**Difficulty**

*by Christian Dickel*

It is an honor to write the first blog post here and being conscious of that certainly influenced what I was going to write about. They say write what you know, but this is a blog so I’m going to write what I think. The blog will hopefully be a place for opinions and discussions. So I’ll begin with a question:

**Do physics institutes need blogs?** Certainly it is a neat additional way to communicate with other scientists, especially to share more provocative thoughts and give people a chance to discuss in the comments. But science is kind of a gated community and a blog is a nice way to open it more. For communication with the rest of society, journalists often come in whenever some piece of science has an air of general interest. But especially in a field receiving a lot of interest and a lot of funding from the public, we should try to explain what we do directly to anybody who is interested enough to end up on our website. A blog is a chance for us to share and discuss our perspective on the story of quantum computing as it is being written.

## Quantum computers and the media

There are news article on quantum computing almost weekly somewhere on the internet and one can use them to follow the story of the quantum computer. But the news has a certain inertia and a need to fit complicated arguments into a single sentence or paragraph. Some of the one-liners are productive simplifications, but they can also be misleading. Exploring all the misconceptions about quantum computing requires more than one blog article. I considered going through the list found here and fact-checking it, but this blog article would not have been very serious then. I thought it better for the first blog article to be a link from the past to today and focus on a single aspect that annoys me in the way the quantum computer story is told: I will try to give a more nuanced view on the relationship between the classical and quantum computer. Maybe later there will be more blog articles on other common misconceptions about quantum computers.

## The classical computer in the story

The quantum computer is usually introduced with the statement that it can vastly outrun classical or even supercomputers on certain problems. Quantum computation is heralded as a disruptive technology that will revolutionize computation. The classical computer is only mentioned as the boring status quo. Of course I believe that quantum computers will be awesome, otherwise I would not spend so much time helping to make them happen. But having been involved in building quantum computer prototypes for almost three years, I see the classical computers that I use every day with different eyes now. Let me remind you that your computer and the server that contains this blog article exchange bits but you see words on a screen. In my day-to-day work, I look at the results of operations on quantum bits on the screen of a classical computer that controls my experiment. My classical computer in the lab is my window to the quantum world. But the quantum computer prototypes have a few qubits where we engineer all their logic gates by hand. We work at the bottom level of computation. This is in stark contrast with the classical computers we use for design, control of experiments, data processing and simulations. Those computers have operating systems, compilers, high-level programming languages and programs. Without them our quest for the quantum computer would be impossible. That is why I want to highlight the continuity from the classical to the quantum computer rather than the revolution.

## A classic media misconception

In some news stories it is pointed out that the number of possible states of a quantum computer grows exponentially with the number of qubits. The argument goes as follows: A bit can have two states, 0 and 1. Two bits can have four states: 00, 01, 10 and 11. Four bits can have eight. It is true that 10 qubits can have different readout results. But this is true also for the classical bits of a “normal” computer. When this argument is cut short here it is misleading. I think the reason for the misunderstanding is that we cannot grasp exponential growth with our intuition, so it already serves as a buzzword. That’s why we tell stories of rice grains and chess boards. The exponential scaling of the number of possible states with the number of bits is part of the classical information theory championed by Claude Shannon. Quantum information theory has similar building blocks and concepts, however, scientists are still busy understanding all the implications of quantum information theory.

The difference between quantum and classical bits is subtle and cannot be explained without invoking the counter-intuitive notions of superposition and entanglement. These special features of quantum mechanics let quantum information scale differently from classical information. It is even a bit more complicated because there is a difference between the classical information needed to represent a quantum system and the classical information that can be extracted from it. While the state of a classical system with bits can be exactly represented by classical bits, this is not true for a quantum mechanical system. The readout of the quantum mechanical system gives a binary result for each qubit, in that way a qubit is like a classical bit and the measurement of qubits gives a classical bit string of length . In fact, the famous Holevo bound states that the information that can be extracted from qubits cannot exceed classical bits of information. However, during calculations on a quantum computer, the quantum state has to be represented by complex numbers or twice as many real numbers. Storing each of these numbers to double precision would require 64 bits. Thus, the required classical memory to store the state of a quantum system grows exponentially with the number of qubits, which makes simulating quantum computers on classical computers impossible for large system sizes. Currently, simulating a 50 qubit quantum computer would be at the edge of supercomputer capacity, simulating a 100 qubit quantum computer seems classically out of reach. So there is a grain of truth in the “quantum information scales exponentially” argument, even though it is often simplified too much.

This example shows that explaining the difference between quantum information and classical information unambiguously is very difficult. As a community we have to decide how we deal with the many pitfalls of explaining our science to the public. News about our field generate a lot of science-fiction enthusiasm with promises of exponential speedups, solutions to impossible problems and misleading terms such as teleportation. For the record, I am not saying that the promises of the quantum computer are exaggerated. Probably a working quantum computer would exceed the expectations of its creators like the classical computer did, but there are many ways to misunderstand our field. This feeling, in part, lead me to writing this article. This is not a problem I can solve in this article, but it will hopefully be the subject of more blog articles. Here, I want to go on making my case that the classical computer is not the antagonist in the quantum computer story.

## Lessons from the classics

The problems we face in trying to scale up our quantum computer prototypes should also sound familiar:

**bringing up the fabrication yield for quantum bits**: Building a ten-qubit chip is harder than building a one-qubit chip. This is especially challenging for nano-scale qubits that run into lithographic limits.**solving the problems of interconnects**: Quantum bits need to be connected to each other as well as to classical control and readout equipment.**managing the heat load of the quantum computer**: Many qubits require very low temperatures at which only limited cooling power is available.**coming up with an architecture**: The growing complexity of the experiments needs to be managed. The level of automation and abstraction needs to increase along with the number of qubits.

All of these problems have been solved for generations of classical computers, but we are still testing different building blocks for quantum computers. We can hopefully solve these problems faster by bringing together academia and the classical computer industry.

## Quantum-classical or classic quantum

Lastly, our current best scheme for a fault-tolerant quantum computer requires a powerful classical computer to run alongside the quantum computer and figure out what goes wrong in each step. This is necessary because quantum hardware is error prone. It is the complex interplay of quantum and classical information that will enable the exponential speedups of the quantum computer. Similarly, the quantum communication schemes that ideally allow for privacy guaranteed by the laws of nature combine the exchange of classical and quantum information. The classical computer parts should be as closely connected to the quantum parts as possible and need to keep up with them in runtime. Note, that the classical computer parts do not perform the same kinds of calculations as the quantum parts, they act more like a control circuit for the quantum hardware. Many qubits are rather short lived, so the classical logic controlling them has to have short latency and fast clock speeds. For this reason our institute is also developing purely classical hardware for qubit control. Ultimately, as many quantum computers operate at cryogenic temperatures, the quantum computer quest might push classical logic into that regime as well. In the process, clock speed and architecture of the classical computer would change alongside its younger quantum brother.

As quantum computer scientists, we would usually say that classical electronics will be part of a quantum computer. But for many applications the quantum computer will be used as a black box with classical information as the input and output. In those cases it might be more honest to introduce the quantum computer as a hardware accelerator technology for the classical computer, like a GPU. Once quantum computers start solving relevant problems, computers will not be judged by how quantum or classical they are but by what they can actually do. Then the news stories will change.

### About Christian Dickel

Chris came to the Netherlands for the food and the weather but stayed for the quantum computer work. Apart from work he enjoys playing music with friends, ranting and soap-boxing.

16-8-2016 updated version: expanded explanation of the difference between quantum and classical systems and the interaction between classical and quantum components in a computing system

It’s a great pleasure to be the first who comments on your interesting and promising blog.

Thank you for this great article.

I’m planning to attend the upcoming quantum cryptography course on EDX as this would help me a lot in my pursue towards a master’s degree in this field.

Looking forward for your upcoming articles. Please, appreciate any useful materials to prepare well enough for this course.

Thank you. I am also going to attend the course! As a PhD student I am working on producing entanglement between qubits, so I might as well learn what to do with it.

Hi Christian,

Through my preparation for the course, I’m reading “Quantum Computing Explained” book as a reference to review and put my hands on all related concepts.

So kindly, do you have any other useful material that would help me in my journey ? I appreciate that a lot.

Unfortunately, I live in Syria, so you would not imagine how difficult it it to be passion about quantum mechanics in a region only thinks about ,so called God, and kills by the name of that God.

I hope to be able to pursue my dream and continue my master’s degree in Quantum Cryptography. Maybe then I would be able to allow the people here to see the real holiness behind quantum :).

Hi Rashid,

I’m sorry to hear about your situation. In my day to day work as an experimental physicist, using equipment easily worth half a million, I sometimes forget how privileged I am, because usually nothing works and it can be very frustrating. I hope the situation in Syria and the region will get better soon.

I think the Nielsen Chuang is not a bad textbook. I also enjoyed reading lecture notes from David Mermin (also there is a book) and John Preskill. Scott Aaronson’s book Quantum Computing since Democritus is a nice book to read cover to cover. On the experimental physics side, I advise reading papers fresh from the arxiv, because the field is currently advancing very fast and there is to my knowledge no textbook keeping up with it.

Hope this helps you, I am sadly not an expert on quantum cryptography at all, ideally the course will change that, I guess!

Thank you dear Christian.

I’m going to have a look at these books until the beginning of the course.

Looking forward to keep in touch with you during the course.

Good luck.