhandu

# Quantum computers are a radically different kind of computer that is based on the laws of quantum mechanics. They have the potential to solve problems that scale up very fast and thus are challenging to classical computers. It is now possible to access real quantum computers through the cloud to conduct experiments and explore new problems.

**Bits and Qubits**

Computation and data storage in all modern systems takes place in so-called ‘bits’ — digital systems with only two discrete states (e.g. the on and off states of a transistor or north and south-pointing magnetic fields which can be extended in quantum cases to up and down pointing of spin). The two states of these bits are referred to (in a mostly arbitrary way) as ‘0’ and ‘1.’ Since

classical bits can occupy only one of the two available states at a time, a string of n bits can represent only one element of a 2^n (2 to the power n) space. Representing the full space, containing 2^n possible arrangements of bits, therefore requires 2^n bits (this assumes no compression which is the case when performing most computations of interest).

A classical bit, the “bit” is realized physically as a level of voltage across a particular element representing the bit in an electrical circuit. This voltage could be across a capacitor or a transistor, etcetera. A quantum bit is realized in a quantum mechanical system with two distinct states, much like a classical bit, but due to the superposition ability of quantum mechanical systems a qubit can exist in a continuum of possibilities between and including 0 and 1. This superposition of states is one of the key differences between a classical bit and a quantum bit.

In summary, classical bits are discrete-number of possible states is 2(0 or 1)and deterministic: repeated computations on the same input will lead to the same output, whilst qubits have an infinite (continuous) number of possible states that are probabilistic: measurements on superposed states yield probabilistic answers (our confidence in these answers builds up through repeated computations) then reduced to 0 or 1.

**Types of quantum computers**

There are several approaches to building quantum computers. The most practical types today are the adiabatic quantum computer, quantum simulation and the universal quantum computer (standard/gate model quantum computer).

*Quantum Annealing*

Also called adiabatic quantum computers, this approach uses a result known as the adiabatic theorem to perform calculations. They are best suited for solving optimization problems, which are ubiquitous across industries and require deep resources to solve by classical computing methods. Quantum annealing is the least powerful and most narrowly applied form of quantum computing. In fact, experts agree that today’s supercomputers can solve some optimization problems on par with today’s quantum annealing machines.

*Quantum Simulation*

Developments in the field of quantum technology suggest that quantum simulators are becoming the first short-term application of quantum computers. The benefit of quantum simulators stems from the fact that they offer a platform to test thoughts and ideas involving quantum mechanics

which their classical peers struggle to handle, and they can deliver on this with modest hardware capabilities. In order to build a useful quantum processor more stringent requirements have to be met. There are a variety of problems where simulators can be employed immediately like in chemical simulation, drug discovery, artificial intelligence, process optimization, high energy physics, and condensed matter physics.

*Universal Quantum Computer*

The most useful and technically challenging device to build because they are extremely hardware-specific. Gate model quantum computers perform

calculations by manipulating quantum states via application of gates — a basic quantum circuit operating on a number of individual qubits. These quantum gates form building blocks of quantum circuits in a manner similar to how classical logic gates form the building blocks of conventional digital circuits. A truly universal quantum computer would likely make use of over 100,000 qubits.

The basic idea behind the universal quantum computer is that you could direct the machine at any massively complex computation and get a quick solution. This includes solving the aforementioned annealing equations, simulating quantum phenomena, enable machine learning that is faster than that of classical computers and more.

Today’s quantum computers include thousands of parts that work together to harness qubits to perform quantum computations. Qubits themselves are incredibly powerful, yet delicate. They quickly lose their special quantum properties, typically within 100 microseconds (for state-of-the-art superconducting qubits), due

in part to electromagnetism, vibrations, and temperature fluctuations from the surroundings. To make quantum computers more reliable and stable there is need to harmoniously combine different technologies that complement each other.

**Why quantum computation?**

Quantum Computation is the art of manipulating the time evolution of highly complex, entangled quantum states in physical hardware registers for computation and simulation. The origins of quantum computation are often attributed to Feynman’s 1982 discussion of a universal quantum simulator. It is from this initial proposal that further theoretical work has been done to develop quantum algorithms, which would work on universal quantum computers and allow for processing speeds that exceed known classical algorithms.

The development of robust quantum algorithms has been somewhat slow, in part due to the challenge of retrieving the answer from our quantum computer. While it would, of course, be possible to perform repeated measurements to map out the full 2^n states in our quantum system this would take exponential time and would negate any time savings from the parallel computation. Effective algorithms must, therefore, find ways to map the 2^n computation states to only n measurement states.

One may therefore ask; why are we so interested in quantum computers and quantum simulators? The basic response is that quantum computers have certain problems they can handle much faster than classical computers. Hard problems are not only a question of whether they take a long time- the question is whether they can be solved at all and efficiently with available resources.

We should take note that by maximally entangling n qubits (coherently) we can create a quantum system which simultaneously probes all elements of the possible 2^n states contained in the computation space. With appropriate algorithms, we can utilize this massive entanglement to parallelize calculations which can only be performed in a serial process using classical computers, thus realizing a massive quantum speedup as problems scale to larger and larger data sets.

A very good illustration of scaling is the famous wheat and chessboard problem. If a chessboard was to have wheat placed upon each square such that one grain was placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent square), how many grains of wheat would be on the chessboard at the finish?

The total number of grains equals 18,446,744,073,709,551,615, (1,199,000 million metric tons) whilst the approximated global amount of wheat produced in 2016/2017 came to about 755 million metric tons.

This illustrates how quickly exponential sequences grow and justify the criticality of the 2^n space to the operation of a quantum processor.

The first useful quantum algorithm was Shor’s algorithm proposed in 1994. This algorithm utilizes some clever, yet fairly straightforward, number theory manipulation to transform the problem of integer factorization into the problem of finding the period of a function. While integer factorization may not seem important to the layperson, it along with the related discrete logarithm, underlies many modern encryption schemes, the most well-known of which is RSA (Rivest-Shamir-Adleman) public-key cryptography. Other popular quantum algorithms include the Deutsch–Jozsa algorithm, Simon’s algorithm, Grover’s algorithm (*searches an unsorted database of**size N in time O (sqrt[N]) while the best classical computer requires time O (N) — classically we can do no better than to look at each element until we find the right one, taking on average N=2 time*), and Quantum phase estimation algorithm amongst others. More specific quantum architectures such as quantum simulators, quantum annealers, and perhaps adiabatic quantum computers may also provide advantages in addressing specific problems of interest.

Consider that to fully model caffeine’s behavior, including quantum mechanical rules affecting its individual particles, is not currently possible with conventional computers and might take up to 160 qubits. A single caffeine molecule is made up of 24 atoms and it can have 10^48 quantum states (there are only 10^50 atoms that make up the Earth). Modeling caffeine precisely is simply not possible with classical computers. Using the world’s fastest supercomputer it would take 100,000,000,000,000 times the age of the universe to process the 10^48 calculations that represent all of the possible states of a caffeine molecule. Currently, Google’s Bristlecone quantum computer has 72 qubits whilst IonQ and IBM have computers with 79 and 50 qubits, respectively. Other players working on this technology include Microsoft, Intel, Rigetti, D-Wave Systems, and Alibaba.

**Applications of quantum computing**

Some of the hardest problems that can be resolved by quantum computers range from accelerating new breakthroughs in science and improving the discovery process for drugs, fertilizers, and sustainable energy resources, optimizing routing and supply chains, managing distributed electric grids, machine learning methods to diagnose illnesses sooner, materials to make more efficient devices and structures, accelerating computationally intensive machine learning algorithms to quickly allocate resources. These challenges are currently intractable using classical computers due to their size and complexity. We just don’t have enough computational power on Earth to tackle them due to the faltering of Moore’s Law which state that processor speeds or overall processing power for computers will double every two years.

The limitation which exists is that once transistors can be created as small as atomic particles, then there will be no more room for growth in the CPU market where speeds are concerned. This challenge makes quantum computing more important as a possible way to continue progress in the industry. As transistors get smaller approaching the nanoscale range quantum mechanical effects start impacting the reliability of circuits. The good thing is that quantum excitations in condensed matter can be harnessed to address computation and storage demands at the atomic level. To stand a chance at solving some of these problems, we need a new kind of computing. Universal quantum computing leverage the quantum mechanical phenomena of superposition and entanglement to create states that scale exponentially with the number of qubits or quantum bits thus allowing massive parallel processing.

**The future of quantum computers**

It is not the intention of quantum computing to replace high-performance classical computing. Quantum computers are good at finding optimum solutions to problems with a seemingly infinite number of variables, protecting sensitive data and communications, and accurately simulating quantum phenomena and molecular behavior.

Quantum cloud computing is emerging as a promising field within the industry. Quantum cloud platforms could simplify programming and provide low-cost access to quantum machines.

That quantum computing will transform industries is not in doubt. It is now a matter of identifying quantum computing use cases with near-term value.

“No one knows where we’ll go off to in the end, but people are starting to see that if you take it (quantum computing) and combine it with classical computing in clever ways, you can get something that might look feasible.” Jeffrey Welser, vice president and lab director at IBM Research at Almaden.

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Farai Mazhandu

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