Quantum Mechanics in your Processor: Quantum Computing

Not long after [Hitler] took control of Germany, his party passed laws forbidding any persons of Jewish descent from holding academic positions in German Universities. This had the effect of running many of the world’s smartest people out of the country, including [Albert Einstein]. Einstein settled into his new home in Princeton, and began to seek out bright young mathematicians to work with, for he still had a bone to pick with [Niels Bohr] and his quantum theory. It wasn’t long until he ran into an American, [Nathan Rosen] and a Russian, [Boris Podolsky]. The trio would soon lay before the world a direct challenge that would strike at the very core of quantum theory’s definition of reality. And unlike the previous challenges, this one would not be so easily dismissed by [Bohr].

Need a bit of catching up? You can check out Complimentarity as well as Tunneling and Transistors but  that is just some optional background for wrapping your head around Quantum Computing.

The EPR Argument

On May 4th, 1935, the New York Times published an article entitled “Einstein Attacks Quantum Theory”, which gave a non technical summary of the [Einstein-Podolsky-Rosen] paper. We shall do something similar.

Under the right conditions, a gamma ray, which is just a very high frequency electromagnetic wave, can turn into an electron-positron pair. A positron is the anti-particle of the electron. It has the same mass as an electron, but

New York Times Headline
New York Times Headline

opposite charge and spin. If the two particles touch, they will turn back into the gamma ray. It’s a basic demonstration of E = mc². But what we’re interested in is the electron – positron pair. Because they were formed from the same gamma ray, the two particles are said to be entangled. Entangled meaning a change to one will affect the other. Now, according to quantum theory, one cannot know the state of a particle until it is observed and the process of observation will destroy other states. For instance, if we observe with precision the position of our electron, we destroy information about its momentum. What affect will the observation of the electron have on the positron? Remember, the two particles are entangled. What happens to one will affect the other. If I observe the position of the electron, then the positron can no longer be considered in an unobserved state. The observation will result in a collapse of the wave function. Because the two particles are entangled, they share the same wave function. Without getting mired in the details – the EPR Argument can be summed up as follows:

By measuring the position OR momentum of the electron, we can know that the positron possesses a position or a momentum. And we can know this without directly observing the positron. Quantum theory denies we can do this. And if things couldn’t get any weirder – this will be true regardless of the distance between the particles. If you make an entangled electron-positron pair, and send the positron off to the nearest galaxy, it changes nothing. When you observe the electron, the wave function collapses for both particles. Instantly. Einstein would go on to argue that such “spooky action at a distance” as he put it, is not compatible with special relativity and its cosmic speed limit.

[Bohr’s] response to the EPR Argument can be summed up as follows:

Yeah, so what? You can’t make such a measurement anyway. So it doesn’t count. ***blows raspberry***

Two Boxes, a Ball and a Cat

[Einstein] loathed the New York Times article and all the attention it was bringing. [Bohr’s] response was predictable, and shed no new light on the paradox. He expressed his frustrations in several personal letters between himself and [Erwin Schrodinger] – a fellow opponent of the Copenhagen interpretation of quantum physics and inventor of wave mechanics. In one of the letters, he summed up his feelings of the theory in a simple thought experiment:

Erwin Schrodinger 1887 - 1961
Erwin Schrodinger 1887 – 1961.

Suppose you have two boxes. Each box has a lid. Removing the lid and looking in a box is considered an observation. In one of the boxes is a ball. There is a 50:50 chance the ball is in the first box. The question is – is this a complete description? Can we know any more information? The answers might surprise you.

A) No, it is not a complete description. There is no way we can predict with certainty which box the ball is in, and must resort to probabilities.

B) Yes, it is a complete description. The ball exists in a predetermined state and not in either box. Opening the lid causes the ball to materialize in one of the boxes. Multiple tries would show that we would find the ball precisely 50% of the time. The description of the box before opening the lid is governed only by probability. There is no reason to look any further for a description.

Einstein was showing the absurdness of the (then) current view of quantum theory on a macro scale. He couldn’t have known that he had just planted a seed in a mind just as brilliant as his own. A seed that would soon grow into one of the greatest paradoxes in all of human history – [Schrodinger’s] Cat.

Quantum Computing

In the 1930’s, it was only possible to talk about what might happen if you did Experiment A and made Observation B. As time went on and technology advanced, it became possible to actually test some of these thought

epr_07experiments, including quantum entanglement. And so far, the evidence suggests that [Einstein] was wrong. It appears the description of the ball in the two boxes was indeed complete. As absurd as it sounds, it’s true. In the quantum world, the falling tree does not make any sound. Quantum entanglement is a mathematically, experimentally proven reality, and somehow entangled particles are linked together outside the realm of space and time. The question is – can we use it to our advantage?

Remember the electron – positron pair? Each share a handful of opposite properties, including spin. Let one spin equal a ‘one’, and the other a ‘zero’. If we change the spin of the electron, the spin of the positron will change, instantly.  Where can we go with this?

When a particle (or wave) is in an unobserved state, it is said to be in a superposition. Meaning it has the properties of both wave and particle. The act of observation will determine which it will manifest in to. Let a wave equal a one and a particle equal a zero. In a superposition state, it’s both a one and a zero. They call this a qubit.

Epilogue

It should be noted that [Schrodinger’s] Cat remains an unsolved paradox. While the current quantum theory and its quantum mechanics continue to stand firm when challenged with experiment, there are some serious philosophical issues with it.

epr_04It goes something like this. A cat is placed in a box with a Geiger counter, a radioactive substance, a jar of poison and an Arduino. The half life of the radioactive substance is known such that there is a 50% chance one atom will disintegrate within one hour. If an atom disintegrates, the Geiger counter will tell the Arduino to break the jar of poison and kill the cat. If no atom disintegrates, the cat lives.

Quantum theory says the action of the atom disintegrating or not disintegrating cannot be known until the observation is made. So the cat is both alive and dead at the same time, the end result is only determined by looking in the box. The act of observing collapses the wave function and the atom is forced into a disintegrated or non-disintegrated state.

What [Schrodinger] did with this very cruel paradox is bring the quantum world and its laws into the macro world. It highlights the fact that the “collapse of the wave function”, a foundation of quantum theory, is a postulate. Who gets to say when the wave function collapses? Why can’t it be the measuring instrument measures the radiation? Why does it have to be by a conscious observer? If it is indeed the observer, one can argue that someone is observing the observer; and will see the observer find a dead cat 50% of time, and a live cat 50% of the other. Who is observing that observer? God? OR, could there be two realities… two universes – one where the cat lives and one where it dies?

There is still a lot to be said about quantum theory. No one knows the boundary where quantum theory ends and classical mechanics begins. It is indeed very useful in making predictions in the outcomes of experiments. But is it a true description of reality? [Michio Kaku] has some thought provoking words on this, as can be heard in the 2.5 minute video below.

Articles in the Quantum Mechanics in your Processor series:

Sources:

The Quantum Story, by Jim Baggott. Chapters 16 &17  ISBN-978-0199566846

54 thoughts on “Quantum Mechanics in your Processor: Quantum Computing

      1. Interestingly though, using the Arduino would very likely influence the 50/50 ratio as conceptually, the Arduino has lots of moving parts. Some of which could be impacted by outside (or even possibly internal) factors such as radiation flipping bits or outright hardware defects.

        It would, in other words, be possible for the Arduino to malfunction (in software or hardware) and both either accidentally trigger or fail to trigger.

        We could make this even more fuzzy by adding a computer to the mix instead. Or even a human.

      2. By using a Arduino you are extending the point of human observation into the quantum sterile environment as the Arduino is limited by being programmed with a fixed number of predetermined expectations in the first place. Now if you had of used a 555 …

      1. From the description it’s a superposition of all possible devices (clones, etc) that a person might anecdotally call an ‘Arduino’. You’ll only know when you open the box.

  1. “If we change the spin of the electron, the spin of the positron will change, instantly.” This is really a poor way of explaining quantum theory and leads to people thinking that it can be used for FTL communication. The EPR paradox does not involving changing the spin of anything, it merely involves measuring it. And the important detail is the angle at which the spin is measured. No matter which angle you choose to measure, if you measure spin up in that direction, measuring the other particle in that direction produces a spin down measurement. By appropriately choosing your measurement angles, you can utilize Bell’s inequalities to prove that no hidden variables exist.

    1. Also, the Michio Kaku video is very annoying. Conflating observation and a human is completely unsupported by anything and contradicted by evidence. The double slit experiment can be made into waves and not waves by observation methods that have nothing to do with a human observer.

      1. I agree that’s it’s an annoying video. The geiger counter might be a sufficient “observer”. Perhaps any movement of information from the atomic level to the macroscopic level has the effect of collapsing the wave.

        I can’t claim to understand all the experiments they do for QM, but I don’t see how they would devise an experiment to determine when the wave collapse occurs, given that a human needs to look at the final results of the experiment. How could you ever prove that the collapse occurred before the human looked at the result?

        1. Occam’s razor is the simplest way to approach it. There is no reason to include consciousness, so why pull it in? Additionally, a claim that a conscious observer is something special that can’t be duplicated by other particle interactions, when the conscious observer himself is made up of particles seems to be an argument for dualism.

        2. “Perhaps any movement of information from the atomic level to the macroscopic level has the effect of collapsing the wave.”

          Perhaps not. That’s the biggest issue in “classical” and popularized explaination of QM. They ignore the fact that the observer is itself a QM system.

    2. Totally agree. But not even that I don’t think a gamma ray converts into a Electron Positron Pair. As far as I know (IANAP) the opposite is the correct description. An electron colliding with a Positron actually emits a pair of Gamma Photons in exactly 180 degrees in between and Quantum Entangled. That is the principle behind PET Scanners

  2. About schrodinger cat, isn’t that really intuitive? I mean, you can’t know if cat is alive or dead until you check the status… why is that paradox?

    You can’t know if it is cold outside unless you check that? You need to observe it first.

    Can anyone explain to me why this is paradox?

    1. It’s more of a thought experiment and not really a paradox. The point of the thought experiment says that if the cat behaves like a quantum system, and opening the box behaves like a measurement, then the quantum theory says that the cat is in a superposition of dead and alive until that measurement. The fact that the cat is experiencing the reality of being alive and being dead, and then suddenly one of those realities goes away is not necessarily a paradox, but a clear break with the way most people think of reality. In reality, keeping a quantum system as large as a cat in a box in any kind of superposition for anything more than the tiniest division of time is impossible.

      It’s a thought experiment based on the EPR paradox.

      1. That but it’s a paradox in that while no one really had a problem with a subatomic particle being in a superposition of states no one would have taken seriously a cat. Schrodinger was employing reductio ad absurdum. Show something logically follows that is ridiculous but instead of rubbishing the theory he didn’t like it became the explanation everyone uses.

        It remains a paradox in that this does not happen for real systems and we don’t know how or why.

        1. It’s clear why it doesn’t happen for real systems. The probability of an event causing collapse is for all intents and purposes is 1. The thing that isn’t clear is if you had an ideal vacuum and a large object at absolute zero, how large could you make it and still have it be in superposition? We make put some pretty large objects into superposition when compared to the size of the atom, but is there a limit?

          http://arxiv.org/abs/quant-ph/0306072

        2. “It remains a paradox in that this does not happen for real systems and we don’t know how or why.”

          It’s very clear why: in a superposition of a dead/alive cat, the alive version is not aware of the dead version.

          We may very well be a superposition of many states, yet each state only contains the information of that particular state and not of the others. Therefore whichever state happens to remain at the end result – if the wavefunction ever collapses to any particular state – it will seem as if everything was always the way it happens to be.

          The problem of the reductio ad absurdum is that there’s nobody who can actually see or experience the cat being both dead and alive as it happens. For the cat, and for the observers outside the box, the cat is always either dead or alive, regardless of the fact that the two possibilities may be simultaneous.

  3. Come ON, this is hackaday! Surely there’s a better way to kill this cat. Poison is soooo 1900s. A singing tesla coil or high-voltage capacitor array would do a much better job at eliminating the cat infestation in our otherwise pristine box. And a _geiger_ counter? More like a $5 webcam from goodwill with its filter removed, which not only tells *if* a particle strikes the sensor, but also the spatial distribution. The whole thing is running on a beaglebone green that we made at home after getting a photo of Seeed’s demo version at shenzhen maker faire, re-designed to fix a couple bugs and produced in our closet with a sharpie, a clothes iron and some hydrofluoric acid (we were going to use sulphuric, but we had lots of this left over from work at the semiconductor fab and it was free).
    Actually the whole thing was working fine until the dog unplugged the system and the memory on the onboard eMMC corrupted, and now it won’t boot anymore. Which is a useful note to our readers — follow _this_helpful_post_ by hackaday user neelzBohr87 to see how to set up your system as a read-only, uncorruptable computer.

    Where were we? Oh yes — the system won’t boot anymore, we’re off working on a software-defined radio project now, and there’s a bad smell coming from the box. Science!

  4. Doesn’t the Arduino/Geiger counter combination do the observation and then either kill or not kill the cat? Does that mean the Arduino is conscious? Of course the Arduino could be replaced with any other even dumber detection mechanism. So why is a conscious observer necessary? I say, if an electron hits an object, the wave function will collapse. The tree falling in the forest does make a sound, or less philosophically it does create air compression waves.

    What if I leave the cat in the box for 24 hours and then open the box? Then what are the chances of the cat being alive? Pretty low, so the only unknowable is really When the cat died.

  5. “By measuring the position OR momentum of the electron, we can know that the positron possesses a position or a momentum. And we can know this without directly observing the positron. Quantum theory denies we can do this.” Quantum theory DENIES NO SUCH THING. Of course you can know the position or the momentum of a positron without directly observing it, just prepare it into an eigenstate of such observable. That’s exactly what the EPR thought experiment does. This is a very WRONG explanation of the EPR argument.

    1. The following is from the referenced book, page 144, second paragraph:

      “…although we have not performed any measurements on particle B following its separation from particle A, we can establish the reality of either its position or its momentum from measurements we choose to perform on A which, by definition, do not disturb B. The Copenhagen interpretation denies we can do this.”

        1. That video is of an order of magnitude more complicated that the referenced book’s explanation and my summary of it. We use position and momentum of two entangled particles, just as the EPR paper did. It’s a thought.experiment. If you want to do the experiment in real life, then you use spin or phase or whatever correlated property you can come up with.

  6. Physicists think about killing cats, psychologists actually do it, with plant pots!

    Anyway I look forward to my infinite wireless range with 802.11-spin (q and s are taken).

  7. The wave function does not collapse. There is no confusion. We cannot divorce ourselves from also being part of the quantum system (observing).
    Consistent Histories is able to define Quantum mechanics and resolve all these paradoexes and be the exact same result as the Copenhagen interpretation but without the Observer.
    I’d encourage you to lookat/buy the (no mathmatical proofs) book called Quantum Philosphy by Omnes http://amzn.to/1Jl5ZXX or read about this approach and decoherence here: http://plato.stanford.edu/entries/qm-consistent-histories/ or on wikipedia of course :)

  8. However, one can positively say that, after a period of time, a qubit will remain in whatever state it is in, regardless of observation, for an indefinite period of time. The cat, on the other hand, will most certainly be dead, regardless of whether the box is open, closed or turned into a biscuit.

  9. Having struggled through various quantum mechanics classes, I frequently find myself appalled by word choices people make regarding wave equations. They seem to act as though the equations themselves take part in causation. A happens –> wave equation changes –> B is observed. I think I’m on solid ground when I say there are not mathematical incantations that can define a single thing in the real world, yet alone participate in causation. Mathematics exists in its own realm, independent from reality, which is what makes it useful for modeling that reality. Once you start muddling the model with reality you not only violate concepts in philosophy of science, you run a chance of completely deceiving yourself. I think the particles in the experiments are a lot less paradoxical than many of the physicists themselves. They know less than they think they do.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s