Quantum computing is one of the first great technologies of the 21st century, and it will change everything someday.

Welcome to the Quantum Edge newsletter. Here you will learn more than just: “quantum computing works because of superposition and entanglement.” The Quantum Edge newsletter will tell you what goes with superposition and entanglement and what those terms actually mean.

Read about the physics, chemistry, and all sciences that create the foundation for quantum computing. Join me in my quest to translate the mysteries of the quantum world to the language of the dinner table and the coffee shop.

In today’s newsletter: Bloch Spheres and Entangled Bell States - Showing Qubits on Paper.

Words can only go so far. At some point most of us like to see something in diagram form. A conventional bit is easy, being just zero or one in value. But how does one show what superposition looks like? I’ve used a few visual analogies to this point, including overlapping on and off light bulbs and overlapping waveforms. Those were my visions. Scientists have theirs too, and one of the most common visualizations is called the Bloch sphere.

The Bloch sphere is one of the more effective visualizations of a qubit. The Wikipedia definition puts it as such: “In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch.“

It is sometimes used in quantum computing as an attempt to visually explain how a particle can hold a multi-dimensional vector value.

Imagine a sphere with a radius of one. The sphere has a center point, so imagine that your sphere has a bar attached at the center point. The bar reaches from the center to the surface, so it is one (1) radius long.

If this sphere were used to represent the possible values of a conventional computer bit, the bar would only be able to be placed at the top (the North pole) for zero and the bottom (the South pole) for one.

When the sphere is used to represent a qubit, The bar can be moved to any point along the surface of the sphere. The angle of the bar is a vector (it has more than one value). Its vector components are the angle away from the x axis, which is given the Greek letter φ (phi), and the angle away from the z axis, which is given the Greek letter θ (theta). The point at which the bar touches the surface, in ket* form, is the compound vector |Ψ⟩ (bar, Greek letter psi, bracket). This is the qubit. While it is in superposition, the value of ket |Ψ⟩ is not known.

The vectors phi and theta hold probabilities of a value - probability vectors. The combined probability gives the likelihood (but not a guarantee) of a one or a zero value when the qubit collapses out of superposition.

In our automobile driving analogy from the introduction to vectors I wrote in newsletter issue 15, the trip was a vector with a speed and a direction:

𝑣⃗ = (65, from Seattle to Tacoma)

The 𝑣⃗ (v with a little arrow on top) is commonly used to represent a vector. The speed (65) is a value, as is the direction (from Seattle to Tacoma), not a probability. However, if you read the rest of the paragraph in the original text in issue 15, I add more detail: “traveling at 70 miles per hour and accelerating from 65 to 75 miles per hour while traveling from Seattle to Tacoma and spinning in circles at 10 rotations per minute because I hit ice.“

The “spinning in circles” component of that traveling vector could be described as a probability. I don’t know what direction I will be pointing when I stop spinning, but it will be a direction. Until I stop, the direction is unknown and can’t be measured. After I stop spinning, I am sitting, pointed in a specific direction that can be measured.

How convenient. That’s more or less how the probability vectors in a qubit in superposition work. While in superposition, you don’t know what the value will be in the end. When you measure it, you get a distinct value but the qubit is no longer in superposition.

If you stop my car from spinning, you will be able to measure a direction, but the car will no longer be spinning. If you stop a qubit from being in superposition, you will be able to measure a value of one or zero, but the qubit will no longer be in superposition.

I was about to write: “Here’s where it gets weird..” but I think it already has.

A conventional bit is one dimensional and has a value of either zero or one. We use the numerals zero (0) and one (1) to show the value. As I’ve said, a qubit in superposition is multidimensional. It’s fine to say that in text, but just like with one and zero, we need the actual digits (0 and 1) to do math. Figure 1, from newsletter issue 26 showed the vertical matrix equivalents of the two key forms of a qubit (|0⟩ and |1⟩) and form basic qubit registers.

The register discussion in issue 26 is pretty important because that is the start of going from a qubit to a quantum processing unit. A conventional computer can’t do much with one bit. It needs groupings of bits: registers, logic gates and complex circuitry. A conventional computer uses small wires to connect everything.

Quantum computers need the same: groupings of qubits in the form of registers, logic gates and complex circuitry. Instead of wires, quantum computers connect everything with quantum entanglement.

Two qubits in superposition are just two independent qubits. What is done to one has no effect on the other. Entangle the two, however, and what is done to one does have an effect on the other. A pair of entangled qubits in superposition are said to be in a Bell state.

A Bell state, (also called an EPR pair or Einstein-Podolsky-Rosen pair - see what I mean?) is a set of two entangled qubits. It’s the simplest form of entanglement and is the building block of quantum computers.

It basically means that when one qubit in an entangled pair is read, the superposition in both entangled qubits collapses and the resulting value would come out of both. Both qubits would show the same value. This is true if the qubits are separated by a fraction of a millimeter or if they are separated by billions of miles.

Debi’s qubit on Earth would instantly show the same value as Jim’s at the far side of the galaxy. But it’s not faster than light communications because neither Jim nor Debi can set the value of their qubit. They take it out of superposition and the value is what the qubit says it is, not what they say it is.

That’s all for today.

New to the Quantum Edge newsletter?

Thinking about re-reading it but want a more transportable format?

I’ve wrapped the first ten issues of The Quantum Edge newsletter into book form. The collection, called “The Quantum Computing Anthology, Volume 1”, is now available in Kindle and paperback on Amazon. The book collects newsletter issues 1 through 10 and has some additional material and edits for continuity and clarity.

Coming soon: Volume 2, collecting newsletter issues 11 though 20 is in the works. Look for it on Amazon soon.

In the meantime, you can order the Volume 1 Kindle or paperback editions on Amazon today: The Quantum Computing Anthology, Volume 1

Check your email box Thursday - probably. (Okay, some of these weekly issues have come out on Friday, or not at all. But, in a quantum world, how can you tell?)

If you received this newsletter as a forward and wish to subscribe yourself, you can do so at quantumedge.today/subscribe.

Positive Edge is the consulting arm of Duane Benson, Tech journalist, Futurist, Entrepreneur. Positive Edge is your conduit to decades of leading-edge technology development, management and communications expertise.