Introduction

Computation

At its most fundamental, a computation manipulates information. Classically, information in the form of bits (0s and 1s) follow basic rules in logic gates, which make up more complicated operations in modules, which in combination can ramp up the complexity of a computation.

Why bother going to the quantum realm?

In quantum computation, information is stored in quantum bits (qubits), which is in a superposition of 0 and 1. Intuitively, there seems to be extra room to store information in qubits, which we hope to exploit. To the best of our knowledge, quantum computing will be more powerful than classical computing. As an example, Shor’s algorithm has already demonstrated that quantum computers can solve a problem that classically seems impossible: the efficient factoring of large prime numbers.

Going quantum will also help physicists understand quantum mechanics. In the subatomic world, there are phenomena that we never experience as humans, so tinkering with quantum systems will help physicists experimentally learn QM. Additionally, physicists hope to simulate quantum physics with quantum computers, which requires incredible amounts of classical computing power.

It’s still unknown whether quantum computing will revolutionize computer science, prove too difficult to implement, or will simply be unimportant. Yet, there’s a lot of promise and cool things to do.

Qubits

So where’s the ‘extra’ information? Instead of taking on discrete values, the qubit takes on a linear combination of quantum states with arbitrary precision in the coefficients α (alpha) which take on complex-number values. Additionally, as quantum systems grow in size, the complexity scales exponentially. For example, a two-qubit system may have four coefficients:

We can imagine a 500-qubit system in which there are 2^500 coefficients to account for all possible states. A system of this size has more coefficients than there are atoms in the universe. Manipulating all these coefficients simultaneously would perform computations with incredible amounts data.

What can we use to make qubits? Anything that behaves quantumly as described in the Double-Slit Experiment! We’ll talk about the consequences of the Double-Slit for our purposes next.