How quantum computing works

A single yellow (state 0) cube.

A quantum computer, on the other hand, uses something called quantum bits, or qubits. Unlike the dichotomous bit, qubits operate at the level of subatomic or elementary particles. A single qubit will always be measured to be either 0 or 1, much like a regular bit. For example, this qubit is in state 0.

A yellow (state 0) and a blue (state 1) cubes moving randomly on the screen behind a frosted glass that makes them look blurry.

Things get interesting when “superposition,” a phenomenon unique to quantum particles, enters the equation. While a bit can only be in one state at any given time (0 or 1), a qubit can be in a superposition, which is essentially a combination of the likelihood that it’s either a 0 or a 1. Upon measurement, superposition “collapses” and we get a 0 or a 1, just like a classical bit.

The yellow (state 0) cube and the blue (state 1) cube stop moving and line up next to each other.

At the beginning of a computation with qubits, each qubit is normally put in an equal superposition, where the probability of the qubit being observed to be in state 0 or state 1 is equal.

Reverting back to having just a single yellow (state 0) cube.

In order to get an answer, the qubits must be reverted to classical bits with definitive states through measurement. Without doing anything to influence the answer, you will just get 0 or 1 essentially at random — not particularly useful!

Four yellow (state 0) cubes lined up vertically in a straight line.

Here is a very simplistic look at how scientists can manipulate the qubits to get an answer that is probably correct. We will start with
four qubits, all in state 0 initially…

Next to each of the yellow (state 0) cubes appears one blue (state 1) cube.

… and put each qubit in an equal superposition of
0 and 1.

A 4 by 4 grid with a total of 16 cubes appears. Each of the cubes corresponds to one of the possible combinations, starting from 0000, though combinations such as 1100 and 0101, to 1111.

As each qubit can be either 0 or 1 until it’s measured, we have
16 (4²) possible combinations. We can imagine these as the following grid of possibilities.

The grid of cubes is put behind a ‘frosted glass’ so that all the cubes appear blurry. The cubes are moving around up and down in random motion.

This grid is, however, only a simplified visual cue of what the quantum system might look like, as qubits in superposition look like

The frosted glass is removed and the cubes move back to their original grid positions. Then all the cubes but for the one corresponding to 1111 fade away.

Assume one of these combinations can lead us to the correct answer to a computational question such as finding the prime factors of a large number. Quantum algorithms can manipulate of which answer is correct to help our quantum computer choose the right one.

The 1111 cube moves up and an axis saying ‘positive’ appears to indicate that the cube has moved in the positive direction (up).

We can think of “the probability” for each combination being the correct answer as the vertical position of the corresponding cube.

The cube for 0000 appears on the grid again and moves down. An axis saying ‘negative’ appears to indicate that the cube has moved in the negative direction (down).

And here’s where some of quantum’s magic comes in: In the classical world, probabilities are always positive numbers and they always all add up to 100%. In the quantum world, “probabilities” work very differently than we are used to and are known as amplitudes.
These are that don’t have to add up to 100%.

The cube for 1111 stays up and the cube for 0000 stays down. Nothing else changes.

Amplitudes can add to something larger (constructive interference) or smaller (destructive interference)

The cube for 0000 fades away. Only the cube for 1111 remains. Then another cube appears and moves an equal distance downwards to the existing 1111 cube. Then both cubes shrink away, indicating that they cancel each other out.

Interference is important because it can take some answers off the table. For example, let’s say one of the potential answers to our hypothetical computation is 1111, but it turns out there are a couple of ways to get there, each with an amplitude that is its opposite. This would, in effect, eliminate 1111 so that we’d never see it come up as the final answer.

All the cubes fade back in and the original grid of 16 cubes is back. Then the cubes all move up or down different amounts. Additional cubes are added and these also move up and down.

The key behind fast and reliable quantum computations is to set up a superposition of qubits that considers all possible answers while being cleverly arranged so that all of the “wrong” answers destructively interfere with each other, including by introducing additional ways of obtaining the answers (adding extra cubes) and manipulating the amplitudes.

All the cubes of the same type pointing in opposite direction with the same amount of vertical displacement start to disappear together in pairs, indicating that they are cancelling out. In the end, only 3 cubes remain.

Here, just three of the initial possibilities remain after interference.

Two out of the three remaining cubes disappear and we are left with just a single cube.

The final step of this process, a quantum measurement, is not guaranteed to return the right answer the first time. But since the number of potential answers has now been reduced significantly, scientists need only repeat this step a handful of times and check (on a classical computer) to see if the answer solves the problem.