Quantum Computer: An Introduction

 Back in the day oil used to be the most valuable commodity, for reasons that are obvious and require no elaboration. Every commanding and capable nation-state aspired to acquire it. This is true to a great extent even today, but in the digital world of the 21st-century data has reached that pinnacle where it stands a robust chance of dethroning oil to become the most lucrative thing.

For a theoretical assessment, data and oil seem to be quite analogous to each other. In the same way as crude oil found in the natural reserves requires refining and filtration to yield Diesel, Kerosene, Petroleum, etc.; correspondingly data in its raw form prerequisites analysis and processing to construct useful and usable information, which can potentially be employed to influence elections, commerce, policy-making, security, sovereignty, and so forth. Data is an enormously treasured resource that could be put to dangerous use. It is out in the open that data is traded today. If not monitored and shielded properly, data can be expended as a tool for exploitation and abuse.

Data is broadly categorized into two types: private and public. Public data is something that is out there in the open, unrestricted, and easily accessible; such as addresses, birth registers, death files, employment details, vehicle registration, etc. In contrast, private data is classified or/and personal and is accessible only to an individual, family, or an establishment – which may be an organization or a country. Private data may comprise banking details, browsing history, chats, family particulars, financial information, mandate, medical records, military intelligence, national secrets, passwords, photographs, transaction records, voting figures, or a combination of these and/or any deductions extracted from their investigation. Private data is exclusive and thus its usage and circulation are restricted, and may count as a criminal offense if violated.

The safety of classified data is the key to the smooth functioning of every entity - from local enterprises to governments. Any compromise in it could lead to chaos and a probable standstill. Law alone is not enough to ensure the protection of private data. Law merely dictates what is permissible and what is not, and how the non-compliant be punished in the event of a violation.

Data protection entails rigorous infrastructure. Building such an infrastructure requires an understanding of the points in the system where safety can be compromised. Roughly, these points can be branded as the ‘banks’ and the ‘roads’. Banks here refer to the storage facility where the files are stored, these may be hard drives or data warehouses. Roads may be described as the communication channel - the pathway through which the data travels between two nodes, these may be wired or wireless. The thief may access the private data from either the warehouse or by tapping into the communication channel illegally.

As in the case of a bank heist, robbing a bank is harder than robbing the bank’s van while it is in transit with the money. Accessing protected data through the warehouse is a comparatively tough job. It is not impossible and can be achieved through a solid disguise, accomplice, or theft. So, the best bet for an eavesdropper or a black hat hacker would be to try to illegally intercept the communication channel and gain access to the data while it travels from one node to the other.

When it comes to data security, cryptography is employed to preempt unlawful interception. It refers to the practice of encoding data so that it could only be read by authorized people. The sender uses a set of rules to scramble (encrypt) the data and transmit it over a communication channel. The receiver upon receiving the scrambled data uses some algorithm (key) to unscramble (decrypt) it. Even if an evil entity intercepts the data, it will not be able to make any sense of it because of the lack of the key.

Back in the day, cryptography was used by kings to transfer messages from one place to another. To maintain secrecy of the message the sender would often make use of various techniques such as:-

1. Transposition ciphers: these involve rearranging the order of letters. An example of this is the Caesar cipher in which each letter in the message is replaced by a letter some fixed number of positions further down the alphabet.
2. Substitution ciphers: it involves systematically replacing letters or groups of letters with other letters or groups of letters.
1. The substitution schemes of Kautiliyam and Mulavediya were utilized in ancient India. In Kautiliyam, the substitutions were based on phonetic relations, such as vowels becoming consonants. In Mulavediya, the substitutions consisted of pairing letters and using the reciprocal ones.
2. Atbaš was an early Hebrew monoalphabetic substitution cipher in which the first letter becomes the last letter, the second letter becomes the second to last letter, and so on.

Upon scrutiny, such classical methods often divulge some statistical evidence that could be employed to break the encoding. The discovery of frequency analysis by the Arab mathematician Al-Kindi in his book entitled Risalah fi Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages) turned out to be advantageous to cryptologists.

Prior to the early 20th century, cryptography was mainly related to lexicographic and linguistic patterns. During WWII, British invention of Colossus – world's first fully electronic, digital, programmable computer –facilitated the decryption of codes generated by the German Army's Lorenz SZ40/42 machine.

In general, Modern Cryptography can be categorized into three types:

1.      Symmetric Cryptography: a system where the sender and receiver use the same key for encryption and decryption.

2.      Asymmetric Cryptography/Public-Key Cryptography: a scheme where a pair of keys is used to encrypt and decrypt the data. A public key is used for encryption and a private key is used for decryption.

3.      Hash Functions: these do not warrant the use of any key, instead a hash value of a fixed length is calculated. The calculated value depends on length of the data, which makes it almost impossible for it to be cracked.

The most indispensable patriots in the encryption war are prime numbers. These are essential to the most widespread type of encryption used today - the RSA algorithm (Rivest–Shamir–Adleman). Small numbers are trivial and can be cracked easily, but when much larger primes, hundreds or maybe thousands of digits long are chosen, the decryption task demands great computation power. The reason prime numbers are vital to RSA encryption is that when two numbers are multiplied together, the result is a number that can only be broken down into those primes. When large prime numbers are used it becomes next to impossible for computers to identify them.

Computers are getting faster and more powerful all the time, so mathematicians continue to search for large prime numbers. But when quantum computers capable of performing billions of calculations each second start unpicking public keys to break them down to their primes, RSA and other such cryptographic techniques will no longer be safe. This is where quantum physics comes into play.

Quantum physics describes the behaviour of atoms and fundamental particles such as electrons and photons. A computer founded on the principles of quantum physics is called a Quantum Computer. It operates by controlling the behaviour of the fundamental particles through superposition, interference, and entanglement. It is totally different from the classical computers – the computers currently in use.

 Superposition means that any number of quantum states can be added together to produce a valid quantum state. Conversely, any quantum state can be represented as a sum of distinct quantum states. Superposition produces entangled states – states that cannot be written as a product of other states, i.e. they are non-separable.

Quantum Entanglement is the phenomenon wherein a pair of particles share spatial proximity in such a manner that the quantum state of one particle affects the other irrespective of the distance between them. The effect of one state on another is instantaneous! Entanglement is a basis-independent result of superposition.

IBM Q System One

Classical computers use binary system for data representation and transmission. Bits, practically a stream of electrical or optical pulses, represent 0 or 1 to quantify computer data. Every piece of information is essentially long strings of binary digits. A quantum computer is completely different. It is not just a more powerful version of the current computers just like a light bulb is not a more powerful candle. You cannot build a light bulb by building better and better candles. A light bulb is a different technology based on a deeper scientific understanding. In the same vein, a quantum computer is a new kind of device based on the science of quantum physics.

A quantum computer uses the quantum counterpart of the classical bit - the quantum bit, or the qubit. A qubit is a quantum state which has a fluid, non-binary identity. In addition to being either 0 or 1, a qubit can exist in a superposition, i.e., a combination of 0 and 1; with some finite probability of being 0 and some finite probability of being 1. In other words, its identity lies on a spectrum.

Before the measurement is initiated a qubit can exist in superposition where it has a relative probability of being in either 0 or 1 state. It is to say that it could have a 70% chance of being 0 and a 30% chance of being 1, or 80%-20%, or 60%-40%, and so on. However, upon measurement, it is observed that the state is either 0 or 1. The key idea here is to give up on precise values of 0 and 1 while defining a state and allow for some uncertainty.

Classical bit vs Qubit

An assembly of qubits can provide far greater processing power than the same number of binary bits. In a conventional computer, doubling the number of bits doubles the processing power; for two bits, 0 and 1, there are four possible combinations, namely, 00, 01, 10, and 11. Quantum physics, instead, permits for superposition of each one of these four states. Hence, while a combination of two classical bits provides only two bits of information, the superposition of two qubits gives four levels of information. Similarly, three qubits would provide eight levels, whereas in the classical realm it is just three bits. It is not difficult to comprehend that for the same number of states, a quantum computer gives an exponential rise in processing power.

Quantum computers could be utilized to build advanced cryptographic technologies. The uncertainty principle can be used to create private keys for encrypting data that is to be transmitted from one location to another. As the no-cloning theorem states that it is impossible to copy data encoded in an unknown quantum state, an eavesdropper would not be able to perfectly copy the key secretly. Moreover, his mere attempt to read the key would reveal his presence because no quantum entity can be read (measured) without changing (disturbing) it. Thus, a bad man would have to break the laws of quantum physics to decipher the key – which is impossible!

Quantum Key Distribution is one of the most well-known applications of the field of quantum cryptography. It is used only to generate and distribute a key; and not to transmit any data. The produced key can then be used with any encryption algorithm of preference to encrypt and decrypt the data, which can then be transmitted over a standard communication channel.

BB84 is the first-ever quantum cryptography protocol, which was developed by Charles Bennett and Gilles Brassard in 1984. It specifies a method of securely communicating a private key for use in one-time pad encryption. The idea here is to encode every bit of the secret key into the polarization state of a single photon. Because the polarization state of a single photon cannot be measured without destroying the photon, this information will be ‘fragile’. An eavesdropper who attempts to detect the photon will inadvertently reveal their presence as the photon transferred through them will be in the wrong polarization state (measurement disturbs the quantum state). The protocol is as follows:

1.      The sender sends a sequence of pulses, each of which, ideally, contains a single photon polarized differently. The 0s are encoded into H-polarized photons while the 1s are encoded into V-polarized photons. This happens only in half of the cases. The other half of the bits, chosen randomly, are encoded using a diagonal polarization basis; where the ‘D’ polarization corresponds to 0 and the ‘A’ polarization to 1.

2.      The receiver measures the polarization to distinguish between the polarization states and the bases (HV or DA).

3.      After a certain number of bits has been transmitted, the receiver publicly announces which basis they used for each bit. The sender then reveals the cases in which they used the same bases. They throw out the bits where the bases turn out to be different, and keep only those where the bases are same. After this procedure, known as key sifting, the length of the key is reduced, and what remains is random and coincides with the sender and the receiver.

4.      Afterward, they check for eavesdropping. To this end, they take a part of the key, say 10%, and compare it. As this procedure is public, the used part (here 10%) of the key is discarded. If eavesdropping took place, the key would contain errors. In that scenario, the entire key is thrown out and the whole procedure is repeated again.

A quantum computer channels the numinous phenomena of quantum physics to endow gigantic leaps ahead in processing power. Quantum machines are set to outshine the most powerful of contemporary supercomputers. Quantum computing promises machines capable of operations no classical computer could perform, such as modelling the physics of molecules or breaking today’s strongest encryption. But to do that they’ll need to contain a great number of qubits – maybe millions, perhaps billions! Though quantum computers have greater computational and processing power, these are more prone to errors because of decoherence – a process in which interaction with environment leads to the destruction of interference resulting in the loss of quantum nature of qubits.

As far as the physical realization is concerned, quantum dots can be employed to physically implement the qubits. As in single atomic systems, quantum dots also have discrete quantum states. However, unlike a single atom, quantum dots can be blended within photonic chips without great difficulty thus making them capable of being used as a source of polarization-entangled photon pairs.

A research time led by Dr. Pan Jianwei in 2017 was successful in achieving a point-to-point quantum key distribution based on entanglement between distances ranging from 100 to 1000 KMs with the use of Mozi – the first ever quantum satellite – and ground telescopes.

Just as the invention of transistor – another consequence of quantum physics – proved to be iconic for the electronic industry, likewise, the camaraderie of quantum physics and nanotechnology will prove to be legendary for the new-age computer industry.