Introduction to Quantum Computing
In this first installment, we will cover a few basics, recent speed achievements, and the considerations of Quantum Computing in the economy.
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I intend to write a series of articles on Quantum Computing. In this first installment, we will cover a few basics, recent speed achievements, and the considerations of Quantum Computing in the economy.
The dictionary definition of the word 'Quantum' is:
an amount of something and the smallest amount or unit of something, especially energy.
As dictionary.com adds, it is also used to mean a large quantity, i.e., as a synonym to bulk, as well as sudden and significant as 'a quantum of productivity.' Thus, we have four meanings of the word quantum in normal usage.
Used as an adjective to other words like physics, mechanics and computing, it forms terms whose significance explodes. As software developers, our area of interest is the one that's pushing the boundaries of the Information Technology industry - Quantum Computing.
As investopedia states,
"Quantum computing is an area of computing focused on developing computer technology based on the principles of quantum theory, which explains the behavior of energy and material on the atomic and subatomic levels."
In classical computers, the fundamental abstraction of computing and information storage is the bit. It has two states: zero and one, represented mathematically as 0 and 1. However, Quantum Computing relies on quantum bits, called qubits. They exist not only in the two states but also in a combination of these states called a superposition state. It is the ability to be in many states at the same time that gives tremendous power to quantum computers.
Quantum Theory uses the bra-ket or Dirac notation introduced by the English physicist Paul Dirac. In mathematics, the inner product essentially is multiplying the components of two vectors and adding them up. Instead of going with the traditional mathematical symbols, Dirac used angle brackets and bar to denote the inner product as ⟨u∣v⟩.
The left part, ⟨u∣ is called a bra and the right part ∣v⟩ is called a ket. The ket is just a different way of representing a vector. The bra represents its Hermitian adjoint, containing the complex conjugates of u's elements. If kets are column vectors, then bras are considered row vectors.
Using the ket notation, the state zero is represented by |0⟩, the state one by |1⟩ and the superposition state by |ψ⟩. The mathematical relationships are as follows:
|ψ⟩ = a |0⟩ + b |1⟩
a and b are complex numbers of the form z = x + iy where i = √-1.
a2 = probability of finding |ψ⟩ in state zero
b2 = probability of finding |ψ⟩ in state one
|a2| + |b2| = 1
The key point to remember is that a general qubit is never observed and when it is measured, it automatically becomes a bit.
Google researchers in 2019 ran benchmark tests to create quantum states on 53 qubits and sampled the resulting probability distribution. A classical supercomputer would take 10,000 years to run the same test. (IBM has contested the claim, though).
In 2020, computer scientists in China reported that using photonic quantum computers they ran a statistical calculation, the Gaussian Boson sampling to detect up to 76 photons in just over three minutes. One of the world's fastest computers, TaihuLight would have taken 2.5 billion years to perform the same calculation.
Going forward, we expect tremendous advancements in the speed and complexity of the tasks that quantum computers would execute. In fact, IBM has released its quantum roadmap towards building an open quantum software ecosystem, of which a key milestone is building an 1121 qubit machine in 2023. To put that in perspective, a 100 qubit machine will outperform all the current supercomputers in the world combined.
It is not just the USA and China that are focusing on Quantum Computing. Governments around the world have been factoring in the impact of quantum computing on their economies and investing in it to propel their growth.
Australia's national science research agency, the Commonwealth Scientific and Industrial Research Organisation (CSIRO) predicts that by 2040, the quantum technologies industry could create 16,000 jobs and over $4 billion in revenue.
A Canadian government website projects that
"by 2030, Canada will be able to grow an $8.2 billion quantum technology industry, employing 16,000 people and generating $3.5 billion in returns for the government. By 2040, when quantum technology is expected to reach 50% adoption, it could grow into a $142.4 billion industry, creating 229,000 jobs and generating $55 billion in government returns. The Canadian economy in 2040 is projected to be $4.2 trillion, putting quantum technology at approximately 3.4% of the economy in that year."
The UK has avowed to remain at the forefront of quantum research and has committed £1 billion to a 10-year program to boost quantum technologies. It has launched the National Quantum Computing Centre (NQCC) with £93 million to foster the commercialization of quantum technologies. Also on the cards is a £10 million quantum computing system that is to be made available to businesses via cloud.
QaaS (qubits-as-a-service) which is already a reality will become more affordable. Society at large will benefit hugely from the advances in quantum computing. Productivity gains in 2020-2024 in the U.S alone are expected to be between $2 to $5 billion. Quantum Computing will create thousands of jobs across the world in the coming years and impact humanity with such beneficial developments as quicker drug discovery.
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