“Do you think we will ever have portable quantum computers, ones that we can put on our desks as we do with laptops?”

Of course, the answer I received was resoundingly:

“DEFINITELY NOT. Never.”

In part, I understood where my professor was coming from, but I just felt as though quantum computing would inevitably lead to smaller and more portable designs. I just dared to dream of a day where there would be a ‘quantum-laptop’…

With Saxon Q’s latest press-release, I think that day has become ever-closer!

What did Saxon Q do?

They built something known as a diamond-based nitrogen-vacancy (NV) quantum computer. In other words, it’s a quantum computer that makes use of the defects in lab-grown diamonds to perform quantum operations. Most importantly, it shatters the previous record of 10 qubits (obtained by Delft University of Technology in 2019) - offering potential buyers 128 qubits this summer or 512 by next year. Incredibly, both systems operate at room temperature, with no cryogenic cooling, no vacuum required and they are very portable. This is extremely rare and very desirable, given there is minimal specialist equipment required. Saxon’s systems fit within a standard server rack and can run continuously without issue via a normal electrical unit. There’s no need to recalibrate the system, nor are there any environmental controls - it’s all sorted for you inside the box. Any company could simply buy it and plug it into the wall! Saxon also claims that their computers are rather energy-efficient, and given cryogenics aren’t needed, this seems most likely to be true. These new quantum computers are protected by 220+ patents and pending applications - so seemingly everyone is going to want a ‘slice’ of this technology. Moreover, according to Saxon’s roadmap, they don’t plan to stop at 512 qubits, they instead plan to reach 10,000 qubits around 2030!

How do these quantum computers work specifically?

Let us go back to the 1970s, where a pair of scientists discovered something rather peculiar. What this duo realised was that certain imperfect diamonds could shine with a marvelous red light when illuminated in a certain way. The study concluded that as a result of radiation damage in diamonds, moving holes - called ‘vacancies’ - were formed. If this diamond also has a small amount of nitrogen impurities in it, then these vacancies and nitrogen atoms can bond together and form a stable center. This is what the qubit is made from! As these nitrogen atoms sit trapped inside the vacancy, a quantum property of their electrons known as spin can suddenly be easily manipulated - without affecting anything nearby. Sometimes such diamonds occur in nature, but naturally it is much easier to create nitrogen-filled diamonds in a lab.

Scientists realised that we could use highly tuned lasers to exploit the electron spin and manipulate it for computation. This is how qubits are formed, and how quantum computation works using NV-centers. What allowed Saxon Q to push beyond the 10-qubit record was more of a materials breakthrough. As they induce radiation damage to create vacancies, they simultaneously implant sulfur into the diamond. The reason for this is because the added sulfur donates its electrons to moving vacancies which in turn improves the chances for NV-center formation. We also want to keep this NV-center negatively charged as quantum computation relies upon this state - so having extra sulfur electrons nearby maintains this negative state.

In turn, not only do we now get a higher efficiency of NV-center formation, but we also get better qubit control. According to their statement, Saxon Q has achieved a 99.92% single-qubit fidelity rate, in other words there is less than one error per 1,000 operations. And that is assuming no active error correction, which you could easily add in to improve the rate even more. However, CEO Grundmann has further commented saying that this fidelity can go up to 99.98% in operations that involve a single-qubit.

How does Saxon Q’s Quantum Computer compare?

Well, it certainly holds-up. I did a quick fidelity comparison via this website, and here’s what I found:

Atom Computing (1180 qubits) - 99.6% fidelity for two qubits

Zuchongzhi 3.0 (105 qubits) - 99.9% fidelity one qubit, 99.62% for two qubits

Google Sycamore (72 qubits) - 99.85% fidelity one qubit, 99.64% for two qubits

IBM Fez (156 qubits) - 99.97% fidelity one qubit, 99.56% for two qubits

So Saxon Q’s numbers generally sit within this ball park, indicating that their quantum computer could compete with the huge players!

Naturally, it is always challenging to compare different quantum computers as their qubits aren’t necessarily made of the same stuff. This means different quantum computers won’t scale-up in the same way, will require different conditions to work and won’t be able to perform exactly the same operations. They also don’t always have the same applications. For example, NV-center systems have also been considered to be an important tool for quantum sensing applications. Nevertheless, if Saxon Q’s computer can demonstrate its worth as it comes onto the market, then it truly would be one of the first fully-functional room-temperature quantum computers to exist!

What’s the verdict?

The team at Saxon Q have indeed pushed the limits of NV-center quantum computing, with the revolutionary idea of implanting sulfur into diamonds. They offer a quantum computer that boasts high fidelities, operates at room temperature and only needs a standard computer rack and standard power unit to work. Because they are selling their two quantum computers directly, it means that clients don’t have to use quantum computers through the cloud and do not need to worry about latency. It might, therefore, mean that these NV computers can offer better computation at a cheaper cost. Scaling beyond 512 qubits is the main challenge ahead and will require even more ingenious solutions to squeeze thousands of qubits onto a single chip.

What excites me most, however, is the shift of focus towards ‘easy-setup’ quantum computers. Imagine a world where you could order a powerful quantum computer to your house, plug it into the wall and run quantum algorithms there and then?! You wouldn’t need to buy expensive magnets, cryogenics or specialised lasers. You wouldn’t need to create an almost perfect vacuum or near absolute zero temperatures. In my opinion, this reality is becoming much less of a dream… and because of advancements from companies like Saxon Q, it makes me believe that quantum laptops are just on the horizon! How exciting!!

Two proteins

The team of researchers used something known as a quantum-centric supercomputing (QCSC) framework to look at two specific large protein-ligand complexes. Let me explain what these terms are:

• QCSC is a type of computing where you integrate quantum computers with powerful normal supercomputers. You let the quantum computer handle things it is better at, and give the supercomputer the tasks that it is better at. This can sometimes give you incredibly accuracy for certain tasks.

• Protein-ligand complexes are biological molecules formed when a protein binds with a much smaller molecule known as a ligand. They essential to life, contributing to our enzyme processes, our immune system and the receptors in our bodies. Without them, our cells simply wouldn’t be able to keep going.

The smaller of the two protein molecules they simulated is called T4-Lysozyme (made of 11,608 atoms). Although this isn’t made in the human body, it is a protein that is used commonly in labs for studying cells and bacteria. It helps break down bacterial cell walls and can be used to extract proteins and DNA, it’s a very useful tool for any biologist. The second, and larger, of the two proteins is called Trypsin (12, 635 atoms) - this protein is essential for nutrient absorption and digestion. It is a digestive enzyme that is produced in the pancreas and binds to proteins to break them down into amino acids - we most certainly need it to function. The team chose these particularly large proteins to make a statement, they wanted to show that quantum computing could be used to study molecules that are large and relevant to current science. They also simulated the binding of these proteins as they were immersed in a liquid water solution which makes the results much more realistic to the internal conditions of the human body.

The details of the experiment

Months before in March, IBM and Cleveland Clinic had partnered to simulate a ‘mini-protein’ consisting of just 303 atoms using the same QCSC method. Now with the addition of RIKEN’s powerful supercomputers, the team have been able to probe molecules that are over 40 times larger than the work in March. They also claim their results boast a much larger accuracy than before, at least in some parts of the overall workflow. The two 156-qubit IBM Quantum Heron r2 processors employed quantum sampling, a process where the quantum computer generates the complex data over time. As you let the quantum computer sample more and more, you start to build an accurate picture of what is going on in your system. Following this, the Japanese supercomputers Fugaku and Miyabi-G were used to process the resulting data.

Just as before, the researchers relied on something known as wave function-based embedding. It’s a process which breaks down a large problem into manageable chunks. They then fed certain chunks to the classical computers and certain chunks to the quantum computer. The ‘quantum chunks’ would generally have more complex interactions within them, for example involving entanglement between many atoms. They would then use a quantum algorithm known as SQD (Sample-based Quantum Diagonalisation) to solve the chunk. Finally, the classical computers would stitch all the chunks back together to give the researchers the final result.

Make no mistake, this process was a huge undertaking. Considering both proteins, the team needed 94 qubits across the two processors, running 9,200 quantum circuits for over 100 hours and ended up with a dataset on the scale of around 1.3 billions points. These numbers, at least for most people who study the field of quantum computing, are insanely large! Simply keeping 94 qubits remotely coherent during a project of this scale sounds unreasonably difficult. There’s also a plethora of technicalities that cannot be overlooked. For example unlike before, this new simulation doesn’t just calculate the electronic structure of the sole protein, it also considers the protein binding to a ligand within a water solution. Equally in the ‘chunking’ process we talked about, it’s very unlikely you can just arbitrarily choose where to chunk. You need to understand exactly where is best to perform chunks such that you preserve the physics/chemistry of the molecule.

There were also many obstacles the team had to deal with. That method of breaking down a complex system into manageable chunks doesn’t scale well - meaning if you were to apply it to a molecule double the size, you’d need 25 times more computing power to make it work. To counteract this, the team realised that at a certain distance from the centre of their Trypsin molecules, effects like entanglement and other non-local correlations were effectively dead and absent. This meant they could truncate, in other words simplify, their chunking approach and still generate accurate results.

Another achievement involved the team improving the algorithm ‘SQD’, calling their new approach ‘TrimSQD’. Generally, SQD can be really useful in quantum chemistry calculations, as one is able to leverage the quantum computer to represent huge electron configuration spaces. This is something a classical computer would inherently struggle with, instead we can use the classical computer to interpret the results and find the solution. However, searching for the solution in these huge spaces can be like the old analogy of a needle and a haystack. TrimSQD works a little better by breaking down the search area into smaller subareas, this in turn helps us identify and filter the useful information from the junk. (oh and by junk I mean things such as quantum noise, decoherence or gate errors… these sorts of things)

What does this result really mean?

This fusion of classical and quantum computation is rather elegant. In order to accurately and truly determine the electronic structure of a protein, we can’t try to solve things in just a classical way. At the smallest of scales, quantum mechanics dominates the interactions - meaning that the best direction to head towards involves a quantum-mechanical treatment of an entire protein. Although powerful classical computers are efficient in modelling certain parts of a protein, this combined QCSC approach pushes boundaries and asks the question of what role do quantum computers have in building and developing new and more accurate research. Not only does this piece of research represent international collaboration but it also demonstrates that there’s merit to combining quantum and classical computing together. And the research itself has so much potential! By pushing the limits of what biological molecules we can simulate, it means we can discover new complexes and develop new medicines or study the mechanisms to complicated diseases. It means that we are getting much better at predicting how biology works at the smallest scales - the scales where quantum mechanics is king. This won’t just have a positive impact on healthcare and medicine. Fields like material science, chemistry and physics will all benefit greatly from a hybrid-quantum computing workflow. So although I don’t usually like to predict the future, it seems clear to me that quantum computers are going to change society for the better!

It was a rather normal day at work for me. I was sitting, reading a paper about nuclear physics. All was well. I was happy.

This paper went on to talk about how nuclei form. In particular, it described the formation of ‘weakly bound nuclei’ which are nuclei which have nucleons that can be removed with very little energy required. As I read on, I learnt for the first time that the reason why these nuclei remain bound (or just about) is due to the delicate balance between the strong nuclear force and the Pauli Exclusion Principle. The strong nuclear force, which is the most powerful of nature’s four fundamental forces, is responsible for ‘gluing’ protons and neutrons together. Without it, nuclei wouldn’t exist. Neither would people for that matter, which are made of atomic nuclei.

Although on the surface this seemed fine, something didn’t feel quite right. The strong nuclear force, is of course, an attractive force. Yet the Pauli Exclusion principle is most certainly not a force of any kind. So then how is this principle able to physically counteract the attractive nature of the strong force - leading to weakly bound nuclei?

To answer this question… I would need to consult the man himself.

Wolfgang Pauli:

Wolfgang Ernst Pauli was born in Vienna in 1900. His father was also called Wolfgang Pauli (confusingly) and his mother Bertha Schütz. Wolfgang’s middle name is rather iconic as it is taken after his godfather Ernst Mach, the inventor of the “Mach Number”. You might have heard in movies about military jets going past Mach 1 or 2? Just two months after graduating from secondary school with a distinction, Pauli published his first paper on Albert Einstein’s theory of general relativity. He would then go on to study for a PhD under Arnold Sommerfield - a prominent German theoretical physicist whose research is foundational to current quantum mechanics and atomic physics.

After receiving his PhD in 1921, Pauli spent a year at the University of Göttingen as Max Born’s assistant, another renowned physicist. It was when he became a lecturer at the University of Hamburg between 1923-1928 that he would develop the Pauli Exclusion Principle, one of the most important rules in quantum mechanics.

But before we go into that, let’s continue Pauli’s story.

Pauli was appointed professor at ETH Zurich in 1928 and was awarded the Lorentz Medal in 1930. Decades later he was awarded the Max Planck Medal, but fell ill with pancreatic cancer that same year, dying in December 1958. However, his important contributions to the field of quantum mechanics lived on and have become a cornerstone in our knowledge of the quantum world today.

There is also an interesting story regarding his last moments in Rotkreuz hospital in Zurich. Throughout Pauli’s life, he had been chasing a particular number in his research. This infamous number was the fraction 1/137 which is nearly exactly the value of the fine-structure constant, a dimensionless constant that quantifies the strength of the electromagnetic interaction between charged particles. When his last assistant, Charles Enz, went to visit, he asked Charles, “Did you see the room number?”. It was 137.

The Pauli Exclusion Principle, put simply:

No two fermions can exist in the same quantum state.

This is what Pauli proved. It’s simple but it has incredible consequences. To be a little more specific, the full principle states that multiple fermions, which are particles with half-integer spins (such as the electron), cannot occupy the same quantum state. It would probably take too long to discuss what makes a particle a fermion, but simply think of fermions as things such as electrons, protons and neutrons.

Pauli was able to derive this phenomenological rule based on atomic spectroscopy experiments of the time. These experiments showed phenomena that could not be described by the latest atomic model theories. Although his proposal of electrons obeying this exclusion principle came first in 1925, he would generalise this to all fermions with his Spin-Statistics Theorem in 1940.

When does the principle physically come into play?

In many, many scenarios.

1. The Pauli Exclusion Principle helps explain the electron shell structure of atoms as well as the way atoms share electrons. This can inform us of the size and structure of the elements of the Periodic Table. It also helps us figure out the chemical behaviour of the elements, such as which elements are more or less reactive or which elements will react with others.

2. The Principle helps us to understand the properties of conducting metals - for example the very copper wires which power our homes. You can use the principle to understand why metals are conductive, insulating or semi-conducting.

3. The Principle also has consequences for astrophysics! For example, it can impact White Dwarf stars - which are dead stars. When stars die, gravity tries to collapse all the matter into the centre, but due to the fact that electrons can’t occupy the same state, the Exclusion Principle counteracts this and prevents further collapse.

Finally, how my confusion was removed!

There are only four fundamental forces (so far at least) and the Pauli Exclusion Principle isn’t one of them. These forces are gravity, electromagnetism, the strong nuclear force and the weak nuclear force. They are considered fundamental as every single interaction that occurs in the universe can be accounted for by one of these four interactions. These four forces cannot be simplified or broken down in to anything more basic. Another condition for a force to be a force is that they must be mediated by exchange particles. In other words there must be some sort of ‘carrier particle’ that carries the force and enacts the force upon matter. The only exchange particle to have not been detected yet is the one for gravity (called the graviton).

What this means therefore is that the Pauli Exclusion Principle is more aptly named a ‘pressure’. This is why we often refer to the effect of the Principle as the degeneracy pressure. There is no exchange particle for the Pauli Exclusion Principle and it is most accurate to consider it as a fundamental constraint. Nevertheless, the principle causes particles to repel from each other - producing a repulsive force at a large scale.

To conclude, the Pauli Exclusion Principle is a pressure that produces a force.

I rest my case :)

References:

1. By Marekich - File:Nucleus drawing.svg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=121635399

2. By Unknown author - original URL (archived URL), CC BY 4.0, https://commons.wikimedia.org/w/index.php?curid=49875210

The Distinguished Professor Emeritus Jim Al-Khalili:

It really would take a long time to name all of Jim’s achievements!

• He was awarded CBE in 2021 for services to science and public engagement in STEM (Science, Technology, Engineering and Medicine).

• He was awarded the Michael Faraday Prize, the Kelvin Medal and Prize and the Stephen Hawking Medal.

• He is known for his numerous science books, TV-shows, documentaries, podcasts and of course the radio.

• He has been made an Honorary Doctor of Science at Royal Holloway, the University of York, the University of St Andrews and the University of Birmingham.

• This list could continue for quite a while!

Jim’s background is in nuclear physics and he completed his PhD thesis in 1989 on Nuclear Reaction Theory - specifically elastic scattering. Here’s a funny excerpt from it that made me laugh:

Yet, over the years Jim’s interests have slowly adapted and moved towards quantum mechanics within biology. Perhaps nuclear physics was simply too easy?! As such, one can see that most of his recent work probes the boundaries of quantum biology, from the role of quantum mechanics in DNA to the way organic molecules interact with each other.

Having taken a quantum biology module, myself, at the University of Surrey (where I too reside) - I can certainly say that this research is cutting-edge and incredibly complex. The field of quantum biology is often perceived as being only a couple decades old. It is in fact almost 100 years old and was first put into the spotlight by some of the greatest scientists we know - Pascual Jordan and Niels Bohr, then Erwin Schrödinger. And in the case of Schrödinger, he wrote a mind-altering book called ‘What is Life - The Physical Aspect of the Living Cell’ - you should read it!

The Talk - Does Life need Quantum Mechanics?

In the beginning Jim showed us exactly what the field of Quantum Biology is - it’s the intersection of Biology, Chemistry and Physics. Intuitively this makes sense, because if you’re trying to develop a holistic description of life - you’ll at least need to involve theories from all of these subjects (and probably some maths too). What makes less sense is the idea that life inherently uses quantum mechanics to it’s advantage. The question instantly begs… how does life know about quantum mechanics? And yet, quantum mechanical phenomena such as superposition, entanglement or tunnelling can play a serious role in lots of biological processes - ones without which humanity would probably never exist.

Before Jim dove into the details about quantum biological processes, something that caught my attention is that he mentioned Max Delbrück. Born in 1906, Max was a German-American biophysicist who was fascinated with genes and what induced genetic traits. He would eventually share a Nobel Prize in Physiology or Medicine in 1969 for discovering the replication mechanism of viruses. What is amazing about Max is that his meetings with Niels Bohr and Wolfgang Pauli inspired him to pursue physics and biology for the rest of his life - and Max in turn went on to spark other physicists interests in biology. Max’s research on gene mutation influenced Rosalind Franklin, Maurice Wilkins, Francis Crick and James Watson, who went on to discover the structure of DNA. This is often the way in the sciences, that multi-disciplinary discussion leads to discovery.

Jim moved on and starting speaking about the numerous biological processes that could be given a quantum mechanical description. It was eye-opening as it changes the way you think about life.

Some processes you may not have thought about before…

For example, how do migrating birds know which direction to fly thousands of miles? It turns out that magneto-reception, an inherently quantum process, is the answer! Magneto-reception is in other words the bird’s ability to detect and see a map of the Earth’s magnetic field lines. Current research suggests that the quantum formation of ‘radical pairs’ inside the bird’s eyes essentially allows the bird to see magnetic field lines and plot a course of migration.

What about Photosynthesis, a process which allows plants to absorb light, water and carbon dioxide and produce energy for itself? Without it, trees would not exist and neither would humans. But isn’t it odd that the absorption and transport of light to the reaction centre happens at close to 100% efficiency and almost instantly? Well it turns out that a quantum mechanical explanation could be the answer here! The packet of energy formed from the interaction between light and a leaf cell, for example, creates something known as an exciton (a packet of energy). This exciton has to travel down a path to the reaction centre of the plant in order to be used. Initially, the consensus was that energy transport in photosynthesis was completely random, like a drunken sailor staggering down a hill. But given such a near-perfect efficiency, the quantum solution makes much more sense. Instead, the exciton exists in a superposition state which allows it to explore all pathways simultaneously and choose the most efficient one. Furthermore, the innate structure of the leaf cell protects the quantum state, keeping it coherent for just long enough that the energy can travel down the optimal path. Thus - near 100% efficiency.

DNA Tunnelling

As Jim said, the idea of quantum tunnelling occurring in DNA goes way back to Per-Olov Löwdin - a Swedish physicist and professor at the University of Uppsala. Löwdin suggested that perhaps the process of protons tunnelling from one strand of DNA to another could drive mutations, leading to genetic diseases, cancer and the ageing process.

The idea of quantum tunnelling is surprisingly simple - or it can be described rather simply at least. Imagine you have a football and you are stood at the bottom of a hill. Now you can either expend a huge amount of energy and kick it up the entire hill. This would be the ‘classical’ way of doing it. Or, you could spend a little less energy kicking it about 3/4 of the way up - and they sometimes the ball will just ‘phase over’ to the other side. This is quantum tunnelling.

Jim’s group conducted lots of fruitful research on this idea, proving that quantum tunnelling was actually dominant in DNA proton transfer. What is even more enlightening is the fact that the DNA structure isn’t defenceless against this process either, as Jim’s group showed in future research. In fact, a particular enzyme that gets produced can suppress this tunnelling and greatly reduce the likelihood of mutation.

And although such quantum processes haven’t been directly observed in the lab (it would be incredulously hard), these high quality simulations reveal a deeper truth about life and processes of the living cell.

And sadly the talk must end…

It really was a wonderful talk. What really excites me is how open-ended the field is at the moment - there seems to be a treasure trove of directions of research. Firstly, I would argue this could be one of the hardest fields to get into. Unlike idealised quantum environments which operate at cold temperatures or in vacuums with lab-grade conditions (this is why I like quantum computers reader), the biological cell is hot and messy. So much noise is generated within the cell and so many interactions take place that quantum states will have essentially no lifetime whatsoever. In other words, they will decohere instantly. Yet life makes use of these infinitely brief moments and has evolved to either maintain the quantum effect for a little longer or to suppress it.

And beyond the pursuit of knowledge, it is also satisfying that the applications of theoretical quantum biology may very well lead to breakthroughs in health and medicine.

Could quantum biology, and indeed quantum computing in the same token, lead to cures and incredible medicines?

Well, it’s becoming less and less of a fantasy and more of a research path every single day!

(Thumbnail photo accessed here)

Quantum computers promise great advantages over normal computers, precisely because they can theoretically solve complex problems much faster and sometimes with less resources. They provide novel avenues for research at academic institutions, leading tech companies and large corporations alike. For example, pharmaceutical companies will be desperate to get their hands on quantum computers as they could revolutionise the method of developing new effective drugs at a cheaper cost.

So where’s the catch? How come the technological landscape hasn’t already been revolutionised and quantum computers aren’t floating around in every warehouse in London? Well, one of the main enemies of quantum computing is something known as decoherence. Decoherence is a phenomenon whereby a quantum system leaks its ‘quantumness’ to the external environment. As the quantum system, which in these computers will consist of a precise array of qubits, starts to decohere - the quantum computer will become less and less reliable. Operations will start to fail and amazing properties that yield advantages such as superposition or entanglement will be less effective. In turn, decoherence makes quantum computers lose their power, rendering them impotent.

Now, the goal isn’t to completely eradicate decoherence. This is impossible. It is like trying to remove every particle of nitrogen from the atmosphere. What is more feasible is to mitigate decoherence. There are many ways to do this: perhaps you add shielding to your quantum computer or maybe you cool your quantum computer to cryogenic temperatures (just above absolute 0K). However, today we are going to be looking at a particular approach within the larger field of Quantum Error Correction (QEC) known as Surface Codes.

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So, what are Surface Codes?

Surface codes might just be one of the most promising roads to Quantum Advantage!

Imagine a chess board with all 64 black/white squares. If you look at the pattern, you might see a sort of 2D square lattice - a collection of squares that join together at the edges and corners. We create a similar lattice, but with qubits instead. By arranging qubits onto a 2D lattice, we can actually perform precise measurements to detect whether a specific qubit has suffered from an error or not! There are many magical effects that can take place here, reader. Another interesting thing we can do is form something known as a logical qubit. Let me explain what this is:

Imagine you have three apples. Every so often, one apple will rot and turn brown, however, you are given the magical power to revert all apples to the ‘majority state’. In other words, if the majority of apples are healthy then you can apply your power and turn them all back to healthy. By continuing to apply this sort of ‘rotting correction’ you can maintain the overall health of the three apples. You can’t guarantee that the individual apples will remain healthy but you can guarantee that all three will post-correction. Therefore, you would only consider that the group of three apples itself is reliable and can be used - and you could call this a logical apple.

(This ‘rotting correction’ procedure we apply to the logical apple is more formally known as Repetition Code)

Within Surface Codes, we group together physical qubits and form logical qubits that are more resistant to errors and have longer coherence times. Although Surface Codes vary, generally our logical qubit is made up of data qubits and measurement qubits. Data qubits, namely so, hold the data of the quantum state. We want these to remain accurate. Therefore we also have measurement qubits, which detect errors in the data qubits in a weak manner such as to not disturb the data qubits. We call this Weak Measurement! Put simply, measurement qubits check the parity of the data qubits - this means they identify which one of the data qubits is the odd one out with an error. Then we can flip this qubit back to its correct state without collapsing the entire logical qubit!

(Remember, reader, we can’t just fully measure the qubit as by definition measurement collapses the qubit and makes it no longer quantum)

Below I’ve sketched out what a simple example of a Surface Code logical qubit might look like for distance-3. We call it distance-3 as each length of the surface has 3 data qubits on it. The reason why we don’t have any smaller distance codes is because it has been proven that distance-3 is the smallest surface code that can correct both types of single-qubit errors at the same time (phase-flips and bit-flips).

What’s so good about Surface code?

1. We can lower error rates by actively correcting qubits during computation.

2. Surface code can counteract both types of single qubit errors (phase/bit-flip)

3. The Google Research team have shown exponential error correction with increasing surface code size using their processor Willow.

Are there disadvantages to Surface code?

1. They aren’t incredibly practical. For example, a distance-7 Surface Code requires 97 Physical Qubits just to make 1 Logical Qubit.

2. Some architectures have more efficient ways to correct errors. For example, in neutral atom quantum computing we can use LDPC (Low-Density-Parity-Check) Codes which have the benefit that they can move qubits around and use less qubits overall.

Some more beautiful examples of Surface Codes!

So the distance-3 surface code I showed above is a known as a Planar code - precisely because it sits flat on a plane. However, there are other variants of Surface Code each with their own unique properties.

Toric Codes:

Namely, they form the shape of a Torus, which is a doughnut. The surface code lies on the surface of this Torus, the shape of which can be seen below1. In certain cases this type of surface code can be advantageous. Think about it… this shape is like a large piece of paper that naturally wraps around meaning that the qubits which are on ‘opposite sides’ can now interact with each other.

Hyperbolic Codes:

Here’s a bit of a trippy one. Hyperbolic codes form an incredible sort of tiling effect which we call a hyperbolic plane. The main property of hyperbolic surfaces are that they have negative curvature everywhere. A negative curvature is like a bit like a horse saddle, it curves ‘inwards’ meaning you couldn’t put a flat piece of paper on it without deforming the paper. Now this is the trippy thing: because the hyperbolic plane is negatively curved, it means that you can actually cram more shapes onto its surface at a single point.

If you had a flat piece of paper and I told you to draw as many squares as you could originating from the same single point, and to make sure that the squares never overlap - you’d only be able to draw four. But the rules change in negative curvature. This means, for example, at a certain negative curvature you could fit 5 squares originating from the same corner. See the image below2 if you don’t believe me!

Finally, a must-watch video:

This is a really good podcast about Surface Codes, hosted by ‘632nm’ and lead by the legendary Austin Fowler - a prominent Quantum Computing Research Scientist. I first came across him from a Coursera course from Google Quantum AI! He has a knack for explaining the complicated stuff with ease. Anyway, if you have a moment you should probably take a look at this podcast/interview.

Thanks as always for reading and a HAPPY NEW YEAR ❤️