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Arrow of time and its reversal on IBM quantum computer (2018) (arxiv.org)
141 points by hownottowrite 9 days ago | hide | past | web | favorite | 98 comments

I don't know enough quantum physics. Is this a qubit equivalent of reversing the mixture of dyes in viscous liquids?


This is more like turning in a single direction to mix, moving some dye around manually, then turning in the same direction again and it un-mixes.

Close enough for a popsci article!

I agree. There are a million of differences, but the main idea is the same. You go from an very ordered state to an state that looks unordered, but it's actually very specific state (with a weird order that is not evident).

Then in one case you reverse the mechanical part and the fluid movement is reversed and you get back to the initial state. (Well, almost the initial state because there is some diffusion and other non reversible effects.)

In the other case, you apply a transformation that reverse the "speed" of the particles (even if they are entangled, without destroying the entanglement, here a few technical details that is better to avoid), and you get back to the initial state. (Well, almost because if you are unlucky soothing can affect unexpectedly the system and you loose the control and you don't return to the initial state. Errors like this are more probable when you use more qbits.)

As a bit of a side note, that was the most striking of the demos I've ever seen from their catalog.

I'm not a physicist, but isn't this kind of like building a fridge and saying it's reversing time because it makes it look like the usual process of heat dissipation is running in reverse? Or is there something more fundamental going on here?

That's not a bad analogy. The difference is that the fridge requires energy input, while quantum "time reversal" does not. I'm putting "time reversal" in scare quotes because it's not really reversing time, it's "simply" (again in scare quotes because actually doing it is not so simple) reversing the normal direction of the evolution of a quantum process.

How do we know that there are no work done by the computer on the states?

They didn't test for eg. 010 back and forth. There might be a 000 bias, etc.

I don't know what you mean by "010 back and forth" or "000 bias", but I'm talking about theory, not practice. Even under ideal conditions a refrigerator requires energy input in order to work. A quantum computer does not. I have no idea whether this particular implementation was dissipative or not.

The autors write that the registers went from 000 to something and back approx. 50% of the time when the random chance of it was really small.

An ideal 386 computer could be thought off as not requiring energy too, right? A looping pseudo random number generator would then be time reversal. It's not saying anything really.

> An ideal 386 computer could be thought off as not requiring energy too, right?

No. Classical computing is necessarily dissipative:


What is time-reversal if not evolution in reverse?

That's all it is.

Considering there are reputable physicists out there that are extremely skeptical a useful quantum computer can ever be made in the first place...

Do you have any references I / others could take a look at? Ive heard such skepticism but maybe not from the most reputable sources. Thanks!

From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist." by Gerard 't Hooft - Nobel Prize in Physics

[0] - https://arxiv.org/abs/1405.1548

EDIT: See page 79 of the referenced paper for the detailed argument.

I've heard a documentary about some physicists saying that quantum hasn't provided anything substantial yet and is hard to prove and often explainable without quantum theory. That said here is a starting point: https://en.wikipedia.org/wiki/Quantum_supremacy#Skepticism

> quantum hasn't provided anything substantial yet

I believe you meant "quantum computing hasn't provided anything substantial yet". I first read it as "quantum theory hasn't provided anything substantial yet", and I was a bit shocked!

Oded Goldreich, Stephen Wolfram, Leonid A. Levin and Gil Kalai are skeptics I know about.

While I'm similarly bearish on quantum computing, in fairness Oded Goldreich is actually a complexity theorist and cryptographer, not a physicist. He works on fundamental things like theory of computing, so his view is applicable. But Gil Kalai is a much stronger reference (and frankly the only one you really need to cite, since if you follow his arguments you've followed all of them more or less).

I'm not a physicist but that seems accurate. Click bait paper.

I mean, non casual filter (time travel filters!) are nothing more fancy than a post measurement analysis where we know y_n+1 at y_n, for example.

> Click bait paper.

The "time reversal operator" and "time reversal symmetry" are usual technical terms in Quantum Physics, the authors didn't invent them. In an advanced quantum physics course you get 2 or 3 weeks about them, and the profesor will spend a long time explaining what they mean exactly.

The problem is that the name is too catchy and it generate a lot of misunderstanding when they are used in the press coverage of the technical articles.

Don't knock it, building the first fridge was a pretty big deal!

It's like saying picking up a ball from point A and putting in point B, then taking it from point B and putting back in point A is "reversing time".

Yeah, this is a poor use of words. I was actually hoping they had read some quantum information "from the future" but in a way that precludes transmitting useful information to the past - similar to how entangled pairs seem to transmit information faster than light, but in a way that doesn't enable FLT communication. But no, nothing about this suggests anything to me about reversing time. Reversing decoherence (if that's a better description) is nice but it's not about time reversal.

FYI, the term “Time Reversal” has long been used by physicists to describe a symmetry of quantum mechanical processes with regard to flipping the sign of t (ie, time). Just like Charge and Parity symmetries which flip the sign of electric charge and position.

See https://en.m.wikipedia.org/wiki/CPT_symmetry

> similar to how entangled pairs seem to transmit information faster than light

If your lover sends you a left-half heart locket through the postal service, when you get it you can assume he has the right-half of the locket "faster than the speed of light". However this is cheating because to know that he has the other half requires prior knowledge of the exchange--either he sent a previous letter where he stated his intent, or you just made an assumption about the state of the environment (namely, that your partner is the only one who would send you presents in the mail). In either case, no laws of physics need be broken.

This is absolutely not how entanglement works. This analogy requires the locket half you receive to be defined at time of "entanglement" (when the locket halves are separated & sent). Half a century of Bell experiments have told us that the result of measuring an entangled system is defined at time of measurement, not at time of entanglement. If it were defined at time of entanglement, the particles would have to carry information with them to "remember" how they decided to collapse (a local hidden variable). Bell experiments disprove the existence of local hidden variables as a means to explain entanglement.

I wish people would stop posting these third-hand metaphors about quantum entanglement being like finding a single right-handed glove in your pocket or whatever. They are irredeemably flawed and completely misrepresent how entanglement works.

Yes my analogy had a hidden variable, but it is "less wrong" than saying that entanglement allows FTL communication, for reasons analogous to those that I provided at the end; entanglement can only convey information as fast as light because the two parties detecting the entangled particles aren't communicating they are just on the receiving end of a shared experience. I don't think I can explain entanglement to a lay person more succinctly than the locket/glove analogy, even though it does hand wave the most quantum-ey part of the experiment.

But I feel this harms more than it helps, like saying "quantum computers compute with every possible value simultaneously in superposition" which gives the audience a very flawed understanding of how QCs work (that they'll be able to solve NP-complete problems in polynomial time for example). By phrasing quantum phenomena in terms familiar to the classical audience, we do them a disservice; we are lying to them.

In this case, the question "why doesn't quantum entanglement enable FTL communication?" is properly that the reduced density operator of an EPR half is the maximally mixed state. All we can do to simplify that is to tell them that quantum concepts exist outside of classical language, and in order to understand them they'll have to learn a new language - mathematics. The most you can say is quantum entanglement enables FTL "correlations" which are stronger than classical correlations but not strong enough to enable information transfer.

Not encountering this for the first time, I've given much thought to your position over the years. But according to many mathematicians, mathematics is within the purview of natural language[1][2]. And wasn't it Feynman himself alleged to have said if we can't explain something in a lecture intended for undergraduate freshmen, we don't really understand it? [3, p19].

[1] https://en.wikipedia.org/wiki/Language_of_mathematics

[2] http://www.cut-the-knot.org/language/MathIsLanguage.shtml

[3] http://calteches.library.caltech.edu/563/2/Goodstein.pdf

EDIT: This is not to challenge your specific assertions on this topic - on which I cannot speak with any particular authority.

Undergraduate freshmen are perfectly capable of understanding basic linear algebra, and thus quantum entanglement.

Regarding the nature of language and how it relates to mathematics, I don't think it's correct to say math is a "subset" of language; there is no satisfactory definition of language that encompasses all the way humans communicate with one another, and it makes more sense to restrict the definition of language to its use in specific interactions (the language of interacting with a cashier to buy an item from a store, and the different language of telling your team what you worked on during standup, for example). In this sense the use of mathematics to describe quantum mechanics is a language in itself.

Sorry, my earlier use of the word subset was a mistake and I have edited the sentence in question to say "within the purview" which is more what I had in mind. I appreciate your reply and do agree with your final statement, though I'm not really sure on the idea of restricting the definition of language as you've described and personally have trouble finding such delineations.

You can read more on Wittgenstein's idea of "language games" here: https://plato.stanford.edu/entries/wittgenstein/#LangGameFam...

Reminds me of a thing people do when playing chess. Sometimes the best move is to move a piece "backwards". In reality the game doesn't care if a move is considered backwards, forwards or sideways, it's just conceptually a new position on the board. But most people see it as going backwards or retreating and struggle to get over this psychologically. Similar to seeing the ball in the previous position as reversing time.

> most people see it as going backwards or retreating and struggle to get over this psychologically

If you return a chess piece to a previous position, it's possible that doing so loses you a tempo. Even if, strictly speaking, the game/board doesn't care about the direction you move, saying it's "just" another position isn't quite accurate, since turns matter, and using up a turn to walk back a piece may give your opponent a +1 turn advantage?

It's more the idea that things can be reversed. How would they have such a "memory" of previous state? It presents such interesting questions. Imagine if we could coerce a human into the exact shape assumed 30 years earlier: that would effectively him backwards 30 years.

In general, yes, but I think you will be very disappointed with this particular work: quantum gates are "linear", so they are readily inversible. All of the "memory" is explicitly baked in in the method proposed here.

If all properties of the ball (and not just position) were "put back", sure.

What other properties does your hypothetical ball have which aren't preserved?

All the atoms making it up would have changed in various ways, which is to say that even if it’s been moved and moved back, one could tell that time has passed with an appropriate observation.

For a single electron, this would not be the case.

Yeah the analogy isn't perfect, but despite that I think it basically works as a macro representation. Obviously the ball isn't a fundamental particle and we wouldn't have all information about how it ages.

But tracking just the ball's position is meant to analogize the fact that we have all information about e.g. a fundamental particle's position.


Okay, that's fair. That property can't really be linearly reversed. I was speaking to an idealized system consisting of a ball in a vacuum moved from one point to another. That's closer to a macro representation of what's happened here.

Well, if you put every atom back, like where they were e.g. in 1960, then it makes sense I think.

That's not comparable unless we have all information about every position the balls have been in from 1960 to the present time. Theoretically plausible, but probably not feasible.

The simple model of a ball shifting from one point to another is a fair macro analogy because, like the quantum system described here, we realistically have all information about the ball as it moved from point A to point B.

I don't think that is true. When you pick up the ball and move it, you are part of the system... and it takes work (and produces heat). No second law violation, right?

Indeed, no 2nd law violation. And this work does not have anything to do with the 2nd law. OP summary is great: they are just doing an operation and then doing it in reverse (albeit in a technically interesting way).

There is also no violation in the proposed experiment because they put energy into the system to do their "reversal"

I suppose this is interesting because unlike cleaning up one's room, (an example of equivalent "time reversal" given by an obnoxious commenter on the article site), this appears to be total time reversal. All properties of the system are set in reverse (where the system obviously does not include the outside world and apparatus which has been contrived to reverse the qubits). Whether this has any real value seems debatable, but it's pretty neat to know that we're even capable of such precise reversal of a basic quantum system.

No, it's actually just like cleaning your room.

Imagine your room (system) has three objects (quantum state) whose respective positions are (a, b), (x, y) and (p, q). You move the objects in your room to positions (a + k_{1}, b + k_{2}), (x + j_{1}, y + j_{2}) and (p + m_{1}, q + m_{2}), respectively. You know where the objects were before and you move them by adding or scaling their coordinates within the room. Thus you know how to move them back to precisely where they were before.

Likewise, this process is linear and preserves all information inherent to the system. Therefore it's precisely invertible, and voila.

It probably has some kind of value and it's a neat result, but this doesn't constitute time travel (in any meaningful sense) in the nonlinear world we reside in.

EDIT: Come to think of it, this probably has value for debugging and auditing the states, as a perfect rewind stepping function.

It's only roughly equivalent to cleaning your room, in a hand-wavey way. Is your cleaned room in an identical quantum state as it was a week ago? No? Well, then the situations aren't the same.

Yes of course it's hand wavey, all analogies are hand wavey. That's why they're called analogies and not lectures. You don't devise an analogy to deliver all the academic rigor of a topic, you devise it to ground something back into the realm of the intuitive and familiar.

Not all analogies are useful, but the reason this one is useful is because it captures the heart of why this isn't meaningfully "time reversal." If you have all information about a linear system, yes you can transform it back into its previous state. That's not at all mysterious or unintuitive even if it's a technical achievement.

Obviously reality is nonlinear, which is precisely the point the analogy is trying to capture. We're not trying to teach quantum mechanics here, we're trying to make sure people don't come away from the article thinking the second law of thermodynamics is (non-locally) violated or that time travel at the macro level is plausible.

The basic idea is that you did a reversible thing, then reversed it.

Cleaning your room increases entropy.

Yeah, though I don't think you're supposed to litigate an analogy that far. The analogy fits because it grounds what's happening as something mundane rather than mysterious. This isn't really "time reversal" in the meaningful sense of the word, because a linear system can always be reversed if you have sufficient information.

It does: reverse a human to the state assumed 30 years earlier. Fountain of youth?

Of course, memory would be a problem.

I don't think this breaks the second law, it sounds like they put some energy into the system to reverse the process

This experiment doesn't break the second law, because they have perfect knowledge of the intermediate states, so they can apply a transformation to invert the evolution.

In a big macroscopic system this is imposible in practice, because you only get a parcial knowledge of a few important properties, not of every detail.

Moreover, in most systems it is imposible to know everything about the system, but in some specially build systems like a quantum computer you can know the state of all the qbits.

The reason I made the statement was because the article said

'"This is one in a series of papers on the possibility of violating the second law of thermodynamics. That law is closely related to the notion of the arrow of time that posits the one-way direction of time from the past to the future," said the study's lead author Gordey Lesovik, who heads the Laboratory of the Physics of Quantum Information Technology at MIPT.'

When I don't see how violating the second law could even be a possibility.

I think we both agree that this is not violating the second law of thermodynamics.

We disagree in that this time reversal operation need energy. It's possible to do this experiment with a frequency doubler [1] crystal in reverse to split a photon in two photons with less energy, then use mirrors to reverse the photons, and then you will be able to "see" that the photons return to the crystal and produce the original photon. [Good luck aligning all the optical equipment perfectly. This is theoretically possible, but it would be very difficult to make the experiment. Perhaps it's easier with other particles.] Anyway, the time reversal operation in this experiment only use a few perfectly aligned mirrors, so it doesn't need additional energy.

In the experiment in the article, they use a setup that is like a quantum computer. It use energy to keep everything working, but the additional energy is not necessary for the main part of the experiment. (The energy is important to make the experiment possible, i.e. transform "perfect alignment" into "we can build this".)

[1] https://en.wikipedia.org/wiki/Optical_frequency_multiplier

That was also my understanding. This looks less like a reversal than a simulation of a reversal. They are using perfect knowledge to engineer a system that operated in reverse to the norm. Actual reversal would reverse everything, including the unknown/unknowable.

If they can read a bit now that had itself set even one microsecond in the future, flash traders will arrive with truckloads of money.

Of course the entropy also only rises necessarily in the statistical average - which is quite strong for any system with a large amount of object.

I don't think this should be getting downvoted, in my undergrad we treated entropy as a measure of the number of possible "equivalent" states, multiplicity or probability equivalently. So if you had a small enough system you might see entropy go down, by chance.

If someone downvotes this can they reply to explain why?

Late answer, I didn't downvote this though.

Anyhow, both formulations of entropy - the thermodynamical one with the integral and the statistical physics one with multiplicity - are equivalent. At least the latter already contains statistics because of the combinatorial part.

And then there is one formulation of the 2nd law which states that on statistical average the entropy rises. So it doesn't break the law if it falls down. Given that this quantum computer doesn't involve many objects, the number of combinations isn't that high. But it's nice to observe Entropy falling! (And there are other situations in which this can happen anyway.)

I didn't read it as breaking the second law, but rather a quantum theory of the second law.

It violates the law locally.

Sounds like they implemented a theoretical architecture called uncomputing. Apparently useful for all sorts of theorized quantum algorithms.


Is this the same quantum computer that had the weird promo video where they talked at length about assembling it in Italy out of aircraft-grade aluminum and didn't mention benchmarks/capabilities?

Sounds like they implemented a theoretical architecture called uncomputing. Apparently useful for all sorts of theorized quantum algorithms. https://www.scottaaronson.com/democritus/lec10.html

Uncomputation is a fundamental concept of quantum computing. You cannot isolate a meaningful result without it.

So did I get it right... Is that what they are talking about as time travel? It sounds a lot like it to me

Alternative theory: they reversed a quantum state while moving forward in time. The researchers, the computer, etc.

Time-travel as popularity conceived is the same: reverse the state of everything outside the time-machine while everything inside progresses as usual.

Interesting that many of the comments here attempt to label this as false research simply because it's taking one state and changing it to another.

Absent from the conversation seems to be agreement on what exactly "time" is.

Much has been studied and said about time, but if we think of time as being something other than an observable change—or that of a recognizable, unified state to one of chaos, aka entropy—what is it?

I'd add here that the observations of this research aren't that striking. We've known for some time that time may not be a single direction arrow but rather one pointing both ways, dependent on what we're observing and our classification of what's possible.

In his book Your Brain is a Time Machine, Dean Buonomano gives an excellent and well-written example of how studies like the one reported here actually work. A favorite quote of mine from that section sums the point as so:

"Decreases in entropy are improbable, not impossible, and given enough time the improbable becomes probable."

These were dumb comments for me to make, I wish HN supported deletion at times like these. Oh well.

Does anyone know if this has any implications for reversible computing? I haven't the expertise to draw links between the two topics.


Aside from the clickbait title, can anyone please ELI5, TL;DR this paper?

From abstract: Here we show that, while in nature the complex conjugation needed for time reversal is exponentially improbable, one can design a quantum algorithm that includes complex conjugation and thus reverses a given quantum state.

Here's my attempt at distilling it:

"Normally in a quantum computer, if we apply measurement function F to input x so y=F(x), it's impossible to reverse F and turn y into x. However, if we constrain y, we can make a special function G_Y such that x=G_Y(y)"

Whilst I don't have time to really dive through all the sections, this seems weirdly click-baity and IBM-promoting for an academic article.

A physics simulation usually simulates the future, but there is nothing stopping you from running the code "backwards" in order to study the past state of the system. If we want to sound fancy we call this "reversing time".

In the case of a quantum computer simulating something (we can not really do this yet, but we are hard at work building the hardware) that type of reversal might require us to calculate complex conjugates of quantum states. For various reasons this is nontrivial and this paper describes ways to do that.

Hasn't quantum chemistry calculations already been simulated using quantum computers?


A bunch of non-scalable examples do exist, and they are very exciting, but we have nothing that can yet reliably simulate molecules of practical interest (we have only "toy" examples that are small enough to be already solvable with a classical computer).

This is the best and most understandable explanation I've seen in the whole thread. Thank you!

Another physics layperson question here: Can this technique of studying a past state reversal apply to compromising one-way hash functions in some manner?

No! Contrary to what the sibling comment says, there are plenty of one-way hash functions that are resistant to quantum computers. Two comments though:

1. This particular work is explicitly relying on the fact that many quantum operations (including the type of time evolution they are considering) are a one-to-one map (not the one-to-many "irreversible" hash functions). Hence this work is explicitly not applicable.

2. Quantum computers do break some form of public key encryption, but this is a solved problem, as there are many other public key encryption protocols that are can not be broken by a quantum computer. Quantum computers do provide modest speedup in all types of brute force searches, like breaking symmetric encryption, but this is trivial to defend against by using a slightly bigger encryption key.

Yes that is one of the reasons for big gubment interest in quantum machines, but allegedly those algorithms require control of millions of qubits and right now the highest qubit machine publicly disclosed is 50 I think.

Quantum computing is reversible right?

Can anyone who knows this field describe what they did? I assume it's more exciting than applying a gate followed by its inverse.

It is not in fact more exciting than that.

The word IBM feels conspicuous.

(Poetry) So does the time arrow marches forward unstoppably?

TLDR instead of traveling through time they just ┬──┬ ノ(° -°ノ). In a simulation.

This is the best TLDR ever written.

Does this mean we can make Pluto a planet again??


Is this like Wheeler's Delayed Choice experiment?

No. This is a quantum system that evolves from a state A to a state B, then is exposed to a very specifically designed potential field that causes it to evolve back to state A. It's actually not that mysterious nor unexpected, just an impressive technical achievement.

For an accessible description of what is going on here see:


I appreciate the link, but fair warning to others - it has a prerequisite of reading three other postings for complete comprehension per the article.

Three? I only count one. (BTW, I'm the author.)

But yes, you do need to understand entanglement and how it relates to measurement before you can understand time reversal. There's a reason QM has a reputation for being a difficult topic.

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