I know, but you could say that a CNOT is an "augmented-XOR" (to give it a name). Classically, if you just copy one of the inputs as one output and then XOR the inputs as the other you have the most analogous classical gate to CNOT (in fact, the truth tables are identical, the only difference is that the CNOT takes superpositions). So it could be argued that CNOT could be more like a quantum two-input XOR gate than a quantum NOT gate. But I think CNOT is already established as a name...
Is there a reason why it's called a NOT gate rather than XOR? Is there some quantum wierdness that makes the thing asymmetric and causes A-inverts-B to mean something different to B-inverts-A?
I guess it's mostly historical, and that XOR is usually associated with a two-input/one-output gate. Controlled-NOT looks pretty intuitive (the target is negated only if the control is 1), but probably XOR is better because A-inverts-B is exactly the same as B-inverts-A (which seems counterintuitive when you think of it as a CNOT, but it's reasonably simple to see that is the case by just looking at the corresponding truth table).
But I would venture that most people working on trying to build quantum computers would be more familiar with CNOT than XOR in the context of quantum computation (QXOR sounds weird, doesn't it?)
More seriously, a qubit (short for "quantum bit") has two well defined states, 0 and 1 (|0> and |1> for those QM buffs) just as a regular (classical) bit. The difference is that the classical bit has to be in either 0 or 1, while the qubit can be in what is called a "superposition" of those. So you could have a qubit in the 0 state, or in the 1 state, or in the "x% 1 and y% 0" state (where x+y=100). Part of the magic of quantum computers comes from this fact: using the proper operations, you can feed your quantum computer a register which is set up to "all possible inputs" so that it applies the algorithm to all possible values. Some people call this "Massive parallelism". You have to be careful, because Quantum Mechanics does not allow to extract the result of all those calculations (that would be great), so you have to go through some tricks to get useful information out of that "parallel processing".
I find it interesting that the first electronic computing gates devised were the AND/OR gates, using basic diode logic. Quantum computing research develops the NOT gate first. I think this has something to do with the esoteric nature of quantum computing. AND/OR gates require two inputs to change to a single value, where NOT is merely an inverter. The idea of entanglement makes the inversion process a likely first step in quantum research.
Keep in mind that this is a Controlled-NOT gate (a two-input gate) and not a simple NOT gate (a one-input gate). It has been proven that if you can implement two-qubit C-NOT and arbitrary one-qubit operations, you can implement a universal quantum computer (that is, one that can run an arbitrary "quantum program").
There is a deeper reason for quantum computers not to use AND/OR gates, which is their irresibility (AND and OR are two-input to one input gate, which makes them irreversible). Quantum Mechanics is intrinsically reversible, so a quantum computer should be reversible too and that's why it is not common to hear about Quantum AND or Quantum OR.
Ok, I want to hear from a single guy in this forum/site, who can take this "teleportation might use quantum dots" information and make some use of it.
There is not much use to it. It seems to be a theoretical calculation on what kind of parameters would work best if you wanted to perform a quantum teleportation experiment with two quantum dots. From my own experience with semiconductor quantum dots and quantum information, the proper quantum dots to perform an experiment like that (a proof-of-concept experiment, nothing else!) have not been grown yet. There have been some advances in laterally coupled quantum dots, but I haevn't seen any that look good for implementing the two-qubit gates needed for quantum teleportation.
So don't hold your breath for any kind of quantum teleportation with quantum dots (although they make fine single photon sources!).
Of couse I haven't read the article, so they might have good suggestion on how to do that or even know of some quantum dot growth I'm not familiar with.
A quantum cryptography implementation with a single photon source is not vulnerable to the "insert a repeater in the middle" attack. This is because it is impossible(1) to faithfully copy a quantum state without knowing a priori what it is. So, any kind of repeater that is subreptitiously inserted in the path will introduce an error rate higher than the expected and thus can be detected, without the need to perform "extra" authentication (as in the classical case).
Current implementations of quantum cryptography don't use perfect single photon sources but rather highly attenuated lasers, which have a non-zero probability of emitting a pair of identical photons. In this case you could, in principle, take one of those photons and let the other go and eavesdrop without being detected (not that it is technically easy, though).
(1): As far as quantum mechanics really describes our physical reality.
For all fields, a Faraday cage, grounded or not, shields the interior from exterior fields.
For all fields, a grounded Faraday cage will shield the exterior from interior fields.
For time-varying fields, an ungrounded Faraday cage will shield the exteror from some interior fields, depending on the composition and thickness of the conductor and the frequency of the field polarity changes. Low frequencies require thicker and better conductive shields than high frequencies.
Yes, it looks right. I'm not completeley sure about the specifics of the time-varying fields, but what you stated seems the right trend.
I'm glad I could help!
Pablo B.
This is how I understand Gauss' law for Faraday cages:
The key thing is that inside a perfect conductor, charges can move very fast (in a real conductor you have some losses, but the main idea is the same). Then, you can use Gauss' law to deduce that inside a perfect conductor, the electric field will always be zero (if you force some field inside it, charges in the material will rearrange in such a way that the total field will still be zero).
Let's think the case of a point charge (charge Q) inside a conductor shell (a spherical shell makes calculations easier but it is not necessary). Using Gauss' law you know that there will be field inside the shell, as there is a net charge. However, if your surface now is within the shell, you know that the field is zero so that the net charge surrounded by your surface must be zero. Now, that means that the charges inside the conductor rearrange so that the inner surface of the shell has a charge -Q and the outer surface has a charge Q (to keep the conductor electrically neutral). This way, everything is consistent and there is no net enclosed charge in your Gauss' surface. Now, if your Gauss' surface is outside the shell, the total enclosed charge will be again Q, so you can have an electric field regardless of the presence of the conducting shell (this is electrostatics, for electrodynamics you will have to take into account the reflections on the shell and all that stuff which will lead to attenuation of a wave originating inside the shell.
If your shell is now grounded, it has access to a charge reservoir (ideally capable of providing an infinite amount of electric charge). Then, the conducting shell needs not to be kept neutral, and can get and extra charge -Q from the reservoir and distribuite it on it's inner surface, so that the total enclosed charge in any Gauss' surface will always be zero.
This is an idea of why the grounded cage is bidirectional while the ungrounded one is not. I hope it is clear enough!
From what I remember from my college physics, the difference is in the grounding of the cage. A grounded cage will completely insulate the inside from the outside ("bi-directionally"), whereas a non-grounded cage will only keep fields from the outside to getting inside (an emitter inside would be most likely attenuated due to reflections and losses, but not completely).
The wetting layer is a by-product of the method used to grow the dots. I can talk about InAs dots in GaAs, which are the ones I know best. In order to grow the self-assembled dots, you first grow enough layers of GaAs so that you end up with an atomically flat layer of GaAs. Then, you start growing layers (one atomic layer at a time, such is the magic of molecular beam epitaxy!), until a certain "critical height" (I think it's around 5 monolayers). At that time, you stop the growth for a little while and the InAs layer spontaneously forms "droplets" in the GaAs surface, which will be the quantum dots after you grow some GaAs on top. The problem is that the droplets don't use up all the InAs that was deposited, so some remains in the surface and forms the so-called "wetting layer" which behaves similarly to a quantum well. I don't remember any references off the top of my head, but look for articles on the "Stranski-Krastanov growth mode".
The quantum dots the article refers to don't have any "coating" (as do chemically synthesized semiconductor nanocrystals). The same matrix of the dots does a good job in "protecting" them. And I think molecular beam epitaxy (what they use to grow those dots) is more sophisticated than thin film scattering. And it certainly allows you to grow single-atom layers. The problem comes in the "self-assembly" of the quantum dots, where the "wetting layer" is created.
Just to add to the other replies, self-assembly is the fastest way to create dense ensembles of dots (useful for example for quantum dot lasers). Besides, I think that the interface properties of self-assembled quantum dots are still better than those of lithographic quantum dots (self-assembled dots have less defects in the interfaces).
Some of the things you are talking about (blinking, poor surface properties) are relevant to the usually called "colloidal semiconductor quantum dots", which are chemically synthesized. These don't have a wetting layer, so the article does not apply to them (their problems are a completely different can of worms). Then there are the "epitaxially grown semiconductor quantum dots" (grown in huge and expensive molecular beam epitaxy systems) which usually DO have a wetting layer (InAs dots in GaAs do have it, I think CdTe quantum dots don't). The article is talking about those kind of dots.
Not really... The "quantum software" for a quantum computer is years ahead of any quantum hardware...
There's even a "Programming Language for Quantum Computers"!
There are some useful algorithms (for factorizing numbers, to search in unsorted databases) that work faster than their classical counterparts, but no hardware to run them but on almost trivial cases! (15=5x3 anyone?).
Good Luck!
What they've done is not a NOT gate but rather a CNOT (Controlled-Not) gate (in fact they haven't donw that either, they performed a CROT, a controlled rotation but you can show that one is as useful as the other). The interesting thing about the quantum gates is that once you are able to construct a few of them (such as a CNOT and single qubit operations) you can approximate ANY quantum operation to arbitrary precision in principle (and polynomially in the number of gates if I recall correctly) by just chaining them.
And I am also waiting for a quantum coprocessor to plug into my desktop.:-)
[ the problem is not entangling the photons in the first place but keeping them in that state, the slightest disturbances (lorries going past, the old woman next door doing the hoovering etc etc) can cause them to become untangled, and so for this reason the whole system must be cooled to absolute zero. ]
As some other people have pointed out, there are quantum error correction codes that allow you to perform quantum operations given that your error rate is below a certain threshold (I don't remember the right number, but I think that you need to be able to perform about 10^4 operations before your system dephases in order to have a "fault tolerant quantum computer". Besides, there are several proposals that look to minimize the dephasing problems.
Other point is that entangling photons is not that difficult (altough not that easy either...). However, entangling electrons in a controlled way in a solid state sample is much more difficult. That is really cutting edge research.I am *really* interested in looking at their scientific paper.
Just as a note, quantum computers are not around the corner and won't be for quite a while, but I don't think we'll ever get a refrigerator so good that reaches absolute zero (unless Lisa Simpson invents it).
This is not exactly a software bug, but I thought it quite funny when I found it. A long time ago, I don't remember why, I wanted to find 2^32 in my Casio FX3800p calculator. You can imagine my surprise when the display shows "4294967295"!! It's the only calculator I know that does not worry about a power of two being odd... Odd, isn't it?;-)
Looking at the recent economic situation in Argentina, I would not be surprised that the discussion is along the lines of "We don't have enough money to buy fuel to get there, not to mention coming back". Keep in mind that the argentinean peso has sunk respect to the dollar and while most supplies are tied to the dollar (and quick to increase its prices given the slightest peso depreciation), government budgets are still in pesos (and most of that money is borrowed, anyway).
Anyway, they should do something fast! (if they heven't done anything by now)
Slashdot Mirror
I know, but you could say that a CNOT is an "augmented-XOR" (to give it a name). Classically, if you just copy one of the inputs as one output and then XOR the inputs as the other you have the most analogous classical gate to CNOT (in fact, the truth tables are identical, the only difference is that the CNOT takes superpositions). So it could be argued that CNOT could be more like a quantum two-input XOR gate than a quantum NOT gate. But I think CNOT is already established as a name...
Pablo B.
I guess it's mostly historical, and that XOR is usually associated with a two-input/one-output gate. Controlled-NOT looks pretty intuitive (the target is negated only if the control is 1), but probably XOR is better because A-inverts-B is exactly the same as B-inverts-A (which seems counterintuitive when you think of it as a CNOT, but it's reasonably simple to see that is the case by just looking at the corresponding truth table).
But I would venture that most people working on trying to build quantum computers would be more familiar with CNOT than XOR in the context of quantum computation (QXOR sounds weird, doesn't it?)
Pablo B.
32? They should be 42!
More seriously, a qubit (short for "quantum bit") has two well defined states, 0 and 1 (|0> and |1> for those QM buffs) just as a regular (classical) bit. The difference is that the classical bit has to be in either 0 or 1, while the qubit can be in what is called a "superposition" of those. So you could have a qubit in the 0 state, or in the 1 state, or in the "x% 1 and y% 0" state (where x+y=100). Part of the magic of quantum computers comes from this fact: using the proper operations, you can feed your quantum computer a register which is set up to "all possible inputs" so that it applies the algorithm to all possible values. Some people call this "Massive parallelism". You have to be careful, because Quantum Mechanics does not allow to extract the result of all those calculations (that would be great), so you have to go through some tricks to get useful information out of that "parallel processing".
I hope this helped some!
Pablo B.
Keep in mind that this is a Controlled-NOT gate (a two-input gate) and not a simple NOT gate (a one-input gate). It has been proven that if you can implement two-qubit C-NOT and arbitrary one-qubit operations, you can implement a universal quantum computer (that is, one that can run an arbitrary "quantum program").
There is a deeper reason for quantum computers not to use AND/OR gates, which is their irresibility (AND and OR are two-input to one input gate, which makes them irreversible). Quantum Mechanics is intrinsically reversible, so a quantum computer should be reversible too and that's why it is not common to hear about Quantum AND or Quantum OR.
Pablo B.
So don't hold your breath for any kind of quantum teleportation with quantum dots (although they make fine single photon sources!).
Of couse I haven't read the article, so they might have good suggestion on how to do that or even know of some quantum dot growth I'm not familiar with.
Pablo B.
A quantum cryptography implementation with a single photon source is not vulnerable to the "insert a repeater in the middle" attack. This is because it is impossible(1) to faithfully copy a quantum state without knowing a priori what it is. So, any kind of repeater that is subreptitiously inserted in the path will introduce an error rate higher than the expected and thus can be detected, without the need to perform "extra" authentication (as in the classical case).
Current implementations of quantum cryptography don't use perfect single photon sources but rather highly attenuated lasers, which have a non-zero probability of emitting a pair of identical photons. In this case you could, in principle, take one of those photons and let the other go and eavesdrop without being detected (not that it is technically easy, though).
(1): As far as quantum mechanics really describes our physical reality.
Pablo B.
Yes, it looks right. I'm not completeley sure about the specifics of the time-varying fields, but what you stated seems the right trend.
I'm glad I could help!
Pablo B.
This is how I understand Gauss' law for Faraday cages:
The key thing is that inside a perfect conductor, charges can move very fast (in a real conductor you have some losses, but the main idea is the same). Then, you can use Gauss' law to deduce that inside a perfect conductor, the electric field will always be zero (if you force some field inside it, charges in the material will rearrange in such a way that the total field will still be zero).
Let's think the case of a point charge (charge Q) inside a conductor shell (a spherical shell makes calculations easier but it is not necessary). Using Gauss' law you know that there will be field inside the shell, as there is a net charge. However, if your surface now is within the shell, you know that the field is zero so that the net charge surrounded by your surface must be zero. Now, that means that the charges inside the conductor rearrange so that the inner surface of the shell has a charge -Q and the outer surface has a charge Q (to keep the conductor electrically neutral). This way, everything is consistent and there is no net enclosed charge in your Gauss' surface. Now, if your Gauss' surface is outside the shell, the total enclosed charge will be again Q, so you can have an electric field regardless of the presence of the conducting shell (this is electrostatics, for electrodynamics you will have to take into account the reflections on the shell and all that stuff which will lead to attenuation of a wave originating inside the shell.
If your shell is now grounded, it has access to a charge reservoir (ideally capable of providing an infinite amount of electric charge). Then, the conducting shell needs not to be kept neutral, and can get and extra charge -Q from the reservoir and distribuite it on it's inner surface, so that the total enclosed charge in any Gauss' surface will always be zero.
This is an idea of why the grounded cage is bidirectional while the ungrounded one is not. I hope it is clear enough!
Pablo B.
From what I remember from my college physics, the difference is in the grounding of the cage. A grounded cage will completely insulate the inside from the outside ("bi-directionally"), whereas a non-grounded cage will only keep fields from the outside to getting inside (an emitter inside would be most likely attenuated due to reflections and losses, but not completely).
Pablo B.
The wetting layer is a by-product of the method used to grow the dots.
I can talk about InAs dots in GaAs, which are the ones I know best. In order to grow the self-assembled dots, you first grow enough layers of GaAs so that you end up with an atomically flat layer of GaAs. Then, you start growing layers (one atomic layer at a time, such is the magic of molecular beam epitaxy!), until a certain "critical height" (I think it's around 5 monolayers). At that time, you stop the growth for a little while and the InAs layer spontaneously forms "droplets" in the GaAs surface, which will be the quantum dots after you grow some GaAs on top. The problem is that the droplets don't use up all the InAs that was deposited, so some remains in the surface and forms the so-called "wetting layer" which behaves similarly to a quantum well. I don't remember any references off the top of my head, but look for articles on the "Stranski-Krastanov growth mode".
The quantum dots the article refers to don't have any "coating" (as do chemically synthesized semiconductor nanocrystals). The same matrix of the dots does a good job in "protecting" them. And I think molecular beam epitaxy (what they use to grow those dots) is more sophisticated than thin film scattering. And it certainly allows you to grow single-atom layers. The problem comes in the "self-assembly" of the quantum dots, where the "wetting layer" is created.
Just to add to the other replies, self-assembly is the fastest way to create dense ensembles of dots (useful for example for quantum dot lasers). Besides, I think that the interface properties of self-assembled quantum dots are still better than those of lithographic quantum dots (self-assembled dots have less defects in the interfaces).
Good Luck!
Pablo.
Some of the things you are talking about (blinking, poor surface properties) are relevant to the usually called "colloidal semiconductor quantum dots", which are chemically synthesized. These don't have a wetting layer, so the article does not apply to them (their problems are a completely different can of worms).
Then there are the "epitaxially grown semiconductor quantum dots" (grown in huge and expensive molecular beam epitaxy systems) which usually DO have a wetting layer (InAs dots in GaAs do have it, I think CdTe quantum dots don't). The article is talking about those kind of dots.
Good Luck!
Pablo.
Not really... The "quantum software" for a quantum computer is years ahead of any quantum hardware... There's even a "Programming Language for Quantum Computers"! There are some useful algorithms (for factorizing numbers, to search in unsorted databases) that work faster than their classical counterparts, but no hardware to run them but on almost trivial cases! (15=5x3 anyone?). Good Luck!
What they've done is not a NOT gate but rather a CNOT (Controlled-Not) gate (in fact they haven't donw that either, they performed a CROT, a controlled rotation but you can show that one is as useful as the other). The interesting thing about the quantum gates is that once you are able to construct a few of them (such as a CNOT and single qubit operations) you can approximate ANY quantum operation to arbitrary precision in principle (and polynomially in the number of gates if I recall correctly) by just chaining them.
:-)
And I am also waiting for a quantum coprocessor to plug into my desktop.
Pablo B.
[ the problem is not entangling the photons in the first place but keeping them in that state, the slightest disturbances (lorries going past, the old woman next door doing the hoovering etc etc) can cause them to become untangled, and so for this reason the whole system must be cooled to absolute zero. ]
As some other people have pointed out, there are quantum error correction codes that allow you to perform quantum operations given that your error rate is below a certain threshold (I don't remember the right number, but I think that you need to be able to perform about 10^4 operations before your system dephases in order to have a "fault tolerant quantum computer". Besides, there are several proposals that look to minimize the dephasing problems.
Other point is that entangling photons is not that difficult (altough not that easy either...). However, entangling electrons in a controlled way in a solid state sample is much more difficult. That is really cutting edge research.I am *really* interested in looking at their scientific paper.
Just as a note, quantum computers are not around the corner and won't be for quite a while, but I don't think we'll ever get a refrigerator so good that reaches absolute zero (unless Lisa Simpson invents it).
Pablo B.
This is not exactly a software bug, but I thought it quite funny when I found it. ;-)
A long time ago, I don't remember why, I wanted to find 2^32 in my Casio FX3800p calculator. You can imagine my surprise when the display shows "4294967295"!! It's the only calculator I know that does not worry about a power of two being odd... Odd, isn't it?
Pablo B.
Looking at the recent economic situation in Argentina, I would not be surprised that the discussion is along the lines of "We don't have enough money to buy fuel to get there, not to mention coming back".
Keep in mind that the argentinean peso has sunk respect to the dollar and while most supplies are tied to the dollar (and quick to increase its prices given the slightest peso depreciation), government budgets are still in pesos (and most of that money is borrowed, anyway).
Anyway, they should do something fast! (if they heven't done anything by now)
Pablo B.