Everyone can learn quantum now, even at a cutting-edge level…and we have the test scores to prove it!
By Bob Coecke
…with Aleks Kissinger, Stefano Gogioso, Selma Dundar-Coecke, Caterina Puca, Lia Yeh, Hamza Waseem, Sieglinde Pfaendler, Thomas Cervoni, Ferdi Tomassini, Vincent Anandraj, Peter Sigrist, and Ilyas Khan
…historically also featuring David Moore, Samson Abramsky, Peter Selinger, Dusko Pavlovic, Eric Paquette, Ross Duncan, Simon Perdix, Giulio Chiribella, and many more…
The teaching of quantum physics is routinely excluded from secondary or high school curriculums all over the world.
This significant omission from the curriculum could, in the past be attributed to the novelty of the subject and the challenge of the mathematics traditionally deemed to be necessary. Even at a university level, the subject has been seen as “challenging”.
As the advent of quantum technologies and quantum computing become real, and the world faces a true industrial revolution with quantum computing likely to affect large parts of our daily lives, the future workforce will need to be far more comfortable with the core concepts of quantum theory.
The time has come to teach quantum to all.
The title of this post refers to significant research that has been conducted over a two decade period, and which was recently taken to an experimental level in an ambitious and wide ranging project implemented in the past 12 months by a team of researchers in physics, quantum computing and education, and over 50 students between the ages of 15 and 17.
The experiment was the subject of a feature in the respected UK national newspaper The Guardian / Observer, “It’s easier to convince kids than adults about quantum mechanics” and in an article by Oxford University, one of our experimental partners, “Research unveils new picture-based approach to teaching physics”.
The experiment has shown that a unique diagrammatic approach to learning about quantum mechanics can equip school children with enough knowledge of core topics — including quantum teleportation, quantum computing and non-locality — to compete at university level exams with some of the brightest graduate students who are specialists in the subject.
More specifically, the experiment showed that by using an entirely new language for quantum mechanics, that can be found in the book Quantum in Pictures, 15–17 year old secondary school students can pass an Oxford University post-graduate exam. In point of fact, not only did the high school students pass the exam — in many cases they excelled.
The 15 to 17 year olds were not selected on the basis of previous achievements, but were chosen at random from around 1,000 applicants who could commit to a 10-week summer course of short lectures in how to use the diagrammatical method for quantum mechanics — and agreed to take an exam at the end. The format of the course was that of a typical Oxford University post-grad syllabus. After the course we asked the young students to take an exam entirely consisting of previous exam questions for Oxford post-grad quantum courses. We stress here again — a post-grad quantum exam.
The results — 82% passed, of which 48% got distinctions.
Exam questions covered material that is considered to be cutting-edge in terms of developments in the field of quantum computing, and that many experienced quantum professionals would have a hard time handling.
There have been several other attempts to teach quantum at secondary school level, but this has generally been done by simplifying the material, including simplifying the language, the examples, the problems, and moreover going a lot more slowly than a traditional quantum course. In contrast, we covered far more material, and did so in less time than an ordinary quantum physics course.
Quantum physics, and even quantum computing, has now been provably shown to have the potential to be disseminated in a much broader context than is usually assumed. This includes reaching today’s young students who will enter the future workforce, and diversifying the range of stakeholders who get to grips with quantum computing beyond the direct users of the technology. We are particularly excited by the potential to expand this educational tool to students in the developing world. Making quantum more available to a broader audience could also make STEM research much more attractive universally.
The story behind the result
The language of the quantum world notoriously comes with a high-bar. Even once learnt, which typically is at university, working in a practical sense with quantum methods is challenging.
Recognising this, some 20 years ago, we started our first attempt to address the “status quo” culminating in the first instance with a paper entitled “Kindergarten Quantum Mechanics”.
Some features of quantum which took quantum specialists a very long time to come up with, such as quantum teleportation (this theory took some 60 years to emerge) became very easy to convey in the newly proposed language for quantum physics. What made it so easy was that the language was entirely pictorial, and the rules to follow could be compared to intuitive actions like bending and untangling ropes.
Using pictures to simplify mathematics is an idea that has a very long history, including the early work of 2020 Nobel Laureate Roger Penrose, who came up with it in the 1960s when he was still an undergraduate studying the theory of relativity.
Pictorial mathematics of the sort defined by Penrose did not immediately catch on in physics, although by the 1990s, it was used by some mathematicians and also found a foothold in computer science. Around that time, mathematicians such as Joyal and Street showed that these pictures actually were rigorous mathematics.
A major step forward was made in 2007, with what is now referred to as ZX-calculus, originating in work I did with my collaborator (and now Quantinuum Head of Software) Ross Duncan, during our time at Oxford University.
So what is ZX-calculus? It is a new language for quantum that can describe and enable one to derive all the equations for qubits, and as many qubits as you want at the same time. A dedicated blog post on ZX-calculus is available here. Today, ZX-calculus is widely used in quantum technology for solving many key problems towards building and using quantum computers.
The experiment
Besides the uses in quantum technology, in 2009 we proposed an experiment aiming to show that using this new language, secondary or high school students could possibly outperform their physics teachers on quantum problems. Over the years, that idea evolved into the experiment we recently conducted. The experiment was not trivial — many aspects were unconventional, and included a number of obstacles. The team needed to design and conduct it was made up of people from a variety of backgrounds, with different skill sets (reflected in the high number of co-authors mentioned at the top of this blog post. It should be noted that the list is not complete.)
A detailed outline description of our experimental design and some more context can be found here. A detailed scientific paper is also in preparation and will be published shortly.
The teaching materials that had to be created consisted of:
- a text book
- lectures, and
- some worked-out exercises.
There is in fact already a textbook on the pictorial quantum language, Picturing Quantum Processes that I co-authored with Aleks Kissinger from Oxford University, but this is not entirely suitable for the experiment we had in mind, as it required some maths background at university level. In preparation for this experiment, Stefano Gogioso from Oxford University and I wrote a short textbook that would provide a rigorous account of some core quantum concepts without needing any prior mathematical training beyond what is in a standard curriculum at the high school or secondary level. As we wrote the new book we ended up uncovering and then including some cutting edge quantum computing content.
Quantum in Pictures, this new work, was published in early 2023 by Quantinuum (and is available for sale). We used the book, along with a set of accompanying lectures — essentially blackboard presentations of the material in the book — for the experiment, and produced some worked-out exercises for teaching purposes. We intend to publish the lectures and exercises as free videos in the near future on YouTube.
Given the nature of the experimental work, we needed to obtain appropriate permissions, which were facilitated through Oxford University, and resulted in a process that took a little longer than expected, and imposed some operational restrictions. One of these restrictions means that, for example, we could only work with UK-based pupils, which was not originally part of our plan.
In order to recruit our participants, we distributed a flyer to schools and on social media, and received some 1,000 applications. From these, we randomly selected 60 to take part, in order to keep tutoring sessions manageable.
The entire course was delivered online, starting mid-June and ending mid-August 2023. Using the book, recorded lectures and exercises, we held weekly one-hour tutoring sessions in groups of, on average 12 students. This lasted 8 weeks, with the students asked to watch one lecture a week, and attend one tutorial session. In practice this means that we stayed as close as possible to the format of a typical Oxford University post-graduate course, albeit the main difference being that our lectures were recorded and not interactive, which obviously is a disadvantage.
We were not allowed to use any social media platforms due to the ethical restrictions, so there was no means for the students to interact with each other after watching the video lectures or joining tutorials. The timing meant that the course intersected with A-level exams and, in some cases, family holidays. This was a less than ideal teaching situation.
Despite the operational challenges and restriction, to the credit of the students who applied to participate in the experiment, the majority had very good attendance levels and completed the learning portion of the experiment. Then it was time to ask the students to take the exam, made up entirely of questions which had previously been used at Oxford University, exclusively for examining post-graduate quantum courses. Again we followed the timeline and format used at Oxford university for post-graduate courses.
Given the constraints we have discussed, and the preconceptions about the difficulty of gaining a rigorous understanding of quantum theory, we are thrilled with the results: 82% passed, of which 48% got distinctions.
What this experiment has achieved
The new language for quantum from Quantum in Pictures, i.e. the basis for the experiment, is widely used in the quantum computing industry and represents the cutting-edge of quantum science and technology.
In summary, the key outcomes of the experiment are:
- making quantum education accessible to everyone, and
- pushing the cutting-edge of quantum technology.
Governments and organisations around the world stress the need to train young people, and make stakeholders aware of and familiar with quantum technologies. We owe it to the next generations to deliver the quantum revolution in a way that delivers the benefits to everyone, and is not a black box that nobody really understands, in the way that is currently happening with AI.
Now we have a tool at hand, precisely for that purpose!
The deeper context of this experiment
The new quantum language is in fact a radical departure from how Western science has developed for over 2,000 years, going all the way back to Ancient Greek thinkers, such as Democritus and Parmenides. The advent of quantum computing is exposing some limitations on our traditional approach — which although very successful, needs updating.
Democritus taught us that the essence of things is the “atoms” from which they are made. We see this in important scientific perspectives such as reducing physics to elementary particles, medicine in terms of anatomy being reduced to organs, biodiversity in terms of genes, mathematical structures in terms of set theory, information reduced to bits, and many more. However this approach leads to reductionism.
On the other hand, Leibniz (among others) emphasised the relation between objects in space and time as more essential than their spatio-temporal properties. In human terms, what makes true friendships is not what people have in their pockets, but how people get along with each other. That’s relationalism.
Schrödinger added a bit extra to this, in that relationships create entirely new entities that in no way can be reduced to the participants and how they relate, but by putting things together, something entirely new emerges.
Parmenides told us that at any moment, we are all living in a single “photo” representing the now, and that’s all that exists and matters. Temporal progress just stacks these photos one after the other, and this is how our theories of physics are mostly made up: the kinematics is the photo, the dynamics tells us how the stacks are made up.
Heraclitus, living at the same time as Parmenides, conceived the world as in a constantly ongoing flux, or process. There is no “now”, there only is the past, causing the future. You are preparing yourself for some lovely person you met earlier since you want to establish a beautiful existence with them in the future. This is known among experts as “process ontology”.
Our new quantum language goes hand in hand with relationalism, in Schrödinger’s sense, and process ontology, treating them as first class citizens. But at the same time, it comprehends the traditional Western scientific traditions.
We are only starting to scratch the surface of this new worldview, which may be one of the most radical shifts in human thinking ever, encompassing science in general, and humanity as a whole. In many respects this has been the promise of quantum mechanics since the very early days of its discovery in the 1920s.
