Nice thanks for the video! A friend of mine works on making quantum computers and it's crazy how the engineering is very exotic condensed matter type physics.
🍎If you want to learn quantum mechanics by doing problems, I'm running a course Jan 6 - 31st 🍎 For 4 weeks you will have homework and weekly tutorials with me📝There's no math prerequisite - it's for curious people from all backgrounds. Last time we had people from many walks of life, but all of them had wanted to understand quantum mechanics for a long time. If you're in the same boat, I think you'll enjoy learning together! looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals1
I always viewed qubit as single real number (anything from 0 to 1 with infinite precision, but still a single real-value), making quantum computer analogous to analog computer with infinite precision. Not sure how correct / close to reality this analogy is, but helped me a lot to navigate the landscape :) (Complex numbers are there to make the math work, imaginary numbers were invented for this very reason: to let us do math beyond some limitations, but the result has to be real - not inaginary, not complex, reality is real) P.S.: It is like with en.wikipedia.org/wiki/Fubini%27s_theorem - you can swap integrals as long as the result is real/finite. Analogy: use complex numbers to solve equations as long as the result is real (as long as infinite series converge etc... infinity is a construct and not only physics but even math itself breaks)
09:20 you could note here, that 0s and 1s in classical computing are a manufactured dualism as well, since the voltage levels are basically arbitrary, and there is an infinite range of other voltages a signal line could hold (of course dependent on the transistors or other hardware that can be used for gates). But we choose specific dualistic voltage values (in multiple different standards), so we can use boolean logic.
Computer logic chips are designed to amplify their inputs to the maximum or minimum output, depending on whether the input is above or below the threshold that's somewhere near the middle of the range. A logical zero state is any value on one side of the chip's threshold, and a logical one state is any value on the other side of the threshold. So, even though there are an infinite number of possible voltages within the range, there are only two possible logic states -- above threshold or below threshold -- and the amplification serves to avoid the threshold and reduce sensitivity to noise.
@@brothermine2292 That is correct, but it is only designed this way, not a physical necessity. My argument is, that we could hypothetically build new logic chips with every base we would like to, because voltage levels are not inherently binary. I found a patent from 1978 "Ternary Logic Circuits With CMOS Integrated Circuits" from Hussein T. Moufah, which shows how to build logic circuits for base 3 numbers with cmos-transistors. It's quite interesting! So there is not only Max and Min Voltage for logical 0, 1 but Max, 0 and Min Volts (+4V, 0V, -4V in an example in the patent) for logical 2, 1 and 0 in ternary.
@@sevfx : I recall a math major at Caltech, Mike Yoder, researched ternary logic in the mid-1970s. If it were more useful than binary logic, it would have found favor. A ternary logic gate is presumably more complicated than two binary logic gates in order to implement the two thresholds & three voltage ranges and amplify the voltages accordingly. Also, I'm pretty sure that ternary logic would worsen at least one of the following, compared to binary logic: (1) noise tolerance, (2) speed, and/or (3) power consumption & waste heat. So, although binary isn't a "physical necessity" for computing, it's a good bet that binary is physically optimal. But perhaps that wouldn't be true for information elements designed to exploit quantum properties that have more than two possible states, such as the many orientations that an electron's spin can take or the many polarization angles that a photon can take.
My understanding is that superposition is when events occur simultaneously without the concept of time. For example, if something has two possible outcomes with varying probabilities, in superposition, both outcomes happen at the same time. However, each outcome still retains its individual probability. Measurement somehow reintroduces the concept of time to the system. Thank you for the video.
Nice vid. It's great how you apply reality to these concepts. One I'd like to see more abstract -> reality is the infinite square well potential. I think a good example of this would probably be quantum dots. Another one I'd like to see is the quantum harmonic oscillator. I know this is how band diagrams are derived from Kroenig Penney model, but it still feels a bit too abstract.
As an x-ray tech trained in the military, the maths were almost non-existent. The highest math I took was college algebra. If I took the class, would the math be overwhelming? Thanks!
No I don’t think so at all! If you want an idea of the level, check out the first 4 videos in this series. If that looks ok, you’ll be fine! Plus I will be there to help as much as possible, so you can email me with your questions and I can help you before the tutorials
12:23 "represented". Is that rigorous representation (e.g. imaginary=circular polarization)? Or rather "complex numbers have enough freedom to represent possible states to make the math work"? Any answer appriciated. I always thought that those complex numbers are there for the "freedom" = "to make the math work", but knowing exact meaning would be nice change (in my understanding, if applicable). P.S.: My knowledge and understanding is 20 years outdated ;)
Great question, and I’m not sure I have an amazing answer. I feel like the exact mathematics you use to describe reality aren’t the reality themselves- because there’s always equivalent but different formulations of the theory with different maths. So I’m inclined to believe that it’s just a convenience to use complex numbers to represent an extra degree of freedom… but I’m not sure about that
@@LookingGlassUniverse Yet the phase of those complex numbers (polar form) seems to be very important for interference (constructive vs. destructive). The freedom (dimensionality) is necessary (real numbers just won't do), but can we associate any good meaning to it? I don't know.
@TimoBlacks Geez I'm not sure, but supposedly the math checks out and predicts exactly the same results as observed. Something to do with a caveat Bell made. In it, reality is fundamentally random/probabilistic though. But consider that pilot wave, which has a particle only at one location at all times (uncertainty principle being a lack of knowledge instead of real) does produce the interference pattern because the waves interfere with itself or something. This has been reproduced macroscopically if I understand correctly. It's not pilot wave though and not deterministic like pilot wave.
Bell showed that QM must violate at least one of the following three axioms: Locality, Reality, or Measurement Independence. (Measurement Independence is also known as Statistical Independence.) Several interpretations of QM that violate Measurement Independence and satisfy Locality & Reality have been proposed... for example, Sabine Hossenfelder's Future Input Dependence.
There are different types of atomic bonds. Covalent bonds are on type and share electrons on their outer shell, if there is "space" for it on one of the atoms. That doesn't mean one was anionic and the other cationic. Example would be O2. Ionic bonds have one neg and one pos like NaCl.
@@RahulSB-vf3cp Yeah, thanks that I took the effort and time to answer your question, to get insulted. My answer is still correct regarding how you questioned it. Don't ask questions in comment sections if you don't want anyone to answer. You better go an ask something like ChatGPT, because your (online) interaction with humans s*cks. Edit: look up electro negativity in atoms and why atoms want to have a full outer shell.
12:40 I think this part was a little misleading how you showed it with your hands. Because the possible spin directions are in physical space, which is three-dimensional over the real numbers, while you show it with your hands in Hilbert space (state space), which is two-dimensional over the complex numbers with basis vectors |0> and |1>. There is no third direction in Hilbert space like you make it seem when you rotate the |1> direction upward. EDIT: Sorry, I think I now get what you meant to say. You attach a complex plane to the |1> direction to visualise one complex dimension as two real dimensions. I think that's correct then. However, it should be stated that the same can then be done with the |0> direction, so that the two-dimensional complex vector space becomes a four-dimensional real vector space. And because of the normalisation |a|^2 + |b|^2 = 1 (where a, b are the prefactors of an arbitrary state a|0> + b|1>) that gives an extra condition, you can identify the three-dimensional physical space with the three free real numbers in Hilbert space.
So if I look at the 2D vector projection on the coordinate axes, can conclude that this is 2 dimensional system or the vector is superposition of these projections. Two different states in the same time? What about a 3D vector? Is it a superposition of 3 different states represented by its projection on the coordinate axes? I do not grasp this concept. My understand about what must be Qu bit, is a physical system with two or more independent states, which ca be manipulated physically and simultaneously in a way that permit mathematical operations. If these 2 or more states are dependent, the computer based on such Qu bits will have no advantage over the classic computers.
Thanks a lot, you really helped me get all that! But I still can't help but wonder how quantum computers actually take advantage of these properties, like physically. 🤔
youtube''s algorithm works sometimes! I enjoyed the video and subscribed because the explaination was so good, but I have some questions - 7:15 I don't get how there could be a combination of up and down, I understood the example of the prism projecting the laser's polarity into a basis of two polarities, but "up and down" does not sound like a basis to me because there is no orthonormality, so what is happening? - also I don't get why the use of complex numbers, in this case it does not add any further dimensions it's just making the 1 state complex, or was it just a way of saying that whatever multiplies the two states 0 and 1 can be also complex? that would make sense because then yeah there would be more dimensions -I also still don't get how qbits can make calculations easier, how could I apply these concepts to speed up calculations? this question probably is out of the scope of the video though maybe someone could answer these questions? I would appreciate it
Hey, great questions! Thanks for asking them! -This Is a confusing point; "up" and "down" aren't at right angles to each other, but when you translate them to the mathematical representation as vectors we treat them as orthogonal. The reason for this is that "orthogonality" in QM has a very specific meaning. If two states are orthogonal, then they are mutually exclusive. I.e. in an experiment, these vectors represent opposite outcomes. Since a stern-gerlach experiment has two outcomes: "up" and "down", the vectors for these must be orthogonal in QM. The vectors don't really represent the physical system (where up and down aren't at all at 90 degrees), but instead represent the information in a useful mathematical way. -Yes, you're right! You can make either the "a" or "b" coefficients complex! -I did a video about an actually "useful" thing you can do with a quantum computer once, if you're interested: ua-cam.com/video/tHfGucHtLqo/v-deo.htmlsi=sQIBKjDQV94aYL0X Thanks again :)
It's unfortunate that the word "measurement" is used to describe the interaction of the photon & crystal and the interaction of the electron & Stern-Gerlach device. Obviously these interactions _change_ the state of the photon and the state of the electron, and they do NOT tell us what their state was _before_ the interaction. For example, if we know the photon was in the "superposition state" |+> prior to its arrival at the crystal, that knowledge was deduced from an _earlier_ interaction that resulted in a photon polarized at 45 degrees, which can instead be described by a wavefunction that has a single term: 45 degrees with a probability of 1. It's unnecessary to describe it by a wavefunction that has a superposition of terms (the |+> "state"). The superposition is merely a prediction of what would be the result of an interaction between a photon in the 45 degrees state and the crystal, assuming the crystal is oriented at a specific angle. It's wrong to think of the superposition as describing the photon prior to its interaction with the crystal, and right to think of the superposition as a prediction of the result of a hypothetical interaction with a hypothetical crystal oriented at a hypothetical angle.
It seems sort of incorrect to say that a quantum system is in a superposition of the two states, because those two states are defined by the basis you choose, and if you choose a different basis, then you have a different two states that it is in a superposition of. Isn't it really in just one state, which is the state of pointing in the exact direction it actually points?
Every time I see a physical or experimental explanation of superposition it seems like what's actually described is an object that isn't actually "in both states at the same time" but is actually "in neither state" because the actual state is the combination of multiple factors. For example, the 45 degree polarization isn't both vertical and horizontal, it's just describable as a combo of the two, it "is" 45 degrees. And we only say it "collapses" to either vertical or horizontal because our measurement device forces it to align to either vertical or horizontal. That's not a measurement, it's a filter. And the entropy of the experiment means we can only know which way it'll go via probability instead of classical mechanics near 100% certainty.
I guess think of it more like force vectors if that helps understand it. If you roll a ball off a cliff at say 10m/s, it is going to travel 10m/s horizontally until it hits the floor. It's also going to drop at ~9.81m/s². So you have it going in a diagonal-ish direction but there is no diagonal force. It's really just going in both horizontal and vertical directions at the same time.
@Iammeandyouareyou That's the same thing I'm saying. Except the ball's trajectory can actually be broken into vertical and horizontal components that relate to the forces acting on it. But we don't say it's in a superposition of moving down and sideways, we talk about the forces acting on it and map them to a coordinate system. We also don't put a measurement device on the floor and say that any balls that hit it must have been in a down state. Or worse, blow air downward on the ball's path to force it down into the down state detector and declare the ball to collapse into a definite state because we "measured" it. QM talks about states of being, not forces of interaction.
How do we know if the result of a quantum computer operation is correct? It could take decades to validate it using current supercomputers. I image that even one misbehaving q-bit could radically alter the result.
There are many problems that are hard to solve but easy to check once you have an answer. One example is finding factors for very very large numbers, which is one of the kinds of things that quantum computers would be good at while supercomputers are much slower.
The nature of quantum computing is such that we do not use any one trial as the answer to the quantum question we are asking. This is for two reasons. 1. Quantum computing relies upon the spread of measurements across a wavefunction to find the answer. This means that the result is statistical and requires many (thousands of) measurements to gain a spectral understanding of the resulting wavefunction for the system. In other words, the noise will affect the spectrum’s clarity, but any one trial, noise and all, is not the “result”. 2. To reduce noise, quantum computing engineers have come up with ways to “error correct” by using groups of qubits to represent one “logical qubit”. So that when one qubit inevitably flips due to noise, the overall group can still be interpreted correctly. This reduces the effect of noise in the system.
@fullfungo Classical bit have two positions either 1 or 0. Quantum bit can be in any position between 1 to 0. Pendulam like Quantum bit can be in any position between -1 0 +1 and independent of temperature. just an imagination!
It's not clear how this is an advantage over just using vector operations. Surely qubits can do more than what simple vectors in linear algebra can do right?
@@LookingGlassUniverse I get that. But then what's the computational advantage? If I'm just adding/subtracting vectors I can just use a GPU and do better than a quantum computer.
You make it sound like it's no different than expressing a vector as components. For example, a vector of magnitude 5 at 45° from the x axis might be expressed as two vectors, one of magnitude 3 at 0° and another of magnitude 4 at 90°. However it can also be expressed as any of infinitely more combinations of other vectors. But that's merely mathematics. Those are three separate vectors (also infinitely many other vectors besides), not one vector in two (or infinite) states. What am I misunderstanding?
This is a very subtle point, but in QM there isn't a difference. I think what's hard to accept about this is that when we say "this light is a superposition of horizontal and vertical" if makes it seem this is the correct or only way to see the light. But yeah, as you said, you could have picked any other basis instead. All these different ways of decomposing the light are equally "physical"- the most useful way to do it though is to use the basis that you're then going to be measuring in later. I'm not sure if that helped at all
@LookingGlassUniverse That does help a bit, thanks. The implication, though, seems to be that there is only one "real" state of the object and we just choose the "lens" through which we observe it to fit the purpose we've set. What does that mean for Copenhagen and the supposed reality of, for example, no definite position for a photon? Does it actually have a definite position and all we do is select the metaphorical angle at which we observe that position, such that it _appears_ that that is the "highest probability" position? (Or however it would be best to say that - I only have a middling layman's understanding of quantum physics.) Also, it's philosophically interesting because it gets into whether mathematics is discovered or invented. Are quantum objects "made of math" such that the infinite mathematical expressions of the object are literally what a superposition of infinite states is? Or is math merely a description of the physical world such that there are any number of ways to describe physical reality, only a few of which we have devised (some better - i.e. more accurate - than others) but none of which are physically real. (I'm very firmly on the side of the latter, BTW.)
@@1newme425 Just a few months ago, I saw a video that gave me a new perspective on quantum objects. (I don't remember the title but I'm almost certain it was by Float Head Physics.) The reason we have trouble understanding quantum objects like photons, electrons, and others is that they simply _cannot_ be described, _at all,_ using the concepts we have for macroscopic physics. "Particle," "wave," even "point," simply _do not apply_ and cannot even be "stretched" to make sense of quantum objects. They are something else entirely. We are comfortable with terms like "particle" and "wave" because they have become second-nature to us. However, until we devise entirely new concepts for quantum objects and those concepts become as familiar to us as "particle" and "wave" are now, we will fail to have anything resembling an intuitive grasp of what those objects are. They are _entirely_ different than what we're used to, so the words we use to describe what we're used to _cannot_ apply to, _cannot_ describe, them. Even with that being the case, however, it's easier to grasp what we're dealing with in quantum objects if we keep that fact in mind. They're not particles, not waves, but something else entirely. Saying that an electron doesn't have a definite position fits somewhat with our normal understanding of physics but doesn't accurately capture the reality because "position" just doesn't apply to something that is not a particle. The same applies for the term "wave." We need new concepts that are not like "particle" and "wave," then we need them to pass into common usage the same way that "particle" and "wave" have. Only then will we reach an "everyday" understanding of the quantum world.
@@MichaelPiz I see maths as a language to describe something. There are different branches of mathematics and you can describe (and solve) a problem with multiple methods of different branches not only one. You can choose what fits best for you. You can use 4dim calculations to make the calculation of a 2dim problem easier, it's still a 2dim problem. Maths can help to understand a problem and then extrapolate from that knowledge. And what is even the truth? Depending on your scale of measurement, the British coastline has either a finite or an infinite circumference.
Google's Willow.. I thought of a light hardrive,, qubit using in 2000s, i think Logans Run movie had light electronics, n I was like that that, light would have different wavelengths and a single photon could hold infinite info. Willow used same concept, for coherence, that I thought would work for a light based harddrive.. group alignment.. i thought and saw other light microchips stuff, in like 2022, and was like, coherence, just send a lot of photons all doing same calculation, and the .. superpostion of a wave.. the photons cohere to the quantum field wave complicated phrasing.. the overall average wavelengths of the photons correct eachother.. group autocorrect.. though IDK how Willow autocorrects an electron cloud exactly.
... and because of that no answer that a quantum computer produces can be treated as reliable, so the whole concept of a quantum computer becomes pointless (other than for gaining investments)
Nice thanks for the video! A friend of mine works on making quantum computers and it's crazy how the engineering is very exotic condensed matter type physics.
🍎If you want to learn quantum mechanics by doing problems, I'm running a course Jan 6 - 31st 🍎
For 4 weeks you will have homework and weekly tutorials with me📝There's no math prerequisite - it's for curious people from all backgrounds. Last time we had people from many walks of life, but all of them had wanted to understand quantum mechanics for a long time. If you're in the same boat, I think you'll enjoy learning together! looking-glass-universe.teachable.com/p/quantum-mechanics-fundamentals1
Awesome, so cool you doing this.
Sure, Got it, I will be there with Einstein!
Please! be my physics teacher 🙏. Jokes aside, you are quite good at explaining concepts 👍
Wow! Great Video
Never understood the logic behind qubits having two states at once until I saw your video!
Thank you for the great explanation🙏
I always viewed qubit as single real number (anything from 0 to 1 with infinite precision, but still a single real-value),
making quantum computer analogous to analog computer with infinite precision.
Not sure how correct / close to reality this analogy is, but helped me a lot to navigate the landscape :)
(Complex numbers are there to make the math work, imaginary numbers were invented for this very reason: to let us do math beyond some limitations, but the result has to be real - not inaginary, not complex, reality is real)
P.S.: It is like with en.wikipedia.org/wiki/Fubini%27s_theorem - you can swap integrals as long as the result is real/finite. Analogy: use complex numbers to solve equations as long as the result is real (as long as infinite series converge etc... infinity is a construct and not only physics but even math itself breaks)
1:38 Nitpick: If the first is at 45 degrees, shouldn't the second be at 135 degrees (not 130)?
oops, yup!
09:20 you could note here, that 0s and 1s in classical computing are a manufactured dualism as well, since the voltage levels are basically arbitrary, and there is an infinite range of other voltages a signal line could hold (of course dependent on the transistors or other hardware that can be used for gates). But we choose specific dualistic voltage values (in multiple different standards), so we can use boolean logic.
Computer logic chips are designed to amplify their inputs to the maximum or minimum output, depending on whether the input is above or below the threshold that's somewhere near the middle of the range. A logical zero state is any value on one side of the chip's threshold, and a logical one state is any value on the other side of the threshold. So, even though there are an infinite number of possible voltages within the range, there are only two possible logic states -- above threshold or below threshold -- and the amplification serves to avoid the threshold and reduce sensitivity to noise.
@@brothermine2292 That is correct, but it is only designed this way, not a physical necessity. My argument is, that we could hypothetically build new logic chips with every base we would like to, because voltage levels are not inherently binary.
I found a patent from 1978 "Ternary Logic Circuits With CMOS Integrated Circuits" from Hussein T. Moufah, which shows how to build logic circuits for base 3 numbers with cmos-transistors. It's quite interesting!
So there is not only Max and Min Voltage for logical 0, 1 but Max, 0 and Min Volts (+4V, 0V, -4V in an example in the patent) for logical 2, 1 and 0 in ternary.
@@sevfx : I recall a math major at Caltech, Mike Yoder, researched ternary logic in the mid-1970s. If it were more useful than binary logic, it would have found favor. A ternary logic gate is presumably more complicated than two binary logic gates in order to implement the two thresholds & three voltage ranges and amplify the voltages accordingly. Also, I'm pretty sure that ternary logic would worsen at least one of the following, compared to binary logic: (1) noise tolerance, (2) speed, and/or (3) power consumption & waste heat.
So, although binary isn't a "physical necessity" for computing, it's a good bet that binary is physically optimal. But perhaps that wouldn't be true for information elements designed to exploit quantum properties that have more than two possible states, such as the many orientations that an electron's spin can take or the many polarization angles that a photon can take.
@brothermine2292 i completely support that 👌
My understanding is that superposition is when events occur simultaneously without the concept of time. For example, if something has two possible outcomes with varying probabilities, in superposition, both outcomes happen at the same time. However, each outcome still retains its individual probability. Measurement somehow reintroduces the concept of time to the system. Thank you for the video.
Nice vid. It's great how you apply reality to these concepts. One I'd like to see more abstract -> reality is the infinite square well potential. I think a good example of this would probably be quantum dots. Another one I'd like to see is the quantum harmonic oscillator. I know this is how band diagrams are derived from Kroenig Penney model, but it still feels a bit too abstract.
You put my heart in a quantum superposition
This is brilliant Mithuna, thank you
Finally! It was one of the most confusing things ever! Thank you!
Your videos are absolutely incredible !thank you!
As an x-ray tech trained in the military, the maths were almost non-existent. The highest math I took was college algebra.
If I took the class, would the math be overwhelming? Thanks!
No I don’t think so at all! If you want an idea of the level, check out the first 4 videos in this series. If that looks ok, you’ll be fine! Plus I will be there to help as much as possible, so you can email me with your questions and I can help you before the tutorials
@LookingGlassUniverse I think it was okay for me... But definitely scraping the edge of my defeat. 😄
12:23 "represented". Is that rigorous representation (e.g. imaginary=circular polarization)?
Or rather "complex numbers have enough freedom to represent possible states to make the math work"?
Any answer appriciated. I always thought that those complex numbers are there for the "freedom" = "to make the math work", but knowing exact meaning would be nice change (in my understanding, if applicable).
P.S.: My knowledge and understanding is 20 years outdated ;)
Great question, and I’m not sure I have an amazing answer. I feel like the exact mathematics you use to describe reality aren’t the reality themselves- because there’s always equivalent but different formulations of the theory with different maths. So I’m inclined to believe that it’s just a convenience to use complex numbers to represent an extra degree of freedom… but I’m not sure about that
@@LookingGlassUniverse Yet the phase of those complex numbers (polar form) seems to be very important for interference (constructive vs. destructive). The freedom (dimensionality) is necessary (real numbers just won't do), but can we associate any good meaning to it? I don't know.
Dr Jacob Barandes has developed an interpretation of QM that features local realism with no superpositions needed.
What's the general idea?
Eg, how would he explain interference pattern, resulting from at atom source placed in front of 2 slits. Roughly?
@TimoBlacks Geez I'm not sure, but supposedly the math checks out and predicts exactly the same results as observed. Something to do with a caveat Bell made. In it, reality is fundamentally random/probabilistic though. But consider that pilot wave, which has a particle only at one location at all times (uncertainty principle being a lack of knowledge instead of real) does produce the interference pattern because the waves interfere with itself or something. This has been reproduced macroscopically if I understand correctly. It's not pilot wave though and not deterministic like pilot wave.
Bell showed that QM must violate at least one of the following three axioms: Locality, Reality, or Measurement Independence. (Measurement Independence is also known as Statistical Independence.) Several interpretations of QM that violate Measurement Independence and satisfy Locality & Reality have been proposed... for example, Sabine Hossenfelder's Future Input Dependence.
Why does neutral covalent atoms bond together and come closer even if they have equal positive and negative charges??
There are different types of atomic bonds. Covalent bonds are on type and share electrons on their outer shell, if there is "space" for it on one of the atoms. That doesn't mean one was anionic and the other cationic. Example would be O2. Ionic bonds have one neg and one pos like NaCl.
@MsSonali1980 did u even understand my problem
And ur answer is trash
@@RahulSB-vf3cp Yeah, thanks that I took the effort and time to answer your question, to get insulted. My answer is still correct regarding how you questioned it. Don't ask questions in comment sections if you don't want anyone to answer. You better go an ask something like ChatGPT, because your (online) interaction with humans s*cks.
Edit: look up electro negativity in atoms and why atoms want to have a full outer shell.
Using an abstract vector space for the state, I feel it is more concrete.
Thanks for the video! 😀
what seems less clear here is how this is superior to just doing vector math.
12:40 I think this part was a little misleading how you showed it with your hands. Because the possible spin directions are in physical space, which is three-dimensional over the real numbers, while you show it with your hands in Hilbert space (state space), which is two-dimensional over the complex numbers with basis vectors |0> and |1>. There is no third direction in Hilbert space like you make it seem when you rotate the |1> direction upward.
EDIT: Sorry, I think I now get what you meant to say. You attach a complex plane to the |1> direction to visualise one complex dimension as two real dimensions. I think that's correct then. However, it should be stated that the same can then be done with the |0> direction, so that the two-dimensional complex vector space becomes a four-dimensional real vector space. And because of the normalisation |a|^2 + |b|^2 = 1 (where a, b are the prefactors of an arbitrary state a|0> + b|1>) that gives an extra condition, you can identify the three-dimensional physical space with the three free real numbers in Hilbert space.
Ah, thanks. This got me a little confused. Because I wondered why there wasn't just a z-component (as in x, y, z axis, 3-dim) introduced then.
So if I look at the 2D vector projection on the coordinate axes, can conclude that this is 2 dimensional system or the vector is superposition of these projections. Two different states in the same time? What about a 3D vector? Is it a superposition of 3 different states represented by its projection on the coordinate axes? I do not grasp this concept.
My understand about what must be Qu bit, is a physical system with two or more independent states, which ca be manipulated physically and simultaneously in a way that permit mathematical operations. If these 2 or more states are dependent, the computer based on such Qu bits will have no advantage over the classic computers.
Thanks a lot, you really helped me get all that! But I still can't help but wonder how quantum computers actually take advantage of these properties, like physically. 🤔
IN YOUR EXAMPLE THE POLARIZED LIGHT QBIT DOESN'T SEEM TO COLLAPSE IN ONE OF THE TWO STATES WHEN YOU MEASURE/OBSERVE IT. PLEASE ELABORATE
Okay but how do I decrypt RSA with that little light and the crystal? Can you do a tuto please
Nice background lighting. What is that?
youtube''s algorithm works sometimes!
I enjoyed the video and subscribed because the explaination was so good, but I have some questions
- 7:15 I don't get how there could be a combination of up and down, I understood the example of the prism projecting the laser's polarity into a basis of two polarities, but "up and down" does not sound like a basis to me because there is no orthonormality, so what is happening?
- also I don't get why the use of complex numbers, in this case it does not add any further dimensions it's just making the 1 state complex, or was it just a way of saying that whatever multiplies the two states 0 and 1 can be also complex? that would make sense because then yeah there would be more dimensions
-I also still don't get how qbits can make calculations easier, how could I apply these concepts to speed up calculations? this question probably is out of the scope of the video though
maybe someone could answer these questions? I would appreciate it
Hey, great questions! Thanks for asking them!
-This Is a confusing point; "up" and "down" aren't at right angles to each other, but when you translate them to the mathematical representation as vectors we treat them as orthogonal. The reason for this is that "orthogonality" in QM has a very specific meaning. If two states are orthogonal, then they are mutually exclusive. I.e. in an experiment, these vectors represent opposite outcomes. Since a stern-gerlach experiment has two outcomes: "up" and "down", the vectors for these must be orthogonal in QM. The vectors don't really represent the physical system (where up and down aren't at all at 90 degrees), but instead represent the information in a useful mathematical way.
-Yes, you're right! You can make either the "a" or "b" coefficients complex!
-I did a video about an actually "useful" thing you can do with a quantum computer once, if you're interested: ua-cam.com/video/tHfGucHtLqo/v-deo.htmlsi=sQIBKjDQV94aYL0X
Thanks again :)
@LookingGlassUniverse quick in the answers too! I should be the one thanking you, I will make sure to watch the video
Why only two levels 0 1?. Why not 0 1 2 3, using different electron energy levels, and using it as a parallel qubit?
It's unfortunate that the word "measurement" is used to describe the interaction of the photon & crystal and the interaction of the electron & Stern-Gerlach device. Obviously these interactions _change_ the state of the photon and the state of the electron, and they do NOT tell us what their state was _before_ the interaction.
For example, if we know the photon was in the "superposition state" |+> prior to its arrival at the crystal, that knowledge was deduced from an _earlier_ interaction that resulted in a photon polarized at 45 degrees, which can instead be described by a wavefunction that has a single term: 45 degrees with a probability of 1. It's unnecessary to describe it by a wavefunction that has a superposition of terms (the |+> "state"). The superposition is merely a prediction of what would be the result of an interaction between a photon in the 45 degrees state and the crystal, assuming the crystal is oriented at a specific angle. It's wrong to think of the superposition as describing the photon prior to its interaction with the crystal, and right to think of the superposition as a prediction of the result of a hypothetical interaction with a hypothetical crystal oriented at a hypothetical angle.
It seems sort of incorrect to say that a quantum system is in a superposition of the two states, because those two states are defined by the basis you choose, and if you choose a different basis, then you have a different two states that it is in a superposition of. Isn't it really in just one state, which is the state of pointing in the exact direction it actually points?
Every time I see a physical or experimental explanation of superposition it seems like what's actually described is an object that isn't actually "in both states at the same time" but is actually "in neither state" because the actual state is the combination of multiple factors. For example, the 45 degree polarization isn't both vertical and horizontal, it's just describable as a combo of the two, it "is" 45 degrees. And we only say it "collapses" to either vertical or horizontal because our measurement device forces it to align to either vertical or horizontal. That's not a measurement, it's a filter. And the entropy of the experiment means we can only know which way it'll go via probability instead of classical mechanics near 100% certainty.
I guess think of it more like force vectors if that helps understand it. If you roll a ball off a cliff at say 10m/s, it is going to travel 10m/s horizontally until it hits the floor. It's also going to drop at ~9.81m/s². So you have it going in a diagonal-ish direction but there is no diagonal force. It's really just going in both horizontal and vertical directions at the same time.
@Iammeandyouareyou That's the same thing I'm saying. Except the ball's trajectory can actually be broken into vertical and horizontal components that relate to the forces acting on it. But we don't say it's in a superposition of moving down and sideways, we talk about the forces acting on it and map them to a coordinate system. We also don't put a measurement device on the floor and say that any balls that hit it must have been in a down state. Or worse, blow air downward on the ball's path to force it down into the down state detector and declare the ball to collapse into a definite state because we "measured" it. QM talks about states of being, not forces of interaction.
The electron is sad because its too negative, in case you were wondering.
How do we know if the result of a quantum computer operation is correct? It could take decades to validate it using current supercomputers. I image that even one misbehaving q-bit could radically alter the result.
There are many problems that are hard to solve but easy to check once you have an answer. One example is finding factors for very very large numbers, which is one of the kinds of things that quantum computers would be good at while supercomputers are much slower.
The nature of quantum computing is such that we do not use any one trial as the answer to the quantum question we are asking.
This is for two reasons.
1. Quantum computing relies upon the spread of measurements across a wavefunction to find the answer. This means that the result is statistical and requires many (thousands of) measurements to gain a spectral understanding of the resulting wavefunction for the system. In other words, the noise will affect the spectrum’s clarity, but any one trial, noise and all, is not the “result”.
2. To reduce noise, quantum computing engineers have come up with ways to “error correct” by using groups of qubits to represent one “logical qubit”. So that when one qubit inevitably flips due to noise, the overall group can still be interpreted correctly. This reduces the effect of noise in the system.
I'm totally confused now, and thinking about a purely mechanical bits using pendulums.
How are bits related to pendulums???
@fullfungo
Classical bit have two positions either 1 or 0. Quantum bit can be in any position between 1 to 0. Pendulam like Quantum bit can be in any position between -1 0 +1 and independent of temperature. just an imagination!
6:30 Why is your electron so unhappy?
Too negative
@@LookingGlassUniverse Ohhhhhhhh!!!!!! Makes sense.
@@LookingGlassUniverse😂😂😂😂😂😂🎉😊
Love from india ... i am pretty sure that i found a good role model for my little 2-year-old daughter when she grows up .
Wonderful work Mithuna
It's not clear how this is an advantage over just using vector operations. Surely qubits can do more than what simple vectors in linear algebra can do right?
The maths of Quantum mechanics is linear algebra with the restriction that all operations are unitary
@@LookingGlassUniverse I get that.
But then what's the computational advantage?
If I'm just adding/subtracting vectors I can just use a GPU and do better than a quantum computer.
You make it sound like it's no different than expressing a vector as components. For example, a vector of magnitude 5 at 45° from the x axis might be expressed as two vectors, one of magnitude 3 at 0° and another of magnitude 4 at 90°. However it can also be expressed as any of infinitely more combinations of other vectors.
But that's merely mathematics. Those are three separate vectors (also infinitely many other vectors besides), not one vector in two (or infinite) states. What am I misunderstanding?
This is a very subtle point, but in QM there isn't a difference. I think what's hard to accept about this is that when we say "this light is a superposition of horizontal and vertical" if makes it seem this is the correct or only way to see the light. But yeah, as you said, you could have picked any other basis instead. All these different ways of decomposing the light are equally "physical"- the most useful way to do it though is to use the basis that you're then going to be measuring in later. I'm not sure if that helped at all
@LookingGlassUniverse That does help a bit, thanks. The implication, though, seems to be that there is only one "real" state of the object and we just choose the "lens" through which we observe it to fit the purpose we've set. What does that mean for Copenhagen and the supposed reality of, for example, no definite position for a photon? Does it actually have a definite position and all we do is select the metaphorical angle at which we observe that position, such that it _appears_ that that is the "highest probability" position? (Or however it would be best to say that - I only have a middling layman's understanding of quantum physics.)
Also, it's philosophically interesting because it gets into whether mathematics is discovered or invented. Are quantum objects "made of math" such that the infinite mathematical expressions of the object are literally what a superposition of infinite states is? Or is math merely a description of the physical world such that there are any number of ways to describe physical reality, only a few of which we have devised (some better - i.e. more accurate - than others) but none of which are physically real. (I'm very firmly on the side of the latter, BTW.)
@@1newme425 Just a few months ago, I saw a video that gave me a new perspective on quantum objects. (I don't remember the title but I'm almost certain it was by Float Head Physics.)
The reason we have trouble understanding quantum objects like photons, electrons, and others is that they simply _cannot_ be described, _at all,_ using the concepts we have for macroscopic physics. "Particle," "wave," even "point," simply _do not apply_ and cannot even be "stretched" to make sense of quantum objects. They are something else entirely.
We are comfortable with terms like "particle" and "wave" because they have become second-nature to us. However, until we devise entirely new concepts for quantum objects and those concepts become as familiar to us as "particle" and "wave" are now, we will fail to have anything resembling an intuitive grasp of what those objects are. They are _entirely_ different than what we're used to, so the words we use to describe what we're used to _cannot_ apply to, _cannot_ describe, them.
Even with that being the case, however, it's easier to grasp what we're dealing with in quantum objects if we keep that fact in mind. They're not particles, not waves, but something else entirely. Saying that an electron doesn't have a definite position fits somewhat with our normal understanding of physics but doesn't accurately capture the reality because "position" just doesn't apply to something that is not a particle. The same applies for the term "wave." We need new concepts that are not like "particle" and "wave," then we need them to pass into common usage the same way that "particle" and "wave" have. Only then will we reach an "everyday" understanding of the quantum world.
@@MichaelPiz I see maths as a language to describe something. There are different branches of mathematics and you can describe (and solve) a problem with multiple methods of different branches not only one. You can choose what fits best for you. You can use 4dim calculations to make the calculation of a 2dim problem easier, it's still a 2dim problem. Maths can help to understand a problem and then extrapolate from that knowledge. And what is even the truth? Depending on your scale of measurement, the British coastline has either a finite or an infinite circumference.
Excelent Job.tks
Would it be so difficult to use better and more accurate terminology so that people are not confused into believing that quantum mechanics is magic?
Google's Willow.. I thought of a light hardrive,, qubit using in 2000s, i think Logans Run movie had light electronics, n I was like that that, light would have different wavelengths and a single photon could hold infinite info.
Willow used same concept, for coherence, that I thought would work for a light based harddrive.. group alignment.. i thought and saw other light microchips stuff, in like 2022, and was like, coherence, just send a lot of photons all doing same calculation, and the .. superpostion of a wave.. the photons cohere to the quantum field wave complicated phrasing.. the overall average wavelengths of the photons correct eachother.. group autocorrect.. though IDK how Willow autocorrects an electron cloud exactly.
I find superposition to be disturbing. If physicists ever discover super-duper-position, I'm probably going to have a conniption.
I have a lot of conniptions. I keep them in a dark closet in a dark corner of my dark basement, and I never let them out.
Helps keep me sane.
brilliant video
Awesomesauce!!
... and because of that no answer that a quantum computer produces can be treated as reliable, so the whole concept of a quantum computer becomes pointless (other than for gaining investments)
So when then say Cat is dead and alive at the same time it means a Qucat.
🐈😑=◼️(🐈😃)+ ▪️(🐈😵)
Your name should be photon
Why? Because she lights up your day?
Mmh Mmh yeah... I know some of these words 😂
Due to probability
Any bit you do in your videos is a cute b- oh i seem to have misréad it.
😆