You might be familiar with the qubit, the fundamental unit of quantum information. As its name suggests, a qubit in a quantum computer performs the same function as a bit in a classical computer, with a major difference: Qubits can be treated as a 0 or 1 simultaneously, allowing quantum systems to process information much more rapidly than the fastest classical systems.
But there’s also a qudit, a different way of storing and making use of quantum information. Gizmodo spoke to Christine Muschik, a quantum researcher at the Perimeter Institute for Theoretical Physics and the University of Waterloo, Ontario, about the computational unit, which could capitalize on a key tenet of quantum systems to do more complicated computing than classical computers are capable of.
Muschik’s team published research last week in Nature Physics that they say “open the door for hardware-efficient quantum simulations of gauge theories with qudits in near-term quantum devices.” Muschik’s new paper comes on the heels of a 2021 paper on the same subject, published in PRX Quantum.
Gizmodo spoke with Muschik by phone to discuss the nature of the research paper and the future of qudits more broadly. Below is our conversation, lightly edited for clarity.
Isaac Schultz, Gizmodo: I realize you have this new paper out, but maybe first we can just talk about the term qudit, and what the heck it means.
Christine Muschik: We want to make computing as efficient and as powerful as possible. So that’s the overarching mission, to make computing as powerful as possible. Step number one is, of course, that we think quantum computers have an opportunity to be more powerful. But once we are on the route of harnessing quantum, what is the most efficient way to do that? The field was very much inspired by how regular computers work, because in regular computers, you have zeros and ones, and you can do logical operations on that. How most quantum computers work is you also take zeros and ones, only you add your bit of quantum to it. The zero and one can be in a superposition, and then, instead of a bit, you have a qubit. But the philosophy is the same. You have zero and one, and that’s how you process your information.
Now you have qudits, with a ‘D’—because why do we stop at two levels? Couldn’t we just go on? In modern day quantum computers you encode your qubits, you have just two levels and all the others you ignore. But what happens if we don’t ignore all the other states, but we encode information [in them]? We started with a qutrit—just one more level—a single information carrier is now three levels, three possible states.
Gizmodo: If you treat each one of those as a different way of encoding information, it sounds like you could encode exponentially more information.
Christine Muschik: You can fit more information by using more levels, but not exponentially more. If I were to send you a bit, I can send you a yes or no, but if I send you a [qutrit], I have the choices between yes, no, and maybe.
Gizmodo: How does that change the operation of a quantum computer?
Christine Muschik: There’s a price to pay, and then there’s the reward that we reap. You have to have more control across more levels, but the reward is that you have a number of information carriers—a register—that is much more compact.
The most important thing is that your circuit complexity shrinks. We’re in the business of designing logical circuits, and what hinders my team and me all the freaking time is that if the circuit gets too long, that’s our bottleneck. Quantum computers are not ever corrected, and every time you make an operation, you introduce a bit of noise. If you have a long, long, long, long, circuit, you accumulate so much noise that in the end you see only noise and not your answer. That’s our headache, and why we don’t sleep properly.
What we realized with these qudits is that, because information is manipulated so efficiently, it’s like you’re putting your circuit on a diet. Everything is more efficient, and you get your result more quickly and with less noise.
Gizmodo: Now we’re really touching on the research—could you speak to your team’s latest paper and exactly what you found? How did it move the needle on this idea?
Christine Muschik: My team had this dream that we wanted to simulate fundamental particle interaction—that’s actually what I got my job for, to simulate fundamental particle interactions. But it’s really hard to do on a quantum computer. You have a lot of noise. We had this dream of fundamental particle interactions and this other team was in the business of building a qudit quantum computer. We joined forces.
I would argue our outcomes moved the needle two-fold. We could simulate fundamental particle interactions beyond 1D—that was the first thing we set out to do. But accidentally, we also accomplished something else: the first full qudit algorithm. We put everything together and took it for a drive, a whole algorithm. Now you have a computing capability we can apply this to now.
Gizmodo: I was going to ask you about applications now that, now that you’ve derived this.
Christine Muschik: The obvious thing is in particle physics, where you can simulate many things. But then there are also other problems you can simulate, like in materials science, and chemistries you can simulate. It’s also extremely useful in quantum enthusiasts’ notion of the quantum internet that people try to build. You can make information more secure in quantum communication. We realized all these things last year in summer in a joint workshop at the Institute of Quantum Computing and the Perimeter Institute, where we brought together experimental people, theorists, and users. This week we started to write a perspectives paper, because we want to make a roadmap of how qudits can be useful in different areas of quantum technology. And also what is missing—there are gaps, holes, and in some cases canyons of missing information. For qudits, how do you do error mitigation, optimal control, error correction? There’s so much to figure out.
Gizmodo: How do these simulations and kinds of theoretical frameworks marry with real world experimentation that’s going on at places like CERN, at LCLS—places where they are colliding particles and looking at such subatomic interactions?
Christine Muschik: All our quantum computers are, like, really proof of concept. They’re small and noisy. We’re very limited by what we can do. We can demonstrate that it works, but we cannot outperform the strongest classical computers. We cannot even outperform my laptop. For a while classical computers will be well ahead [of quantum computers], but eventually they will hit a roadblock. But once we build [a quantum computer] there’s nothing blocking it. There are particle collisions at CERN—the quantum computer, hopefully based on qudits—that can make a prediction for the collision and you can compare that to the experiments. For instance, we simulate particle-particle pair creation, which is something we cannot see in experiments just yet. In the future, there will be experiments that rip particle-antiparticle pairs in QED out of the vacuum, and so we want to compare to that experiment.
But there are some problems where the classical computer is so good, there’s no reason to build an expensive quantum computer for it. But if you have conditions with a lot of matter, or anything dynamical—think of a neutron star, or the beginning of the universe—regular particle physics computing is out of the window.
Gizmodo: You mentioned that qudits should be in the game when we’re talking about particle collisions. Other strategies or quantum computing approaches are being workshopped that might compete in that space?
Christine Muschik: Oh they’re very, very compatible. Some people think that qubits and qudits would be competitors, but we had one quantum computer whose register was comprised of both. I call it a seamless merging opportunity—you can really plug and play according to what you need.
Gizmodo: What specifically are their synergies, and what kind of questions are better explored using qubits versus qudits and vice versa?
Christine Muschik: In our example, we have a gauge theory—just a fundamental particle interaction—and it has two fundamental ingredients. One ingredient is matter—in our case, we had electrons and positrons. It turns out there’s a very natural description in terms of qubits for an electron and positron, so we leave that to qubits. But force fields—what some call quantum gauge bosons—naturally have many different levels. You make everything super inefficient if you try to describe these force fields with two-level systems. We could get a lot more efficiency using qudits for that. Your infrastructure is the same, you just decide what you want to use.
Gizmodo: What are your team’s next steps, and the next step for qudits in general? What does this mean for quantum physics more generally?
Christine Muschik: We simulated for the first time, fundamental particle interactions with the matter and the force fields beyond one dimension. What we need to do next is we need to go to three dimensions, right? We also want to go to more complicated theories. We talked about electrons and positrons and how they interact. But next we want to include quarks and gluons. A few weeks ago we dove into quantum sensing with qudits. And we also need to investigate how to do better error correction on these qudits. If you could have this [qudit] efficiency but also error correction on top of that, then you’d really be in business.
