Length: ~2000 words, approximately 8 minutes
Status: Draft
The crazy thing about computing is that there are so many ways to do it. One way is to use transistors, like our modern CPUs, but systems as diverse as strands of DNA, molecules, and Tinker Toys can be made to compute. Of course, you don't necessarily want to build a computer out of Tinker Toys. The costs, power consumption, and mean time between failure make such a computer fairly useless as a technology. As a toy, of course, it is fantastic.
Back when I was a graduate student (1997 to 2001, Go Bears!), it seemed like every week there was a paper published in Physical Review Letters showing that "hey my favorite quantum system can be made into a quantum computer." There are also many ways to quantum compute! But so far, what has been much harder is to find a quantum computing technology.
The primary reason for this is that our quantum technologies seem to be far more suspectable to the effects of noise and imprecise control. This is not a fundamental reason. We have known since the mid-1990s that there is a way to take systems that are noisy and which we cannot precisely control, and put them together into a machine where these issues are of a magnitude that they don't matter anymore (for a sufficient definition of not mattering). This is done using the theory of fault-tolerant quantum computing, a prescription for the gadgetry necessary to reduce errors and increase control. Long may fault-tolerance live, and far may she sail!
As far as technologies, most people segment quantum hardware by the different substrates out of which one can build a quantum computer, superconducting circuits, ions, electron or nuclear spins, photons, and more. But there is a more fundamental schism in quantum computing. This is between the brute forcers and the naturalists.
The brute force approach is essentially the idea that we already have our qubit substrate defined, and it is "just" a matter of scaling these up. With some amount of increase in gate fidelities and qubit lifetimes, brute force approaches will eventually execute fault-tolerant protocols and this will be the point where quantum computers become a technology. Brute forcers don't necessarily believe that there won't be necessary improvements and innovations to get to the fault-tolerant scaling regime (or at least the non-hype-saturated brute forcers don't believe this). But they do believe that existing qubits or slight variations of these will be the qubits executing in fault-tolerant protocols of a future quantum computing technology.
The naturalist approach, on the other hand, believes that not all qubits are created equal and that it is possible for there to exist qubits that are fault-tolerant without having to actively engineer fault-tolerant protocols. In analogy with classical computing where transistors are fault-tolerant because of the physics of how they work, naturalists think that finding the correct fault-tolerant substrate is the way quantum computing will be a technology. The main approach here is that of topological quantum computing, where qubits exist as a global protected state in a many-body quantum system. In this approach the properties of the materials out of which one builds the quantum computer are the key ingredient (just as semiconductors were key to the transistor).
Today, the brute force approach is ascendent, most of the companies that are trying to scale up quantum computing are on a path to brute force their way to a technology. The major exception to this is Microsoft's decade-plus effort in topological quantum computing.
It is uncontroversial to say that the naturalist approach, so far, has not been successful. There are currently no (publicly) known working topological qubits that have done even small computations. But is also pretty obvious that if there was a qubit that had the properties predicted for topological quantum computing, that technology would leap to the front of the pack for quantum computing technologies. Which is not to say that it would obviously leapfrog the brute force approaches, as there are many complexities to what makes a technology work than just the basic properties of the topological quantum computer (cost, yield, power, etc. All the stuff companies leave off in their glossy investor presentations.)
Given this state of affairs, where the brute force approach has made tremendous progress in controlling individual and coupled quantum systems, and yet we know that there should exist physical systems that are better qubits, one question to ask is whether there is some way in which these two can be brought together. Is there a quantum middle way?
Of course, no essay asks a question like this in the middle of the essay without believing that the answer is "yes". What would this middle way look like?
To answer this it is useful to understand the two major advances presented by topological quantum computing. The first of these is that there exist realistic physical models whose ground states are quantum error correcting code states, and these models also have an energy gap between these states and their excited states. This means, roughly, that if you could build a system that matches this physical model, at a temperature well below the energy gap, the quantum system can be frozen into this ground state. Any quantum error will need to overcome this energetic barrier to create an error. In addition any small perturbative quantum error, even when spread out over the entire system, does not change the properties of the ground state. This is the first lesson of topological quantum computing: physical systems whose energy eigenstates are quantum error correcting code states should be robust to errors.
The second part of topological quantum computing that makes them natural quantum computing systems, which is I think less widely appreciated, is the way in which one computes on these systems. If the information is encoded into the ground states, and any small local operation cannot disturb this information, how does one get at this information? There are actually a variety of answers to this question, but one of the important facts about these methods is that they "set their own clock".
In the brute force approach, a common thread (though there are exceptions) is that the qubits are energy levels of a system, and therefore the qubit is constantly undergoing evolution which phases between these two energy levels. This means that in order to precisely control this qubit, you really need to be precisely keeping track of this phase. This is very challenging, and effectively means you need something like a clock to keep track of this. One can contrast this with classical transistors. There are rising and falling signal triggers the computations. CPUs have a clock which is distributed to its computing elements and the rising and falling of that clock triggers the computation. (Side note: an additional difference is that in the classical computing world, the data moves across the device as the computation is enacted, whereas in quantum computing we most often bring the control to qubits fixed in space.)
What topological quantum computing offers is something similar. In one form of how to compute on topological quantum computers, one can apply localized fields to a part of the system, and then by adiabatically moving these fields around, one can enact a gate. The topological part of this is that the gate that is implemented only depends on the space-time braid that moving such localized objects around induces. To do a gate, one completes one of these moves. In this sense, these systems "set their own clock", the rate of their gates is set by the rate of doing these braiding actions. There are a variety of variations on this theme, for example using only measurements to enact the topological quantum computing, but similarly, these allow one to not have to precisely track the phase of one's qubits.
One of the challenges of the topological approach to quantum computing is that while it is known that some models of many-body quantum physics give rise to the desired state of matter, it is very hard to go from this model to the real world. Condensed matter systems are notoriously messy: they often have defects and disorder that makes the system you are trying to build not exactly match the model you want. It remains a real challenge to go from the theoretical model to experimental physical systems that support the desired topological phase of matter.
Contrasting with this, we have the brute force approach, which has shown tremendous ability to build qubits and perform small quantum algorithms on them. We know a lot now about how to engineer coherent quantum systems. The middle way then says, well can we take that knowledge of engineering quantum systems, and turn it into the part that is hard for the topological systems, engineering the physical model that yields a topological model? Can we build systems that have energy eigenstates that are error correcting codes, and which we can manipulate using methods that set their own clock? Maybe not gigantic many-body materials, but out of our current systems that admit precise control?
Disclosure. I have been thinking about the middle way for a very long time. A full two lifetimes ago, I wrote a paper with Ken Brown and K. Birgitta Whaley (my advisor) called "Supercoherent Quantum Bits". Damn Physical Review Letters made us change the title to Coherence-Preserving Quantum Bits (grumble grumble something about not inventing new words in titles.) The basic idea of that paper is that there is a four qubit system, that when you turn on exchange interactions between all four qubits has a ground state that is two-fold degenerate, and which is also a single qubit error detecting code. That latter code property means that single qubit errors necessarily require energy in order to excite out of the ground state, much in the same way that topological quantum systems do with many many more qubits. One interesting challenge of this approach is that one of the important properties of topological quantum computing is that there is a constant energy gap, regardless of system size. But there is a lot of wiggle room here, if we make a 9 qubit system, and have strong enough interactions, does this offer a gap that is large enough for protection?
When we were thinking about supercoherent qubits (and related ideas in compass model qubits), one thing we really didn't know was how to manipulate these systems in a manner similar to how the topological quantum computers set their own clock. But one day I was riding on a ski lift with Steve Flammia and Carl Caves, and I realized that I had a big problem. I wasn't getting papers rejected. (Biggest humble brag ever here, could not resist.) Was this an indication that I was playing it too safe? So Steve agreed that we would work together and make sure we got papers that were rejected. This lead to Adiabatic Gate Teleportation, Adiabatic Cluster State Quantum Computing, and Adiabatic Topological Quantum Computing (with C. Cesare, A. Landahl and A. Neels). And yes some of these got rejected! For me it became clear that there were ways to build adiabatic protocols that yield gate based actions, in a manner very similar to that of the topological quantum computing.
There are a small number of people thinking about this sort of approach to quantum computing. It's certainly not mainstream, yet I think it is a viable approach. If I was Bill Gates rich, I'd fund it. Ok, even if I was minor celebrity rich, I'd fund it.
The middle way is a Buddhist term with a couple of meanings. One is to describe a path that steers between a lifestyle of abstinence of sensual pleasure and a lifestyle of sensual overindulgence. The other is to describe a view between eternalism, the idea that there is an eternal self, and annihilationism, the idea that the self is utterly annihilated at death. (Apologies for the condensation of a much more nuanced and complicated concept into two short paragraphs.) I will leave it as an exercise to the reader to map each of these to the brute force and naturalist factions, but am hopeful that some attention can be given to the quantum middle way.