A tale of two qubits: how quantum computers work

Just how do quantum computers work? It turns out that most of the magic of quantum computers can be seen in the very simplest of systems. We take an in-depth look at systems of just one or two quantum bits, and see what they're doing when no one is watching.<BR><BR><a href='http://meincmagazine.com/science/guides/2010/01/a-tale-of-two-qubits-how-quantum-computers-work.ars'>Read the whole story</a>

 

[smartalco]

Oh god my brain.<BR><BR>This was quite an informative read though.<BR><BR>But oh god, my brain.

 

[Ainamacar]

Great article, I wish it had existed 10 years ago when I was first learning the technical details of QM and QC as an undergrad. A piece like this to help the intuition would have gone a long way when slogging through the parts of Nielsen and Chuang I just wasn't ready to handle conceptually.

 

[Beanaroo]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">A largescale, <I>working</I> quantum computer—the kind of quantum computer some scientists think we might see in 50 years—would be capable of performing some tasks <I>impossibly</I> quickly. </div></BLOCKQUOTE><BR><BR>Still have to read through it all, but this made my head asplode! Italics are mine. If it's impossible, it can't be done. But if a working quantum computer can do it, then it's not impossible.

 

[NavyGothic]

I thought I had a reasonable layman's understanding of how quantum computing (and quantum mechanics as a whole) worked.<BR><BR>This article took that notion out into the alley and issued a cruel beating, leaving my brain a broken and battered pulp on the cold ground.

 

[Akhen]

The first rule of quantum mechanics is.. never assume you know quantum mechanics. :I

 

[hoblet]

Very well-written. Very appropriate Pratchett reference at the end <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15">

 

[bedward]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by smartalco:<BR>Oh god my brain.<BR><BR>This was quite an informative read though.<BR><BR>But oh god, my brain. </div></BLOCKQUOTE><BR><BR>Oh come on, it wasn't that hard. Just defocus your eyes, click 'next' five times, and nod knowingly at the witty last sentence. It worked for me.<BR><BR>This looks like a really good article, but my reading instructions are a little too close to the truth for me to know for sure. Especially when it got to the math section. I think I have a grasp on the concept of local realism and most of the single qubit section, so that's a personal victory.<BR><BR>In any event, thanks for trying to explain it.

 

[maschnitz]

I think the writing was terrible - florid, showy, parenthetical crap. It really distracted me.<BR><BR>Read "Politics and the English Language" sometime.

 

[tigerhawkvok]

Excellent piece. Handily the most technical thing I've read on Ars to date, but quite nice to read about the computing aspects of quantum mechanics. My brain is definitely going to be stuck on the entanglement of quantum measurements, though. Hmmmm.

 

[bartfat]

Turtles all the way down? What's that supposed to mean?<BR><BR>Great read BTW. Thanks for explaining it, but wow quantum computers are complicated, I never knew it was that complicated. I mean I knew that the measurements changed the state of a quantum computer, but wow, I had no idea about the other properties. Mind blowing!

 

[scratt]

Joseph, great article. Thanks.<BR><BR>A question for you, if you don't mind, because this "spooky actions at a distance" thing still intrigues the hell out of me.<BR><BR>I understand that states need to be entangled between two particles at some point when they are together, but there is something that myself and some friends disagree on in our understanding.<BR><BR>Basically, let's say we create a stream of entangled particles (say photons) and split them at our location, and then buffer a local stream whilst transmitting the other stream a long distance... *If* we then maintain absolute parity in measurement at both locations, and ensure against outside influences prematurely observing these particles. Could we actually transmit information over large distances *instantaneously* by "observing" according to an agreed protocol that would allow us to expect certain results and then perceive error or success in those "observations" at the "receiving" location as the form of the data?<BR><BR><BR><I>This comment was edited by scratt on January 19, 2010 09:55</I>

 

[Fissioninferno]

My brain has been thoroughly mashed and destroyed. Now I shall use this information for great justice.<BR><BR>This was actually a really interesting and informative piece, and read out sort of like a suspense novel. It even had a twist at the end.

 

[Loomis]

I'm really confused about the circular polarization effect he's refering to. "(Test this out in a 3D movie—tilting your head won't ruin the effect.)"<BR><BR>Tilting you're head completely ruined the effect, so what is he talking about?

 

[EvilYoshi]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">You don't want the entire movie to change when you tilt your head, so using horizontally and vertically polarized lenses is out. Likewise, diagonally and anti-diagonally polarized lenses won't work. (Test this out in a 3D movie—tilting your head won't ruin the effect.) </div></BLOCKQUOTE><BR><BR>Actually, when I went to see Avatar in 3D, I could hold the left lenses of two pairs of glasses together and they would let through light, but if I tilted one of them 90 degrees all of the light would be blocked. The reverse would happen if I held a left lens and a right lens together. Doesn't that mean they were, in fact, horizontally and vertically polarized? Or am I missing something here?

 

[scratt]

I feel sorry for your whomever you were with who could not watch the movie in 3D while you did your experiments. <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_wink.gif" alt="Wink" width="15" height="15">

 

[Illissius]

This was a rather hard slog, though I think I got most of it. Probably only about half of the last part. That could've used some more/better clarification. <BR><BR>Regarding Figure 11, how can you describe every possible state as a combination of |L> and |R> when |L> and |R> are two endpoints of a single axis? Doesn't that only let you describe the points along that axis?<BR><BR>For the quantum equations, it would've been helpful to have defined the conceptual meaning of the mathematical operations between states ahead of time. By the end it became clear what they meant -- effectively addition is union, or "either this state exists or that state exists", and multiplication is intersection, or "both of these states exist", so |a>|b> + |c>|d> means "either both a and b are the case, or both c and d are the case" -- but when you just started throwing equations out there I was just like, "what?". I /still/ don't get the whole thing with phases. Intuitively multiplication-by-number would indicate weighting, or in this case probability, but they actually mean phases and pulsing and all that, so I don't think that's right (plus, the numbers are complex...). (As an aside, mathematically what kind of value is a quantum state? Is it a vector of three numbers, corresponding to the three axes? Or does entanglement mean it's something weirder?)<BR><BR>Also, at the part where you go to define |H> and |V> in terms of |R> and |L>, it's sort of odd that you do it the way you do -- usually, when you define something in terms of other things, you do it by putting it on one side of an equation by itself, not inside of the equation. Why this way? And what are all the 1/sqrt(2) factors for? (Intuitively I would assume it's to normalize things, so that the sum of probabilities remains 1, but if multiplication-by-number doesn't actually have to do with probability weighting but with... pulsing... then I have no clue.)<BR><BR>Last, does this measuring-is-entangling idea bear any relation to the many worlds idea? E.g., that every time a quantum event happens, the universe forks itself in two, with the event going one way in one of them and the other way in the other, so that in the end there are endless parallel universes for every possible reality. Does this measuring-is-entangling idea imply effectively the same thing formulated differently, as "all possible realities exist simultaneously in an entangled quantum state" (rather than in parallel universes), or are they two different things? What's the difference?

 

[joshv]

I once knew, and understood (at least I have vague memories of understanding) all of the basic QM represented here - and even for me, it's a bit too much. It took me a quarter of grad school to begin to wrap my head around the stuff, I think this is a level of detail that's not appropriate for general public consumption.

 

[scottyo3921]

I don't think the reason he went on to discuss the quantum measurement problem was to not deprive of us critical information.<BR><BR>I think it was so he could get in the riff on stacked up turtles!<BR><BR>BTW, I'm almost certain the turtles quote much predates Pratchett's use of it; Wikipedia has a sheaf of possible attributions for its origin. I believe I saw it in something from the late 19th or early 20th century (Alan Quatermain??), though my brain cells are currently heavily entangled and probably not reliable on this.

 

[Carewolf]

God damn. Don't make me curious enough to bring out my old quantum physics book. I put it in a corner for a reason! I dropped out of physics for a reason!.. Damn you Ars! <img src="https://cdn.arstechnica.net/forum/smilies/biggrin_classic.gif" alt="Big Grin" width="15" height="15">

 

[Taoism]

Good article... my brain hurts... keep posting stuff like this... this is why I love Ars! <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15">

 

[zeotherm]

Excellent article! Thanks for writing it Joseph. <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15">

 

[Immune]

My touchstone on the turtle reference is Yertle, by Dr. Suess. <BR><BR>I too thank you for your effort. As a biologist, I respect this fundamental layer of description of our world, and am gratedful that it collapses before I really need to worry about it.<BR><BR>I get the phase issues, by analogy to "Beating" in sound waves, and cancellation. Though I've always puzzled about where the energy goes if you are standing at a zero point.<BR><BR>I'll try to read it again. I may have already spent my quota (quanta?) for the day.<BR><BR>Oh, and I liked the style, so I disagree with the critic.

 

[joe.altepeter]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> Let's say we create a stream of entangled particles (say photons) and split them at our location, and then buffer a local stream whilst transmitting the other stream a long distance ...<BR>Could we actually transmit information over large distances *instantaneously* by "observing" according to an agreed protocol that would allow us to expect certain results and then perceive error or success in those "observations" at the "receiving" location as the form of the data?<BR> </div></BLOCKQUOTE><BR><BR>This is a great question, and one of the most commonly misunderstood aspects of "spooky action at a distance". Entanglement cannot be used to communicate faster than light. <BR><BR>The reason is that while measurement results on entangled particles are always perfectly correlated, as you point out, they are also totally *random*. The scheme you describe will result in two parties instantaneously sharing a string of *random* bits. Although one can think of that information as being transmitted instantly, neither of the two parties has any control over what information is measured, making it impossible to use this effect to send a message. (Note, however, that this is *exactly* how <a href="http://en.wikipedia.org/wiki/Quantum_cryptography">quantum key distribution</a> works).

 

[scratt]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by joe.altepeter:<BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> Let's say we create a stream of entangled particles (say photons) and split them at our location, and then buffer a local stream whilst transmitting the other stream a long distance ...<BR>Could we actually transmit information over large distances *instantaneously* by "observing" according to an agreed protocol that would allow us to expect certain results and then perceive error or success in those "observations" at the "receiving" location as the form of the data?<BR> </div></BLOCKQUOTE><BR><BR>The scheme you describe will result in two parties instantaneously sharing a string of *random* bits. </div></BLOCKQUOTE><BR><BR>Thanks for your reply. The bit I quote from you is where I always get stuck on this. Let's forget the impossibilities of the logistics of all this for a moment. What I thought was that if "observing" is synchronised and you are "observing" the same particles then you can get predictable opposite results based on what you choose to "observe"? <BR><BR>I am most definitely over simplifying there! ( I must say that I love how ridiculous all these statements sound! )<BR><BR>Is there really no way to create that situation, even theoretically? Because if there isn't I need to go read the article again as I have misunderstood something fundamental! <BR><BR><I>This comment was edited by scratt on January 19, 2010 14:59</I>

 

[ThomasKenobi]

An excellent article really. I've read upwards of half a dozen articles regarding quantum computers and this is the first time, I can say, I understood its principles on at least a basic level. This also served, to bring my knowledge and comprehension of quantum entanglement, to a level beyond that of starter Quantum Mechanics university classes.<BR><BR>Kudos and thank you

 

[joe.altepeter]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"><BR>Regarding Figure 11, how can you describe every possible state as a combination of |L> and |R> when |L> and |R> are two endpoints of a single axis? Doesn't that only let you describe the points along that axis?<BR> </div></BLOCKQUOTE><BR><BR>Good question. Figure 11 shows how to describe any point on the *surface* of the sphere as a combination of |L> and |R>. Said another way, it shows how to describe any point on the surface of the sphere in reference to |L> and |R>, by noting the latitude (theta) and longitude (phi) of a point relative to those two poles. To also describe the points inside the sphere, you have to add a third decoherence parameter. Because the equations were already getting confusing, I decided to leave this out.<BR><BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"><BR>(As an aside, mathematically what kind of value is a quantum state? Is it a vector of three numbers, corresponding to the three axes? Or does entanglement mean it's something weirder?)<BR> </div></BLOCKQUOTE><BR><BR>Quantum states are represented in different ways, depending on your assumptions. For the most part, you can describe an N-qubit quantum state which has not been subjected to decoherence as a column vector with 2^N entries. If you want to describe states which have been partially decohered, you need to use a more general mathematical object: a square matrix with 2^N columns and 2^N rows. In either case, every entry in the vector/matrix is complex, that is, it has a real and an imaginary component.<BR><BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"><BR>And what are all the 1/sqrt(2) factors for? (Intuitively I would assume it's to normalize things ...)<BR> </div></BLOCKQUOTE><BR><BR>Your intuition is correct. To find the probability of measuring any one quantum state in a sum of quantum states, you square the magnitude of that state's coefficient (that coefficient is called an amplitude). The square of 1/sqrt(2) is 1/2, meaning that any term with a 1/sqrt(2) in front of it has a 50% chance of being detected in that state.<BR><BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"><BR>Last, does this measuring-is-entangling idea bear any relation to the many worlds idea? E.g., that every time a quantum event happens, the universe forks itself in two, with the event going one way in one of them and the other way in the other, so that in the end there are endless parallel universes for every possible reality. Does this measuring-is-entangling idea imply effectively the same thing formulated differently, as "all possible realities exist simultaneously in an entangled quantum state" (rather than in parallel universes), or are they two different things? What's the difference? </div></BLOCKQUOTE><BR><BR>This is a *great* question. The measuring-is-entangling idea is strongly related to the many worlds interpretation of quantum mechanics (see http://en.wikipedia.org/wiki/M...rlds_interpretation).<BR><BR>As you point out, the many worlds interpretation posits that every time a quantum measurement happens, the universe splits. If at some point quantum measurement becomes irreversible (a collapse to classical physics), these multiple universes would be forever separate and unrelated. If the turtles really do go all the way down, they are part of a giant entangled state, and as such can continue to *interfere* with each other, continuously merging and splitting forever. (Note that here I'm using the technical quantum mechanical meaning of <a href="http://en.wikipedia.org/wiki/Interference_%28wave_propagation%29>interference</a>.)

 

[sckmcck]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by hoblet:<BR>Very well-written. Very appropriate Pratchett reference at the end <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15"> </div></BLOCKQUOTE><BR><BR>It's actually a Feynman reference.

 

[joe.altepeter]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"><BR>Is there really no way to create that situation, even theoretically? Because if there isn't I need to go read the article again as I have misunderstood something fundamental! <BR> </div></BLOCKQUOTE><BR><BR>Regarding trying to use entanglement to communicate faster than light, it really is impossible, even theoretically. To follow the analogy of the article, let's say you set up a measurement for the hero/villain pairs. You're going to ask them both the same question about Love or War. Although you know they'll always disagree, you have no idea which will answer "Love" and which will answer "War".<BR><BR>If you'd like to break the system and design an FTL communication scheme, imagine you have two magic coins that when simultaneously flipped will always give totally random but always opposite results. So regardless of the distance between them when one comes up heads, the other comes up tails, but it's impossible to predict which will be which. If you can use these coins to communicate faster than light, then you can use entanglement to communicate faster than light. (HINT: You can't.)

 

[scratt]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by joe.altepeter:<BR>So regardless of the distance between them when one comes up heads, the other comes up tails, but it's impossible to predict which will be which. </div></BLOCKQUOTE><BR><BR>I must be dense but following that analogy literally, if I see tails on the receiving end then I *know* there is a head on the other end.

 

[joe.altepeter]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by scratt:<BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by joe.altepeter:<BR>So regardless of the distance between them when one comes up heads, the other comes up tails, but it's impossible to predict which will be which. </div></BLOCKQUOTE><BR><BR>I must be dense but following that analogy literally, if I see tails on the receiving end then I *know* there is a head on the other end. </div></BLOCKQUOTE><BR><BR>Absolutely right. Now try to use that knowledge to send a message from one coin to the other.

 

[daemonios]

Brain... hurts...<BR><BR>I have to congratulate you, Joseph. You made a very interesting read - even if impossible to follow at times for me, but I put that down to my complete ignorance of physics.

 

[Ozy]

IMAX 3D uses linearly polarized light (think each lens is perpendicularly tilted 45 degrees)<BR><BR>Real3D uses circularly polarized light.<BR><BR>So, at the IMAX3D movies, tilting your head will ruin the effect, and you should be able to take two pair of glasses and rotate their lenses with respect to each other and see them get light and dark as you match and unmatch the polarization.<BR><BR>The Real3D lenses should always be dark when paired against the oppositely polarized lens, regardless of how you rotate them.

 

[Milliways]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by scratt:<BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by joe.altepeter:<BR>So regardless of the distance between them when one comes up heads, the other comes up tails, but it's impossible to predict which will be which. </div></BLOCKQUOTE><BR><BR>I must be dense but following that analogy literally, if I see tails on the receiving end then I *know* there is a head on the other end. </div></BLOCKQUOTE><BR><BR>You received that information at the speed of light, since you visually saw it.

 

[Eldorito]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by sckmcck:<BR><BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by hoblet:<BR>Very well-written. Very appropriate Pratchett reference at the end <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15"> </div></BLOCKQUOTE><BR><BR>It's actually a Feynman reference. </div></BLOCKQUOTE><BR><BR>Actually, it's Hawking, it's from a brief history of time <img src="http://episteme.meincmagazine.com/groupee_common/emoticons/icon_smile.gif" alt="Smile" width="15" height="15">

 

[nitsujmai]

Yes! Thank you for one of the best Ars articles in a very long time. Superb!

 

[Citrus538]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">If the phonebook has 10,000 entries, on average you'll need to look through about half of them—5,000 entries—before you get lucky. </div></BLOCKQUOTE> : \ Phone books are usually sorted alphabetically, so on a classical computer you would only need to see about 14 entries at worst.<BR><BR>That statement is true when the data is unordered, though.

 

[Penforhire]

Excellent article! Even if I only grokked some % of it.<BR><BR>I always figured the action at a distance was tied to the wave function of particles. I was taught that the probability function extended to infinity. That allows the possibility of "tunneling" between two arbitrary locations.<BR><BR>This entanglement is a very creepy at-a-distance thing.

 

[EtrnL_Frost]

Ow. I need to read this over coffee and baileys, at home, over at least an hour.

 

[Illissius]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Your intuition is correct. To find the probability of measuring any one quantum state in a sum of quantum states, you square the magnitude of that state's coefficient (that coefficient is called an amplitude). The square of 1/sqrt(2) is 1/2, meaning that any term with a 1/sqrt(2) in front of it has a 50% chance of being detected in that state. </div></BLOCKQUOTE><BR><BR>Hmm, I see. I'm still having trouble reconciling "amplitude" and "heartbeat", but I'll keep trying.<BR><BR>Would turtles all the way down also imply that if a friend of yours sent you a letter from many thousands of miles away, which world you're in -- what's in the letter -- would only be determined for you (the split would only happen) at the point where you actually open the letter and look at it? And until you do, the entire rest of the world, from your perspective, is in a quantum superposition of all possible realities corresponding to all of the possible contents the letter could have? (And that, until you open the door, the person who knocked really could be anyone). (I was actually thinking about this earlier today, completely independent of this article, so the article is pretty fortuitous; at the time it seemed like a pretty radical new view (for me) of life, the universe, & everything, and hours later it turns it might be "mainstream".)<BR><BR>Thanks for the answers!