What are quantum computers?

Quantum computers compute with quantum states using the subtleties of quantum mechanics to, for suitable problems, do more than we know how to do with classical computers. They are particularly beneficial for simulating other quantum systems such as problems in chemistry and biochemistry where the electrons that form chemical bonds behave quantum mechanically.

That's a big deal: Unlike classical computers that struggle to do in silico (by computers) what is relatively easy to do in vitro (in a lab experiment), quantum computers will excell at computing even what is hard to do in the lab. That includes things like designing proteins for tasks where mother nature does not provide a template: It goes far beyond even the big dreams genetic engineering fuels, it levels that up to become highly targetted genetic engineering. Imagine fuel plants that are truly climate neutral by igrowing a tap for alcohol fuel, or retrofitting human cells to combat effects of aging: Quantum computers can be the solution to the really big challenges and ambitions.

Would you like to know how quantum computers work? Then read on!

How do Quantum Computers Work?

What is a Qubit and What can one do with it?

A qubit or quantum bit is the smallest unit of information that a quantum computer can operate on. It consists of two states which one calls state 0 and state 1 (or |0> and |1> using a common notation named after Nobel Laureate Paul Dirac).

A qubit is more than a regular bit. A bit can only ever be in one state, either 0 or 1. A quantum bit can be in any superposition of these states, meaning that it can (but does not have to be) in both states simultaneously.

That's not magic but quantum mechanics: Every state represents some kind of wave (which we don't necessarily have to imagine as such). But if you know waves, you know that they have amplitudes (their height) and phases (the timing where they are on the way between crest and trough). And it all goes in circles, like any of the following ones:

trough crest neutral opposite neutral
-i |0⟩ i |0⟩ -|0⟩ |0⟩
-|1⟩ |1⟩ -|0⟩ |0⟩

Just like a wave can be pictured as a rolling wheel (first picture), states can be changed like rotating a circle (next two pictures). The difference between the two pictures relating to states are the directions in which we turn what really is not a 2-dimensional circle but the surface of a 4-dimensional sphere to which the circles belong.

That is all one can do with a single qubit: Rotate it. In fact, that is all one can do with a number of qubits, except that the dimensions along which one can rotate become huge quickly: They grow exponentially in the number of qubits.

What is a Quantum Gate and how does it act?

The rotations that can be done to qubits have a name: They are called quantum gates in analogy to the circuit elements, or gates, that form classical computers. Quantum gates are drawn as a box with a letter or other description inside. The qubits used as input and output are drawn as horizontal lines from left to right. Everything together is a quantum circuit, such as this:

|0⟩ H

This quantum circuit is called a (true) random number generator. It does something classical, digital computers cannot really do because, given a definite input, they produce a definite output. So how does this simple quantum circuit manage to one-up the strict definition of a classical, digital computer?

Reading from left to right, the quantum circuit says to start with a qubit initialized to the state |0> and to feed it into a H gate. The H gate is named after the mathematician Jacques Hadamard and hence often called Hadamard gate. It says to rotate a qubit such that an input state |0> ends up half-way between that state and the |1> state. Finally, the rightmost symbol in the quantum circuit instructs a quantum computer to measure if the qubit is in the |0> or in the |1> state.

Measurements are to this day hard even for quantum physicists and have started big debates about "interpretations" of quantum dynamics. But the basic math behind them is clear: The outcomes |0> and |1> occur with a probability proportional to the square of the abscissa of the point on the circle that corresponds to the input state. In our case, the abscissas are equal and so are the probabilities: Our quantum computer outputs |0> or |1>, each with the probability one half.