What Are Superposition & Entanglement in Quantum Computing

Quantum computing is quite different from classical computing, and there are new fundamentals and terms to learn. Two of these are the concepts of superposition and entanglement — big ideas you need to grapple with as you're learning about this new kind of computing.

Superposition

The state of possibility that's available to qubits is called superposition, where super means many and position means possibilities. A traditional bit can be either 0 or 1. A qubit in a state of superposition does not have a defined value because it holds many potential values at the same time. But when we measure a qubit, we just get 0 or 1 back — whichever value the qubit’s energetic wave function collapsed to when it was measured.

Superposition is the first of two major pillars underpinning the power of quantum computing. The other, entanglement, is described in the next section.

Welcoming foreign entanglements

George Washington once warned Americans to avoid foreign entanglements. But with qubits, we welcome entanglement as an additional, powerful tool in our quantum computing toolkit.

Entanglement is a kind of connection between two or more quantum particles. For instance, quantum particles have a property called spin, which we can measure as either down or up (0 or 1). If two quantum particles are entangled and one of them is measured as having an up spin, we know without measuring that the other entangled particle will have a down spin. And if we influence the spin of the first quantum particle so that it changes to up when it is measured, we know without measuring that the other quantum particle will change to down.

The figure below illustrates the connection between two entangled qubits, which have opposing spins. Measuring the spin of one tells you that the spin of the other is the opposite; changing the spin of one qubit in one direction will change the spin of the other in the opposite direction.

As mentioned, entanglement is the second pillar supporting the power of quantum computing. With entangled qubits, influencing a single qubit can have a knock-on effect on many others.

Entanglement and superposition work together

When an entangled qubit is in a state of superposition, each of its entangled connections is also in a state of superposition. These cascading uncertainties exponentially increase the potential power of quantum computers.

To program and run calculations on a quantum computer, the potentiality of the entangled qubits must be maintained by keeping them coherent and free from noise. We then measure the qubits (which causes them to decohere) and record the results, a 0 or 1 for each qubit.

For much more about superposition and entanglement, and all aspects of quantum computing, check out our book Quantum Computing For Dummies.

Blowing past C

Albert Einstein wears two hats in the history of quantum mechanics — and the two hats don’t fit comfortably on a single head.

One hat comes from Einstein’s discovery of relativity, published in 1905. Relativity says that speed in this universe depends on your motion relative to other observers, but that the speed of light — about 186,000 miles per second, or 300,000 kilometers per second — is always the same for all observers. This universal speed limit is called locality.

The other hat comes from Einstein’s discovery of the photon, also in 1905. (This discovery, not relativity, is the source of Einstein’s sole Nobel Prize.) The discovery of the photon is fundamental to quantum mechanics.

Einstein’s problem is that quantum mechanics later asserted that quantum particles, such as photons, can be entangled with each other, so that reading the spin (for example) of one photon tells you the spin of the other. And this relationship is instantly true, without regard to the speed of light. Physicists call this an assertion of nonlocality, which is supposed to be forbidden by relativity.

Einstein hated this, calling it “spooky action at a distance.” He and his colleagues spent a great deal of effort trying to disprove it, even as Einstein continued to make breakthrough quantum discoveries, such as the identification of Bose-Einstein condensates, which are superconducting gases that can be used to create qubits.

Today’s mainstream computers are subject to classical mechanics and limited by the speed of light. Quantum computers depend on quantum mechanics and, in their use of entanglement, are not limited by light speed.

The Nobel Prize for Physics in 2022 was awarded to physicists who showed that entanglement is real. So researchers in quantum computing who depend on entanglement can say, after Galileo: “And yet it computes.” (Galileo, on trial for asserting — correctly, as it turned out — that Earth is not at the center of the universe, is famously said to have whispered: “And yet it moves.”)

Enabling quantum computing with coherence

Qubits can be used for quantum computing only when they’re kept in a state of coherence, free of interaction with their environment. To do quantum computing, qubits need to follow the rules of quantum mechanics, and these rules apply to only coherent qubits.

Quantum particles zipping around the universe — photons emitted by the sun, for example — are in a state of coherence. What causes them to decohere? Any interaction with excessive interference (such as vibration or a strong magnetic field), a solid object, or a measuring device.

Keeping qubits coherent is hard. Heat decoheres them, so qubits are kept cold. So do vibration (think of a truck going by on a road) and any collision with their environment. To prevent such collisions, qubits often use strong magnetic fields or targeted laser beams to prevent the quantum particles inside them from colliding with their physical containers.

Decoherence is not the only disaster that can affect qubits. Temperature changes, vibration, or physical interaction may change the value of a qubit in an uncontrolled manner without causing it to decohere. This noise causes errors in the results of quantum computations. Minimizing noise and detecting errors are two of the biggest challenges facing quantum computers.

To manipulate each qubit — to program it, for instance, for quantum computing — the qubit must be controlled in such a way as to adjust its value without causing it to decohere. Magnetic fields and laser beams are among the means used to manipulate qubits without causing decoherence.

When we measure the value of a qubit, two things happen:

• The qubit decoheres, becoming subject to the rules of classical mechanics.
• The qubit’s value collapses from somewhere between 0 and 1, inclusive, to either 0 or 1.

The qubit must be reinitialized — returned to coherence — before it can be used again for computing.

Some argue that the potential of quantum computers is very limited — that the level of coherence needed for quantum computers to achieve useful results is impossible, in theory and in fact.

In the extreme version of this argument, leaders in quantum computing are accused of deliberately committing fraud, which would mean that the entire field is a massive conspiracy. Only further work will show the limits to quantum computing, if any, but the fraud allegations are just a conspiracy theory.

The math for the power of quantum computing

It’s challenging to fully grasp the potential power of quantum computing compared to classical computing because that power is based on quantum mechanical principles. But we can sum it up in just a bit of math.

Because the bits in classical computing can hold only one of two values — a 0 or a 1 — at the same time, the number of states that a classical computer can hold is represented by the number of bits, n, to the power of two: n². But a set of entangled qubits can hold all the possible values of the qubits at the same time. For this reason, the number of states that a quantum computer can hold is represented by two to the power of qubits, n: 2ⁿ. For example, to represent a million possible states would require 1,000 bits but only 20 qubits.

Today’s computers contain billions of bits, but we have to throw a lot of them at our most complex problems to get anywhere. Today’s quantum computers have a small number of qubits — a recent IBM quantum computer release clocked in with 433 — but we need only a few hundred qubits to begin tackling very complex problems.

The power of today’s quantum computers is limited by errors and short coherence times. But as these factors are addressed, the results are likely to be amazing.

What will quantum computing do for people?

It’s easy to spend time geeking out on the strangeness and power of quantum computing. But what difference will quantum computing make to humanity?

To understand the answer, we first have to address a common misconception. People today tend to worry about how powerful today’s computers are: to worry about the power of the internet, social media, and machine learning and AI.

But there’s also a big problem around how powerful today’s computers aren’t: They simply aren’t up to big computational challenges in areas such as better batteries to fight climate change, better aerodynamics, better routing in complex transportation networks, and better discovery of new drugs, to name a few important examples.

And these big computational challenges are exactly the areas where we expect quantum computing to make a big difference. Future quantum computers will be able to solve problems we can’t touch today, and to do so far faster, more cheaply, and with less energy expenditure than today’s computers.

Quantum computers can only “do their thing” in partnership with computers of the kind we use today. So, when you see descriptions of what quantum computing can do, understand that these accomplishments will also require a whole lot of conventional computing power.