Let Me Try to Blow Your Mind With Quantum Qudits For Far Faster Processing and Communications

[This post had not gone under my normal editing process and may contain typos and grammatical errors. I’m rushing to create and post as I head out the door on vacation, so there could be even more errors than usual.]

I often write about how sufficiently capable quantum computers will soon crack today’s traditional asymmetric encryption and how everyone needs to start preparing their environments, NOW, for that eventuality. Use this free guide (https://cloudsecurityalliance.org/artifacts/practical-preparations-for-the-post-quantum-world/) or my book on the subject (https://www.amazon.com/Cryptography-Apocalypse-Preparing-Quantum-Computing-ebook/dp/B07Z837R86) to prepare.

But quantum information sciences and devices will also bring us many wonderful things. Think of how many wonderful things (ignoring the bad things for the moment) that the Internet has given us. Quantum is likely to give us the same type of revolutionary push. We will get tremendous services and devices we cannot even imagine today.

People often assume that quantum computers can do any calculation or solve any problem significantly faster than a traditional, “classical”, binary computer. This is not true. Quantum computers are only faster at solving particular types of problems. Someone has to figure out a way to do something faster using a quantum computer and then try it out. But quantum computers can’t, at least today, do everything faster and better. We are not even completely sure that quantum computers can do anything faster and better than classical computers, although it seems they can do some things faster and better.

This is until we start to harness the supercharging power of quantum qudits.

Today’s classical and rudimentary quantum computers are binary. This means that all data and processing happens as only one of two possible states. A binary digit (a bit) is logically represented as a 1 or a 0. In today’s classical computing world, 1’s and 0’s are usually created using groups of electrons (if electrical) or photons (if light-based). The appearance or absence of a particular charge or level of light will be interpreted by the involved classical device as a 1 or a 0, and then that information is used to do processing and compose high-level data. For example, eight 1’s or 0’s may be constructed to create an ASCII character such as an A or B. A collection of ASCII characters may end up creating a source code program or a literary document. Today, our classical and quantum worlds are mostly binary.

Note: Kudos to Jack D. Hidary’s Quantum Computing: An Applied Approach book, Chapter 3, for introducing me to the concept of qudits and qutrits.

Today’s quantum computers are binary, using quantum bits (or qubits). The information created and processed by a quantum computer can be a 1 or a 0, or more accurately, can be a 1 and a 0 and both states at the same time (i.e., 3 states all at once). This is a property known as superposition. In a classical computer, any two bits can only be two pieces of information. The only possible states of 2-bits in a quantum computer are 00, 01, 10, or 11. You have two bits which can be four different pieces of data, but that data can only be one of those pieces of data (i.e., 00 or 01 or 10 or 11) at any single moment.

Quantum computers significantly ramp up the possibilities by allowing two qubits to be all those possible states at the same time to solve problems: 00 and 01 and 10 and 11. The property of superposition gives us a new computing dimension to solve particular types of problems faster than a classical computer (or so we think so far).

But that’s only considering the binary world. Today, both classical and quantum computers are binary. We are still messing with 1’s and 0’s. But it doesn’t have to be that way, in either classical or quantum computers. However, quantum computers seem to have a distinct advantage over classical computers when going past binary data representations.

One of the properties of quantum computers is that the represented state of data can be any possible state the involved quantum particle (i.e., electron, photon, quark, etc.) can represent. And all of those quantum particles can represent many different possible states, not just two. Right now we using quantum particles to represent two states: 1’s and 0’s. And superposition allows us to use all of the possible binary states: 0, 1, and 1 and 0, all at the same time.

Behind the scenes, on quantum devices, this is accomplished by measuring the presence or absence of a quantum particle (say a photon) or some property of that quantum particle (e.g., polarization, color, charge, direction, spin, etc.). For example, a quantum computer may decide that a photon with left polarization is a 1 and a photon with right polarization is a 0. This is binary thinking.

The reality is that most properties of a quantum particle have more than two states. A photon isn’t just a left- or right-polarized particle. Really, it has a bunch of other states of polarization. We have just, so far, decided that we will always look at a polarized photon and classify it as right or left (or whatever the polarization state being measured is). As long as the polarization is pointing more toward the right versus the left, we’ll call it right-polarized, and vice-versa. But it’s not like every photon is perfectly polarized right or left. We are artificially deciding we will classify it as right or left. Our measurement devices are artificially categorizing photons as right or left. The measurement device has no ability to classify photons as any other polarized state. But there are many more states between right and left.

Per quantum physics, there are many different answers and states along a “waveform” of possibilities. That waveform is a representation of all the possible answers. So, we can take any particular quantum particle or property of a quantum particle and read many different possible states. Instead of just expecting or reading just 1 or 2 states, we could perhaps, for example, look for and read 3 or 10 different states. So instead of just having 3 possible states (e.g., 0 or 1 or both 0 and 1), we could have many more possible states.

Qudits are the general idea of multiple quantum states or levels. Qubits are two-level systems. Qutrits are three-level systems. And computers can have any number of states/levels only limited by all the possible states of the particle or property being measured. And this opens up a floodgate of speed and possibilities. Each additional level supercharges the number of possible states and outcomes exponentially.

Note: Classical computers can also have more than two states. For example, we call a 3-level classical system as using trits instead of bits. But quantum computers seem to be more open to multi-level systems as compared to classical systems, but this has not been proven.

A binary classical computer with 100 bits can represent 2^100 possible states but only a 100 different states all at the same time. Quantum superposition really increases the number of possible states that can be represented all at the same time. For example, in his book, Hidary calculates that a quantum computer with 100 qubits can have 2^100 states (or 1.26765E+30), whereas a quantum computer with 100 qutrits can have 3^100 states (or 5.15378E+47) or 17 orders of magnitude more capable. So, we go from a 100 possible states to numbers that are nearly unimaginable. And that’s only with 100 qudits. And a 100 qutrits is 17 times better than a 100 qubits.

The end result is that not only can quantum computers do some wonderful new types of calculations that are simply not possible with classical computer devices, but they can store and process much more information at the same time. And as we add more states, beyond our traditional binary thinking, those possibilities just explode.

The end result is that quantum computers, devices, and networks will be able to store, process, and communicate significantly more information all at the same time, which makes it seem faster. What I mean is that quantum computers aren’t necessarily moving information around faster…they aren’t able to exceed the speed of light or be “faster” than a classical computer, but each computing or transmitting cycle of a quantum device can pack far more information into the same space, and that equates to a wonderful increase of processing power and data transmission with the same number of data units and time. Increasing the number of possible states that we measure will in turn like it’s being done “faster”…but the data is not being sent “faster”…we’re just able to process or send more data within the same time chunk.

Here's what I want to leave you with, so you can impress your friends. Today’s quantum devices are soon to deliver many wonderful things that we could not imagine before. Quantum computers will solve particular types of problems way faster than we think we could have ever solved them using traditional, classical computers. And that’s just considering binary states. But quantum devices can have more than two-levels to play with. They have 3-level and n-level systems only limited by our the number of possible states of what we’re measuring and our ability to discretely measure it accurately. Once we move quantum computers and networks past qubits to qutrits and beyond, then what we get is going to be really crazy and wonderful.