Modest Proposal for a Quantum Minicomputer Based on a 4x4x4 Cube of 64 Photonically-connected Near-perfect Discrete Qubits with Full Qubit Connectivity

I’ve been thinking a lot recently about the potential for a Quantum Minicomputer based on qubits as discrete components, comparable to the original transistors before integrated circuits were invented, with photonic connections to and between the qubits. Denser and denser chips are all the rage for quantum computing, for hundreds, thousands, and millions of qubits, but chip technology is expensive, unwieldy, and difficult to work with — a very high bar for a nascent technology like quantum computing where agility, experimentation, and rapid evolution are the most valuable qualities, not something that is ready to be turned into final chip form, just yet.

At least at present, a critical quality is to keep qubits far enough apart so that unwanted interference or crosstalk don’t corrupt sensitive quantum state. So packing them close together seems like a really bad idea.

I’m also a fan of enabling amateur experimentation and lower-cost academic experimentation, which just isn’t possible for dense, expensive chips.

So, my proposal is for a simple, 4 x 4 x 4 cube or 3D lattice of 64 near-perfect qubits, each qubit roughly the size of a sugar cube (Qubes?!) or, dice, which would be so appropriate given the probabilistic nature of quantum computing, with photonic links between the qubits, and optical switching to be able to dynamically route quantum state for full any-to-any (all-to-all) qubit connectivity. The goal is to be able to execute a physical quantum circuit on physical qubits with zero errors for several thousand physical gates at least 90%, 95%, or even 99% of the time. A relatively small number of circuit repetitions (shots) can be used to find the dominant result if only 1–10% are incorrect — different from the majority. A fairly modest goal. I think that’s enough qubits to do a fair amount of computing and even achieve a significant degree of quantum advantage. Again, this is a proposal for a quantum minicomputer, not a high-end quantum computer.

The intention is limited to a Quantum Minicomputer, with no intention to scale to thousands or millions of qubits. But limited scalability is still possible, like from 4 x 4 x 4 or 64 qubits to 5 x 5 x 5 or 125 qubits, 6 x 6 x 6 or 216 qubits, 7 x 7 x 7 or 343 qubits, or even 8 x 8 x 8 or 512 qubits. Maybe it could scale a bit more, maybe even 10 x 10 x 10 or 1,000 qubits. But the goal is that it’s just a minicomputer, not truly high-end.

To be clear, this proposal for a quantum minicomputer is designed to be a fully-functional, general-purpose quantum computer capable of running real, but low-end, practical real-world applications. This is not a mere demonstration system or educational tool as some very low-end quantum computers are, which are intended simply to learn about quantum effects rather than to do practical work. It is intended to be appropriate for corporate and academic researchers, who are intending to actually do useful work with these systems. It would be comparable to the level of capability that the early classical minicomputers offered, such as the DEC PDP-1, PDP-7, and PDP-8, and maybe even the PDP-11.

The hope is that the combination of significant physical spacing and photonic connectivity would have the best chance of reducing error rates and increasing coherence times to beat even most high-end quantum computers that are based on densely-packed qubits.

The assumption is that these would be superconducting qubits, either transmon, silicon spin, fluxonium, or other similar technologies. And it is presumed that a cryostat will be necessary.

Whether diamond NVC (Nitrogen Vacancy Center) qubits operating at room temperature would be suitable for such a quantum microcomputer is an interesting question, probably hinging on gate error rates. I’ll defer that possibility as outside of the scope of this modest proposal, at least for now.

Whether trapped-ion or neutral-atom qubits would be appropriate for a quantum microcomputer could be debated, but for now, I presume that the answer is no since their error rate is too low and the physical setup is too complicated.

The main reasons that such a high-performance quantum minicomputer is not feasible using current technology and by current vendors and researcher are:

1. Too heavy a focus on high-end systems. A quantum minicomputer doesn’t appeal to them. They’re thinking big, intentionally.
2. Too much focus on high-end scaling. Focusing on thousands and millions of qubits.
3. Too heavy a focus on using custom chips. Complex, expensive, difficult to work with.
4. People have fallen head over heels for the fantasy of quantum error correction. Adding lots of complexity and still far out in the future.
5. Tolerance for relatively high error rate. People should be panicked that they can’t achieve a full three nines of qubit and gate (and measurement) fidelity, but they haven’t.
6. Excessive focus on quantum simulation for physics and chemistry rather than on analytical calculation. Less need for full connectivity.
7. Lack of priority and commitment for full any-to-any (all-to-all) qubit connectivity, maybe because they can get away without it for quantum simulation.
8. General belief that no practical applications are possible without hundreds to a thousand or more qubits.
9. People are too willing to pursue software workarounds to deal with hardware defects and deficiencies. What I call overtooling.
10. Lack of commitment, priority, and resources to address hardware defects and deficiencies. Little apparent interest in addressing problems at their source.

The goal would be that the qubit cubes could literally snap together, Lego style, including the photonic links between adjacent qubit cubes. Simple, straight line, photonic links, in three dimensions. With optical switching embedded in the individual qubit cubes (qubes?!). No special tools required to assemble.

Given the significant spacing between qubits to maximize isolation and minimize crosstalk, should the actual superconducting qubit circuit within each qubit cube be much smaller or much larger than is common today to optimize for longest coherence time, fastest gate execution time, and lowest error rate — optimizing for the largest and deepest quantum circuit that can be executed before the cumulative error rate compromises results of circuit execution (full circuit of several thousand gates executes without any error 99% of the time)?

This proposal is dedicated to and focused on maximum physical fidelity of qubits and gates, without any error correction, error mitigation, or error suppression. Not a single atom or photon wasted on complicated error correction schemes.

Do whatever it takes at the hardware level to achieve the lowest error rate, maximum coherence, and minimum gate execution time. Minimizing — actually, eliminating — the need for complicated and costly error correction, error mitigation, or error suppression. Just say no to Magic State Distillation and other complicated, expensive, and unwieldy approaches. Just say no to fault-tolerance — by saying no to common faults. Keep It Simple, Stupid! (K.I.S.S.) This proposal can do this because its focus is on producing a quantum minicomputer, not a high-end quantum computer.

Since the qubits are all separate, they can be mass-produced in large quantities and then individually tested and characterized (QC — quality control) so that bad or mediocre qubits can be discarded, so that the qubits in a given lattice (4 x 4 x 4 cube of qubits) can all be of the highest quality. Or at least matched for a target quality level if one wanted to minimize cost vs. maximize quality at a higher cost.

An intensive effort to identify and eliminate, not just mitigate, the causes of so-called TLS defects and any other causes of parasitic coupling may be essential to achieving the near-perfect qubits required for this proposal for a quantum minicomputer.

And controlled experiments become possible with different quality levels or different ranges of quality, such as how closely matched (tolerance) do they need to be for most applications, and what’s the lowest quality level or widest mismatch which is still generally useful.

How would the qubits be numbered or addressed? Rather than a linear 0–63 address, a 3D address might be appropriate, with four possibilities in each of the three dimensions, so that qubit numbers would be a triple, (0–3, 0–3, 0–3), with two bits needed to specify each of the three dimensions.

Even though full any-to-any qubit connectivity would be fully supported, there would be some optimization potential for nearest neighbors. With three dimensions, that means that each of the interior qubits would have six nearest neighbors rather than four, and each of the non-edge exterior qubits would have five nearest neighbors rather than three.

The goal for what I am calling a Quantum Minicomputer, would be absolutely ZERO redundancy, other than using circuit repetitions. Maximize physical hardware performance, even if for a more modest number of qubits.

Another way of phrasing it is to ask what is the largest quantum computer which can execute a physical quantum circuit on physical qubits with zero errors for several thousand physical gates at least 90%, 95%, or even 99% of the time. Maybe that’s somewhat below 64 near-perfect qubits (say four to five nines of physical fidelity), maybe somewhat above 64 qubits.

Logical qubits have no relevance. That’s the whole point, to maximize physical performance.

Room temperature has no relevance either. Biting the bullet and accepting the need for a cryostat.

What do I mean by a near-perfect qubit? I’ll leave the details rather vague, although I have written extensively about that elsewhere, but simply state it as a much lower error rate for gates than a typical (or even best-of-breed) NISQ quantum computer, but well-short of what the “perfect” logical qubits of quantum error correction (QEC) are promising. Roughly somewhere in the four to five nines of fidelity, but maybe a little less but still far enough above three nines so that the error rate is not a significant problem for modest to moderate quantum circuits of a few thousand gates. Simply think of a near-perfect qubit as having a fidelity being midway between a NISQ qubit and a logical qubit.

To be clear, this is not a photonic quantum computer. The connections between qubits are photonic, but the qubits themselves are not photonic.

Another design goal is to have a fully functionally-complete gate set, including arbitrary qubit rotations so that compilation is dirt-simple, not requiring any complexity or extensive resource demands. Just say no to the Solovay-Kitaev Theorem and complex compilers.

A goal is to fully eliminate any perceived need for what I would call overtooling — having any tools whose only real, main reason for existence is to compensate for or mitigate limitations or defects in the hardware. Fix the damn hardware!

Very high-end quantum computers may have a need for complexity, but a quantum minicomputer must not.

Simplicity and ease of use. Those are the watchwords.

That’s the basic idea.

An open source, collaborative effort would be best. More about co-petition — cooperative competition — than closed competition and proprietary intellectual property. I can envision a dozen or more research groups all focused on this one vision of a quantum minicomputer. They may cooperate and collaborate on some aspects, while pursuing alternative approaches on some aspects, and then sharing the results of the alternative approaches based on successes and failures. There may indeed be a dozen or more successful alternatives for a quantum minicomputer, each optimized for different technical criteria, performance, cost, and other factors.

Might this inspire a lot more innovation and experimentation, and enable a broader range of smaller labs to get a lot more deeply into the design, research, and development of quantum computers?

So, a simple polling question, is this a good idea or a bad idea?

I have three basic questions for serious readers who might be in a position to implement or at least use such a Quantum Minicomputer:

1. Does this type of machine make sense from your perspective and can you anticipate practical applications with 64 near-perfect qubits and full qubit connectivity?
2. Do you have contacts in the academic hardware research community who might be interested in pursuing research and experimentation for such a machine, and potential for funding? With the proviso, that it should have high probability for rapid commercialization. VCs should be interested, too, but the research needs to be solid first.
3. Would you be interested in turning this informal paper of mine into a formal research note, with or without me as a co-author, on the potential for such a machine and some of the main research areas needed? A call to action. This proposal is good enough for my own interests, but may not be sufficient for others, particularly researchers and funders, who insist on a bit more formality.

My strongest interest is for a young person interested in quantum computing to take this modest, informal proposal and turn it into reality, either by fleshing out all of the details, or hooking up with a research institution that can provide the necessary support to bring these ideas to fruition. This could be:

1. A masters-level student.
2. An advanced (or super-smart, super-motivated) undergraduate.
3. A super-smart and super-motivated high-school student.

Okay, that’s it, in a nutshell. I know this modest proposal is very light on details, but that’s as far as I personally wish to take it. I’ll leave any and all details to those who might wish to take up the challenge and run with it.

I would strongly encourage any and all efforts to pursue, collaborate, and communicate, both formally and informally, all aspects of this modest, informal proposal, ranging from blog posts to research notes. There are plenty of aspects which need plenty of attention. And such efforts, especially collaboration and communication, should continue even if or when anybody might begin an actual effort to begin a research project to actually build a quantum minicomputer.

For now, for me, this is simply a thought experiment. I’ll leave it to others to consider turning it into a reality.

For more of my writing: List of My Papers on Quantum Computing.