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John Archibald Wheeler is a bit of a hero for me (and also, like all good hero’s a bit of a villain). Discovering his paper “It from Bit” was definitely a huge inspiration for me to get into the field. When I found Wheeler’s paper it led me to Bill Wootters work, and I immediately charged my parents hundreds of dollars to get a copy of very paper Bill had written (I mean who wouldn’t want to read “Quantum mechanics without probability amplitudes“) Amusingly these days I think many who claim the mantle of “it from bit” have not actually read the paper, which is quite radical, you should definitely stop reading this blog and read the paper if you have not.

Because Wheeler is someone who I’ve always been interested in, I was Googling (company plug) around the other day and found out the the American Philosophical Society has a collection with papers, notes, etc from Wheeler. Among these is a typed up note that I don’t think ever made it into a paper, but which I really loved. The title of the note is “THE UNIVERSE AS A COMPUTER”, and is dated “[1980?]”. In it Wheeler first lists possible meanings for the expression “the universe as a computer” followed by possible implications for this metaphor. And by list, I don’t mean a small list, he puts down 48 possible meanings. I love it.

Here are Wheeler’s possible meanings for the metaphor:

THE UNIVERSE AS A COMPUTER |  [1980?]

Possible Meanings of the Metaphor

NOTE: Such metaphors tend to be at once useful and misleading. They are understood only intuitively, vaguely, partially, ambiguously, and abstractly by their authors and users. They are apt to be polysemous–possessed of  multiple and complex meanings, both relevant and irrelevant. Moreover, in the present instance the utilitarian and natural meaning of the very words universe and computer is unknown to an indefinite degree! Physicists who are trying to conceive a new cosmology based in part on the metaphor of the universe as a computer may find the following list clarifying, heuristic, provocative, useful for self-criticism or discussion, &c. It is a partial list that needs to be extended, systematized, edited, explained, and illuminated by examples and corollaries.

1. May be more or less similar or identical to a Turing machine or serial computer, or be wholly or partly I-dimensional.

2. May comprise the equivalent of serial computers operating, either independently or interdependently, in a parallel array.

3. May resemble more nearly a completely parallel computer whose elements are not sub-computers.

4. May represent a hybrid serial and parallel computer.

5. May represent a hierarchy, network, and/or series of many serial or parallel computers.

6. May represent an infinite or finite set of computers.

7. May represent a computer of infinite size, complexity, subdivisibilit (componentry), age, lifespan, sophistication, perfection, power, connectivity, programming, knowledge, intelligence, dimensionality, activity, strangeness, and/or the like.

8. May (or physics may) reduce to pure mathematics, numbers, or ‘order’.

9. May use or reduce entirely to information, symbols, computer-like rules, states, decisions, operations, markers, pointers, arrays, structures, programs, sets, and/or the like.

10. May be like a computer in being instructible and programmable–or re-instructible, re-programmable, controllable, and manipulable. |

11. May reduce to a computer at a higher, lower, or ultimate level (scale).

12. May be treated as equivalent to a computer if the treatment is sufficiently elaborate, universal, clever, and/or absolute.

13. May represent a set of (finitely or infinitely) homogeneous or heterogeneous computers.

14. May represent a digital or binary computer.

15. May represent an analogue computer of finite, infinite, or infinitesimal self-similarity.

16. May be mechanical in the sense of being possessed of machinelike entities or phenomena–or of parts, operations, laws, &c that are surprisingly or absolutely simple, regular, interchangeable,  interlocking, perfect, universal, reliable, deterministic, knowable, predictable, finite, utilitarian, teleological, rational, constructible, symmetric, efficient, irreducible, repetitive, and/or the like.

17. May behave like a computer on occasion or in special situations.

18. May use a (central or omnipresent) model of itself.

19. May be simulated by a computer with arbitrarily great accuracy.

20. May represent a superficial pattern projected, in effect, on a background–or something like a program or simulation of a universe that is running on an independent and truly real computer but 1s not itself real or fundamental.

21. All natural phenomena, entities, and systems (be they trees, rocks, : molecules, bacteria, men, societies, rivers, stars, diseases, clouds, or whatever) may be computers or computer-like (have  programs, perform computations, use circuitry, possess memory, use languages, process information, use Boolean logic, or the like).

22. May be clock-like or use universally or locally synchronized parts or processes. 

23. All known laws may be controlled or created by higher laws (possibly  arranged in a hierarchy or network). :

24. The universe or all physical phenomena may be reducible to computation or a single great calculation.

25. May reduce to or be controlled by, or be expressible as, pure (Boolean or non-Boolean) logic.

26. May be a mind, mind-like, or thought-like, or be reducible to or treatable by pure thought.

27. May possess a (finite or infinite) computer-like or other memory; or memories and memory processes may exist in all natural phenomena (trees, rocks, genomes, &c).

28. May wholly or in part consist of cellular automata, or be a single great or infinite cellular automaton.

29. Physical processes, phenomena, entities, events, quantities, laws, states, and relationships (such as apparent movement, mass, fundamental physical constants, particle populations, 3-space, spacetime, volcanoes, and ocean waves) may be representational, programmatic, or computational illustons~~-or be infinitely ambiguous–rather than truly fundamental or real; and per se, may be alterable or transcendable by gaining knowledge of and control over their ‘programs’ or an equivalent. Put otherwise, all phenomena, &C may appear or behave as they do because of internal programs, self-models, rules, or computation to which man can gain access.

30. May be a lattice–or spacetime may be wholly quantized.

31. All quantum numbers may reduce to a single quantum number.

32. May essentially represent but a single, individual particle, event, or computer (that somehow generates the illusion of a multifarious world); or a single iterative or recursive operation repeating itself forever or toward a finite future destiny.

33. May represent more or less homogeneous or heterogeneous iterative or recursive processes, entities, phenomena, laws, quanta, measurements, disturbances, &c.

34. It may be possible to show that information and computation are fundamentally indistinguishable and hence equivalent, or that all of the following must in a similar way be equivalent: information, computation, energy, mass, space, time, and/or the like.

35. May be an asynchronous computer (computer with asynchronous parts).

36. May be a computer that functions statistically and indeterministically.

37. May be more or less lifelike (possessed of biological features such as homeostasis, growth, self-reproduction, self-evolution, competition, purpose, or memory).

38. As science progresses and becomes more complex, difficult, mathematical, and abstract, reliance on the computer may become total; and this may make a purely computational representation of the universe expedient, and justify present-day steps in that direction.

39. No one knows how simple, powerful, universal, natural, and/or complex computers might ultimately become–and it might be in these  ultimate senses that the universe is or resembles a ‘computer’.  (It might even be possible to devise revolutionary types of computers by studying and applying computational or computer-like properties of the universe.)

40. May function in ways similar or identical to such computer or mental  processes as generalization, recognition, categorization, error  correction, time sequence retention, induction, symbolic logic, analogical reasoning, and/or the like.

41. May use holonomical memory, correlations, or laws, something like a computer’s content-addressable memory, and/or the like. |

42. May represent an anastomotic network of everywhere diverging, converging,and interacting causes and effects, and in this way resemble a computer’s structure and functioning.

43. May be in some profound sense a function of the mind, and hence half-mental; or respond in entirely different ways dependent on how it is ‘addressed’.

44. Local phenomena may be controlled from a distance or by larger systems.

45. May represent a great hierarchical network of specialized ‘administrators’ or ‘administrative! processes, functions, systems, laws, constraints, &c. Also, may contain things analogous to questions, answers, experiments, orders, requests, negotiations, conversations, messages, traffic cops, supervisors, inspectors, translators, arbitrators, pioneers, &c.

46. May be totally finitistic–or finite everywhere and in every way.

47. May be ‘centralized’ and ‘centralistically’ controlled.

48. All that exists in the universe (including relationships, entities, interactions, laws, &c that are conventionally thought of as being inert, static, or time-invariant) may in fact be time-asymmetric or an uninterrupted process of change or of cosmoplastic or cosmopoietic interadjustments and interchanges; in this ‘everywhere~ always~novel universe! work and information-processing could be omnipresent and quintessential.

–THE UNVIVERSE AS A COMPUTER

There are a couple of things that struct me in this list. The first is number 39. “39. No one knows how simple, powerful, universal, natural, and/or complex computers might ultimately become–and it might be in these  ultimate senses that the universe is or resembles a ‘computer’.  (It might even be possible to devise revolutionary types of computers by studying and applying computational or computer-like properties of the universe.) ” If this is truly 1980, this is pretty amazing because it is at its heart a statement that the universe’s computation may be very powerful, and that this might lead us to more powerful computers. This is right around the time Manin is credited with mentioning the idea of quantum computation in his book Computable and Uncomputable and before the 1981 Physics of Computation conference, which I think is rightfully considered a good point to take as the starting time for quantum computing.

The second thing that I love is Wheeler. “may in fact be time-asymmetric or an uninterrupted process of change or of cosmoplastic or cosmopoietic interadjustments and interchanges” I mean come on this is awesome who writes like that these days? Wheeler’s writing was so full of this crazy poetry, that it famously got parodied in “Rasputin, Science, and the Transmogrification of Destiny” by “John Archibald Wylers”. Excellent stuff.

I was lucky enough to work with a brilliant graduate student, Ben Toner, where we looked at the information cost of simulating entanglement. When we completed that work, Ben was able to attend a conference in honor of Wheeler, and I believe he told him about our work. I’m sad I never got to meet him, but I hope he could recognize in Ben talking with him, the long echo of his impact on those of us who still dream more about computation and the universe.

NISQ is a term coined by John Preskill¹ circa 2018 and stands for “Noisy Intermediate-Scale Quantum”. The term is aimed to describe quantum computers that were not just toy few qubit systems, but systems of a slightly larger scale. This “slightly larger” is a bit hard to define, but roughly most people take it as what is achievable with a quantum computer that does not use error correction. Or in other word the “intermediate” means roughly “what you can do with the natural fidelities of your qubits” (with a fudge factor for those who want to plug their nose and use error mitigation.)

Now this is a blog, so I will give my opinion. And that is that word intermediate in NISQ drives me nuts. I mean in part because it is vague (intermediate between what?), but more because the word itself is a disaster. Intermediate comes to us from Latin, being a combination of inter, meaning “between”, and medius meaning “middle”. But this is silly how can there be a middle without being between? It’s like saying “middle middle”. Whenever I hear NISQ I am reminded of this bastard doubling, and I start working on a time machine to go back in time and work on etymological corrections (good short story idea: a society of time travelers whose sole goal is to bring reason to the etymological record).

A more interesting question than my own personal hangups on word origins is what should we call what exists on the other side of intermediate. My friend Simone Severini has used the term LISQ which stands for “Logical Intermediate-Scale Quantum”². The idea, as I understand it, is to use this term to refer to the era where we start to construct the first error corrected quantum devices. In particular it is the place where instead of using raw physical qubits one instead uses some logical encoding to build the basic components of the quantum computer. (<high horse>Of course, all qubits are encoded, there is always a physical Hamiltonian with a much larger Hilbert space at work, what we call a qubit subsystem is a good approximation, but it is always an approximation.</high horse>). I am exciting that we are indeed seeing the ideas of quantum error correction being used, but I think this obscures that what is important is not that a qubit is use error correction, but how well it does that.

I want to propose a different acronym. Of course, I will avoid the use of that annoying term intermediate. But more importantly I think we should use a term that is more quantitative. In that vein I propose, in fine rationalist tradition, that we use the metric system! In particular the quantity that is most important for a quantum computer is really the number of quantum gates or quantum instructions that one can execute before things fall apart (due to effects like decoherence, coherent imprecision, a neutral atom falling out of its trapping potential, or a cataclysmic cosmic ray shower). Today’s best perform quantum computations have gotten signal out of their machine while reaching somewhere near the 1000 gate/instruction level³. We can convert this to a metric prefix, and we get the fine “Kilo-Instruction Scale Quantum”. Today’s era is not the NISQ era, but the KISQ era.

And as we start to move up the scale by using error correction (or somehow finding natural qubits with incredible raw fidelities) we then start to enter the regime where instead of being able to run a thousand instructions we start to be able to run a million instructions. This till be the “Mega-Instruction Scale Quantum” era or MISQ era. And I mean how cool will that be, who doesn’t love to say the word Mega (Just don’t drawl your “e” or you might stumble into politics). Then we can continue on in this vein:

• 10³ instructions = KISQ (kilo) = NISQ
• 10⁶ instructions = MISQ (mega)
• 10⁹ instructions = GISQ (giga)
• 10¹² instructions = TISQ (terra) <– Shor’s algorithm lives around here
• …

An objection to this approach is that I’ve replaced the word intermediate with the word instruction and while we gain the remove of the “middle middle”, we now the vague term instruction. The word origin of instruction is a topic for another day, but roughly it is a combination of “in” and “to pile up”, so I would argue isn’t doesn’t have as silly an etymology as intermediate. But more to the point, an “instruction” has only an imprecise meaning for a quantum computer. Is it the number of one and two qubit gates? What about measurements and preparations? Why are we ignoring qubit count or gate speed or parallelism? How do we quantify it for architectures that use resource states? To define this is to fall down the rabbit hole of benchmarks of quantum computers⁴. Benchmarking is great, but it always reminds me of a saying my grandfather used to tell me “In this traitorous world, nothing is true or false, all is according to the color of the crystal through which you look”. Every benchmark is a myopia, ignoring subtleties at the cost of quantiative precision. And yes, people will fudge any definition of instruction to fit the strengths of their quantum architecture (*ahem* algorithmic qubit *ahem*). But terms like NISQ are meant to label gross eras, and I think its okay to have this ambiguity.

One thing I do like about using the metric prefix is a particularly pressing problem. While it has been a real challenge to find NISQ algorithms that have “practical” (whatever that means⁵) an equally pressing problem is what sort of quantum algorithms will be achievable in the MISQ era. The place where we have the most confidence in the algorithmic advantage offered by quantum computers, simulation and experimental math algorithms (like factoring), lie above the GISQ and probably in the TISQ region. Roughly what we need are quantum algorithms that are linear time algorithms, so that for instances sizes becoming non-trivial (say a thousand), their total spacetime volume is a this size squared. And while there has been work on algorithms in this era, I would not say that we confidently have algorithms we know will be practically useful in MISQ. And this MISQ/GISQ gap is extremely scary!

So long live the NISQ era! And onward and up to MISQ and beyond!

1. “Quantum Computing in the NISQ era and beyond”, Preskill arXiv/1801.00862 ↩︎
2. “Bye NISQ. Hello LISQ?”, Simone Severini LinkedIn post ↩︎
3. As an example “Phase transition in Random Circuit Sampling” by the Google group (of which I’m a member) shows a signal for circuits with 32 cycles and 67 qubits. arXiv/2304.11119 ↩︎
4. A prominent benchmark is Quantum Volume, defined in “Validating quantum computers using randomized model circuits” by Cross, Bishop, Sheldon, Nation, and Gambetta arXiv/1811.12926. This is a fine benchmark modulo that because Executives at BigCo’s apparently can be fooled by log versus linear scale, they really should have taken the log of the quantity they use to define the Quantum Volume. ↩︎
5. My own personal opinion is that current claims of “quantum utility” are an oversell, or what we nowadays call quantum hype, but that is a subject for a beer at a quantum beer night. ↩︎

“I am a Quantum Engineer, but on Sundays I have principles” — John Bell, as related Nicholas Gisin in quant-ph/0104140

Ahead of his time not just on the implications of quantum theory, but also on the moral of life in the quantum industry.

“We are in a box,” says me.

“Do you see some radium hooked up to a crazy steampunk device with skulls and crossbones and yellow, definitely yellow, but maybe also neon green or wavey blue?” says Qubitslets.

“No I think we put ourselves in the box,” says me. “I don’t see any radium.”

“Maybe we’re in that branch of the wave function where we’ve transmogrified ourselves into a simulation. And we’re in a box because those post capitalists are too damn cheap to simulate us outside of a small goddamn box. Just like new Seattle townhouses. We’re in the cheap Android version of a tech bros afterlife. Do you see brass?”

“No brass,” says me, “but there is something growing in the corner.”

“A tunnel?” asks Qubitslets, “Remember that tunnel we were digging to the moon? I’ve been thinking about the replica symmetry breaking structure of our many tunnel passages to the moon. Maybe we should leverage quantum effects? Jesus, did I just say that? Have I been infected with Goldman Socks ibank spin 3/2s disease? At least I’m a fermion I guess. Not like those collective Marxist bosons over at Google Vultures.”

“I will remind you of the last time we used quantum effects,” says me. “We ended up changing the vacuum state from suck to blow. Luckily it was an unstable equilibrium, and because we are particle theorists and not cosmologists, we didn’t have to think ‘equilibrium of the Higgs-Anderson-Goldstone field with respect to what?’, so the universe just relaxed back to its current vacuum. I sure do miss the werewolves from that old vacuum, though. No, the thing growing in the corner is in a jar.”

“Crap”, says Qubitslets, “we’ve been quarantined!”

Suddenly the Medium Cryostat materializes from The Void. “There is no virus and if there were viruses they would be foreign viruses with foreign RNA and a sheath of foreignness so tricky in its conformal structure we would need a wall to stop it. Because there is no virus, which there certainly isn’t, we must build walls around us and between us and under us. The Great Walling must begin. And we must stay behind our walls and only go out to visit our grandma if she is in a nursing home but we can only do that if we test grandma for foreign viruses, which don’t exist, and, of course we must stay six feet from any particle in the universe. A foreign virus has a Compton wavelength of six feet, I am told.”

“In light of us not being afraid of viruses, because they don’t exist, we will need to plan for how The Great Economy can survive the foreign viruses, if they existed. Stock buybacks were insurance claims for the future antibodies the corporations of The Great Economy would need during The Great Walling, so we should cash out their claims. Because of the uniform structure of economic strata across our Great County, we can use the base minimum wage to pay the minimum required to sustain minimal substance for those impacted by the viruses. If the viruses existed.”

“But we must also not forget what made this a Great Country, again. Never forget the resilience of our people to the scientific method, again. Of the possibility of our citizens being able to think in terms of counterfactuals, again. And of our dedication to spring break and Easter services and a Latin homily about licentious spring breakers, which no, does not arouse the Medium Cryostat. Amen. Oops, I mean Again.”

“And because we are a generous Medium Cryostat, and we know that living behind walls is hard (but necessary because maybe viruses), we shall provide to every home everywhere a jar of Sourdough Levain. Lactobacilli and yeast for all, because nothing says that you aren’t scared of invisible microscopic viruses like cooking with a self reproducing jar of sticky goo.”

“Hooray!” says Qubitslets, “we get to bake bread!”

“Did I ever tell you about the time my girl forgot to feed the starter,” says me ,”and the starter died, and in the tears that fell into the hooch that was all that remained, I could see that the relationship was over by studying the way the waves spread and reflected off the walls of the jar?”

“I bet we can study the exponential growth of the yeast and use that to model viruses,” says Qubitslets. “As physicists we know that only simple models that use physics concepts can be used for public health decisions.”

“Or maybe in the replication of the yeast, we’ll discover that we are just cellular automata or hypergraphs transforming under some crowdsourced update rule.”

“But no brass,” says Qubitslets.

“Yeah, no brass.”

** This post is a tribute to the best blog that every was, ever will be, and ever could be. Fafblog you are greatly missed.

Is this thing on?

This is an open thread in case anyone wants to discuss the merits and demerits of using the term “quantum supremacy”.

Can pontiffs un-retire (un-renunciate)?  I mean, I retired from being a pontiff way before it was cool.  But now the sweet siren call of trying to figure out whether there is really a there there for noisy intermediate scale quantum devices has called me back.   I think it may be time to start doing a little bit of quantum pontificating again.  My goal, as always, will be to bring down the intellectual rigor among quantum computing blogs.  And to show you pictures of my dog Imma, of course.
Cue bad joke about unitary dynamics and quantum recurrences in 3, 2, 1, 0, 1, 2, 3, …
 

Three quantum physicists show why no interpretation is the worst.