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.

Here you will 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: Expanding on the description of quantum logic gates.

Superposition is the biggest mystery in quantum computing. Nobody knows how it happens, why it happens, or even exactly what is going on within a subatomic particle in superposition. We are able to harness superposition to a certain degree because whatever it is doing is mathematically predictable. That predictability allows us to get a qubit to perform its magic upon command and it allows us to read the results.

Entanglement is the second quantum nonsensical (referenced in newsletter Issue 10, or book Volume 1 chapter 11). I would have to say that it is much less of a mystery for practical purposes. We don’t understand why or how entanglement happens, but its effects are easier to comprehend. You could describe it as a magical wire that gives one particle some awareness of and some ability to impact the goings-on in another particle. Under the right conditions, we can make entanglement happen and make use of it.

Superposition may be the real magic, but entanglement is the workhorse. Entanglement is the structure that allows qubits in superposition to become quantum logic gates. Quantum logic gates allow us to construct a quantum computer.

Again, quantum logic gates are a close analog to digital logic gates but are not an exact match. Some quantum gates are used to put qubits in superposition, entangle them and set operating conditions. Other types of gates perform the work in quantum computing.

We learned in the last issue that conventional computers operate based on Boolean logic which has three fundamental expressions: NOT, AND, and OR. Computer circuitry is based on logic gates that conduct those three operations. There are another three basic gates which round out the set: NAND, NOR, and XOR. Most of a conventional computer logic comes from those six gates. Circuits comprised of logic gates are referred to as asynchronous circuits, or clockless circuits. As soon as the input is stable, and the electrons have had enough time to push through the circuitry, the output is stable.

Another important structural component of a computer is called a flip-flop. Flip-flops do something when triggered by a clock signal. They might flip a value, store a value, or pass a value from input to output. They are called synchronous because their action is synchronized with a clock signal or some other sort of trigger signal.

Conventional computers are mixes of asynchronous circuitry and clocked synchronous circuitry, though the vast majority of conventional processor operation is clocked. Quantum processors are largely synchronous devices. Quantum operations happen when qubits are directed by photons (of a type dependent upon the type of qubit). The photons are sent from the supervising computer guided by a master clock signal.

The term register shows up a fair amount in the real world. A cash register temporarily stores money at a store. It keeps money in little bins thorough the day. Money is put in from customer cash purchases, and it is taken out to give change back to customers. It is only for short-term storage so, at the end of the day, it is emptied and the cash is taken to a bank. It is refilled again the next morning with money from a bank.

A computer register has a similar function. It is for short-term storage of small amounts of data. Long term storage takes place in a memory bank. The smallest conventional computer register holds a single bit of information. Most registers, in practice, hold bytes or words (8-bit byte, and maybe a 64-bit word in a typical desktop).

Register values can be written out through the use of brackets like this:

[0] is a single bit register holding the value zero.

[1] is a single bit register holding the value one.

[0, 0, 0, 0, 0, 0, 0, 0] is an 8-bit register holding the value 0.

[1, 0, 1, 0, 1, 1, 1, 0] is an 8-bit register holding the value 174 (101011110 in binary = 174 in decimal).

Qubits can also form registers. representing them in text is a bit more complex though because qubits hold vectors containing more than one possible answer. Qubits with known values are written as |0⟩ and |1⟩. We pronounce these as “ket zero” and “ket one” respectively. You can (and I often do) loosely say that those values are analogous to 0 at 1. However, it is more correct to represent then as a vertical vector with two dimensions.

In computers, registers temporarily hold small amounts of data. A common conventional computer math operation will involve several registers. Figure 2 below shows the registers used in a 4-bit addition (ADD, in computer language) operation. Conventional computer registers are shown horizontally.

The 4-bit binary adder shown in the previous newsletter issue (included here for your convenience as figure 3 below) has inputs as A and B and an output Q, which refer to the registers in Figure 2. In the most simplistic version of a conventional computer, the addition process would go something like the following:

The ADD operation sends the data from the registers to a part of the CPU that looks a bit like the circuity in figure 4 from the prior newsletter.

Conventional logic gates take combinations of ones and zeros as input and delivers a one or zero at the output based on the combination of input and the type of gate. Groups of conventional logic gates are wired together to create circuits that add, subtract, multiply, and do everything necessary for all of our computing needs. Quantum logic gates do the same for a quantum computer.

Logic operations are pretty simple when your digit options are a simple one or zero. But qubits don’t hold a simple one or zero when in superposition. They hold both states and hold a probability of being one or the other state. How does that fit into or out of a gate?

The simplest gate* (conventional or quantum) is the NOT gate. It changes a zero to a one or a one to a zero. The simplest quantum gate is called the Pauli gate. It performs a similar invert function, but it comes in X, Y, and Z variants because qubits are multi-dimensional.

The Bloch sphere is commonly used to represent a qubit visually. It shows spin up (|0⟩), spin down (|1⟩) and a three dimensional sphere in between. Probability values of the qubit being spin up or spin down are factors of the x, y, and z directions within the sphere. Hence, the X, Y, and Z variants of the Pauli gate.

Next time, more detail on the Bloch sphere, Pauli gate operation, matrix representation for quantum gates and the CNOT gate.

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?)

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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.