Quantum Computing for Everyone

by Chris Bernhardt

quantum computing and classical computing are not two distinct disciplines, but that quantum computing is the more fundamental form of computing—anything that can be computed classically can be computed on a quantum computer.

The book concludes with the realization that quantum computation is not a new type of computation but is the discovery of the true nature of computation.

A qubit can be represented by the spin of an electron or the polarization of a photon.

In quantum mechanics, we are often considering tiny particles like atoms or electrons. Here bouncing photons off them has an effect that is no longer negligible. In order to perform some measurement, we have to interact with the system. These interactions are going to perturb our system, so we can no longer ignore them.

There is no real randomness in classical mechanics, just what is often called sensitive dependence to initial conditions—a small change in the input can get amplified and produce an entirely different outcome.

Although the actual computation will involve qubits, the final answer will be in terms of classical bits.

We have only just started our study, so we are quite limited in what we can do. We can, however, generate random strings of binary digits. The experiment that generated random strings of Ns and Ss can be rewritten as a string of 0s and 1s. Consequently measuring spins of electrons first in the vertical and then in the horizontal direction gives a random string of 0s and 1s. This is probably the simplest thing that we can do with qubits, but surprisingly this is something that cannot be done with a classical computer. Classical computers are deterministic. They can compute strings that pass various tests for randomness, but these are pseudorandom, not random. They are computed by some deterministic function, and if you know the function and the initial seed input, you can calculate exactly the same string. There are no classical computer algorithms that generate truly random strings. Thus, already we can see that quantum computations have some advantages over classical ones. Before we start to describe other quantum computations we need to develop a precise mathematical model that describes what happens when we measure spin in various directions. This is started in the next chapter where we study linear algebra—the study of the algebra associated with vectors. * We will keep using the term spin because it is the standard terminology. But we are just determining the axis of the poles of a magnet.

If the lists are written vertically, we call them column vectors or kets. If the lists are written horizontally, we call them row vectors or bras.

Vectors of length 1 are called unit vectors. Later we will see that qubits are represented by unit vectors.

Once quantum computers have more than 72 or so qubits we will enter the age of quantum supremacy—when quantum computers can do computations that are beyond the ability of any classical computer.

In this light, classical computation seems an anthropocentric version of what computation really is.