When the world’s first digital computer was completed in 1946 it opened up new vast new worlds of possibility. Still, early computers were only used for limited applications because they could only be programmed in machine code. It took so long to set up problems that they were only practical for massive calculations.

That all changed when John Backus created the first programming language, FORTRAN, at IBM in 1957. For the first time, real world problems could be quickly and efficiently transformed into machine language, which made them far more practical and useful. In the 1960’s, the market for computers soared.

Like the first digital computers, quantum computing offers the possibility of technology millions of times more powerful than current systems, but the key to success will be translating real world problems into quantum language. At D-Wave, the first company to offer the technology for commercial use, that process is already underway and it is revealing massive potential.

# Introduction to Quantum Computing

**[CBPrice Draft1 17 ^{th} March 2012]**

**[CBPriceRev5 20 ^{th} March 2012 10.00]**

## Introduction

Quantum Computers use atoms or molecules or photons of light to compute. These are all incredibly small compared to *classical* objects such as billiard balls or integrated circuits, and so to understand how they are designed, we need to understand *quantum physics* rather than *classical physics* since it is quantum physics that describes these small entities. There’s some surprising behaviour to be had at this atomic scale as we shall discover. As an aside, it is possible to compute anything, using billiard balls!

Let’s remind ourselves of a classical computer gate, the NAND gate. This is a fundamental gate since all computing circuits (the CPU, memory etc.) can be constructed using only NAND gates. Here’s a NAND gate with its associated *truth table* which explains how the outputs are generated from all possible inputs.

This is simple to understand, each input consists of a *bit* which can either be in the state “1” (on) or “0” (off) and the output bits are also either 1 or 0. When we are dealing with quantum computers, we also think in terms of bits, we call these *qubits* (pronounced “kewbits”), though these are fundamentally different from classical digital bits. The notation for a qubit is a little strange, the “on” and “off” qubits are represented using the notation and . These strange symbols are called “kets”, they are the right-hand bit of a “bra-ket”. Whenever you see a ket, think qubits! Consider a single input quantum gate, the **X-Gate** which we shall discuss shortly. It has a single qubit input and a single qubit output. But there’s something strange about the output. Whereas the output of a classical gate *has to be* either 1 or 0, the output of a quantum gate can be or , but it can have *any value in between*, for example 0.7*+0.7*. This is really strange. Even stranger is the fact that when we actually look at the output of the quantum gate, then this in-between value will “collapse” into either or . This will be explained in detail below.

An example may help. Let’s think of a quantum computer built using atoms. An atom can exist, e.g., in two energy states, low and high. You could get the atom to move from a low to high state of energy in many ways, you could zap it with a pulse of laser light, or you could put a load of atoms into a box and heat it up.

We could associate the low energy state with the value and the high energy state with the value . But the atom’s energy could be anywhere between the low and high states. Only when we observe the atom does it jump into either the low or the high e

nergy state. This is illustrated below.

# The Concept of Base States and Superpositions. A Single qubit.

Just like classical gates must have an output 0 or 1, quantum gates can have an output or . These qubit states are called the **base** states. But we mentioned that qubits can exist in any in between state. A good way of representing the state of a qubit is as a position on a circle. This is shown below. The left circle shows the location of the base states on the circle. State has coordinates (1 0) and state has coordinates (0 1). These pairs of numbers are called *vectors*. The right circle shows a qubit in a mixed state, half

and half . Remember that until we measure the output of a quantum gate, the output qubit’s value may exist anywhere on the circle.

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References :

heres-how-quantum-computing-will-change-the-world

Introduction to quantum computing