Why Quantum Computing
Exploring the Nature of Quantum Computation — Part 1
Introduction
Classical computers have come a long way over the last decade, both in terms of the increase in computing power and the reduction in cost of computing power. For research purposes, there are also supercomputers available, with thousands of CPU and GPU cores to solve difficult problems. However, even supercomputers struggle to solve certain very complex problems as these are still binary-code based machines. This is where quantum computers come in as theoretically these computers would be able to solve these complex problems.
This article will not go into the details of quantum mechanics but will dive into how the laws of quantum mechanics can be exploited for complex computation. Before we delve into the details let’s explore why do we need quantum computing in the first place.
Why Do We Need Quantum Computing?
To illustrate the advantages of quantum computing, let’s explore using a game of pachinko but instead of a ball we will use a photon with beam splitters at every corner of the pachinko.
Let’s assume that the beam splitter provides a 50% probability of the beam to either go right or left. When we shoot a single photon, we can easily calculate the probability of each outcome. When we shoot two photons at the top of grid, the game now behaves differently to the classical game with balls. When the two photons meet on the grid, they interfere with each other, whereby they can add up and appear like two photons or cancel each other out. Given this interference, the only way for us to computationally predict the outcome is to trace every possible combination of paths for each photon and calculate the interference effects where the photons meet. How computationally expensive is that to simulate on a classical computer? Not so much on a small grid but if the grid becomes too large then it becomes expensive and at some point too complex for the classical computer to solve.
For a game with 2 photons, for a classical computer to simulate every possible path and interference will take roughly 2ⁿ² x t. For the quantum computers, think about solving this slightly differently. Instead of trying to solve it deterministically by finding probability for each outcome, we will add detectors at the end of the pachinko game to observe where the photons emerge from and then calculate the probability of each outcome. We do not have to compute all the paths based on the rules of quantum mechanics, because quantum objects follow quantum mechanics as a matter of course. The time to perform this experiment would be n x t, where t is the time it takes to observe one experiment. Now as the game gets bigger and more layers are added, the time for the quantum experiment increases linearly while the time for classical computation increases exponentially.
The difference between both approaches is that with classical computers we were doing a calculation whereas with quantum computing we are doing calculation by doing measurements of an experiment on quantum objects. This is where quantum computing is different and provides an advantage to classical computers. To the extent, we can define our computational problem onto quantum objects, we will be able to solve that problem much faster using quantum computing.
As of the date of this article, a universal quantum computer is a major goal in the field of quantum computing. The majority of quantum computers currently existing are either specialized or noisy intermediate-scale quantum machines (NISQ). These are not yet universal and are limited in their capabilities, primarily due to issues like error rates, quantum decoherence and limited numbers of qubits. Having said that, stay tuned to learn how to construct quantum circuits, perform quantum teleportation, break the RSA algorithm (prime factorization) and error correction.
This is Part 1 in a series of articles on quantum computing. The links to all the parts are below:
