It’s great you learned about entanglement! There’s a bit more to it though :) (also sorry, this got long, I got a bit carried away)
Have you had any linear algebra at all? It’s the best way I can explain it without introducing any “quantum” terminology.
Basically, with our normal digital computers we operate on bits that are 0 or 1. We read those bits, store those bits, shift them, flip them, etc. Quantum computers, on the other hand, are more like analog computers, but with a twist.
Quantum bits (qubits) are not represented by a single binary digit. Instead, they are represented by two complex numbers (a vector) [a, b] with |a|^2 + |b|^2 == 1. You can represent this visually as a point on the surface a sphere with radius 1. A qubit’s state can be any point on that sphere. That’s the notion of superposition. When measuring a qubit’s state however, nature forces us to choose just one axis along which the qubit can point. So let’s say we choose the up/down axis, and we make the qubit point somewhere perpendicular to that, we will measure either a 0 or a 1 with 50% probability.
Entanglement means two (or more) qubits are strongly correlated. To represent the state of two qubits, let’s extend our vector to four complex numbers [a, b, c, d] (still with norm 1).
[1, 0, 0, 0] means “qubit A and qubit B are both pointing up on their spheres”,
[0, 0, 0, 1] means “A and B are pointing down”.
[0, 1, 0, 0] means “A points up and B points down”
[0, 0, 1, 0] means “A points down and B points up”
And any combination of those is possible. This state for example: [1/√2, 0, 0, 1/√2] means: “A and B point up together and A and B point down together”. A and B are entangled. Nature doesn’t let us observe this directly, but we can measure it statistically by repeating an experiment over and over. And the measurement results should show that A and B always point in the same direction (in a perfect world, that is). And while we can’t ever observe entanglement directly, we know that these states are possible and that we can use them.**
So how do we use these qubits? We rotate them and make their rotations correlate and then rotate them some more and… we measure. And repeat this a bunch of times. In mathematics world this means we multiply these vectors above with so-called unitary matrices. In the physics world this means we send microwaves and/or RF waves and/or laser light at the qubits.
What’s the use of all this? Well, for one it’s much closer to how nature actually works and we can use it e.g. to simulate complex chemicals. Plenty of use-cases in machine learning are also being researched (as you can imagine, large matrices with floating point numbers map quite well to qubits).
As for what this article means though… to non-researchers, not much. Qubits are analog and thus they (and operations on them) have errors. Especially today’s qubits. This means you need 1000s of qubits that still must be of much higher quality than today’s qubits to do anything remotely practically useful (and we try not to think about this too much…).
** Side-note: I should also mention the small mistake in your explanation. Changing one qubit’s state doesn’t change it’s entangled counterpart. Let’s stick with the example entangled state. If I rotate A to point, let’s say, along the “left/right” axis, then the state could be “left/up and right/down”. I.e., only A’s state rotates. If this were otherwise, faster-than-light communication would be possible.
Don’t ever apologise for getting carried away. Sharing something you’re passionate about is a gift for your audience!
Can you also explain quantum advantage for me?
And share your thoughts on what you think the timeline will look like for the development of quantum computing?
Also I’m sorry but I have one more question for you, Being a bit of a tech nerd I’ve had a few conversations with people about quantum computing and encryption. Obviously there’s concerns that current cyphers will be obsolete, but I’ve always wondered is this not a problem that we could easily solve by just drastically ramping up entropy?
I haven’t delved too much into the theory side of this, but so far “quantum advantage” has meant that researchers found a particular algorithm (doesn’t need to be practically useful) that their quantum processor can execute, but a “classical” computer cannot feasibly do (it would cost too much memory or too much time). Different research groups put different nuances on the term “quantum advantage” so it’s hard to give a straightforward answer.
And share your thoughts on what you think the timeline will look like for the development of quantum computing?
Difficult to say. There was a paper by Microsoft that showed what it would take to realize one of the first real practical applications (simulating chemical reactions for nitrogen fixation in fertilizers). On page 22 there is a table. When it comes to “clifford error rate”, the best qubits today can reach 10^-5 or so, and our control electronics are actually too noisy to get below ~10^-7 - 10^-8 if everything else were perfect. The best we can do on “required code distance” in practice up to now is 5.
TL;DR, 3 decades to get there would be a very optimistic estimate if we continue improving our current technology.
But, the “current technology” (the ones that all these papers by IBM, Google, etc. are about) is superconducting qubits. Many other platforms are being researched and show promise to be higher quality, but are simply not scalable yet. Microsoft is betting on the most stable, high-quality qubits we can think of (“Majorana qubits”), but they are so early in the research stage they haven’t even proven that you can actually make qubits that way.
Obviously there’s concerns that current cyphers will be obsolete, but I’ve always wondered is this not a problem that we could easily solve by just drastically ramping up entropy?
Quantum computers will be able to break asymmetric encryption that rely on prime factorization, like RSA, which happens to be by far the most widely used encryption algorithm today. Increasing the cipher length is not going to help you much since the quantum computer can scale much faster. Action should be taken now for critical environments (e.g. government, military) because of store now, decrypt later attacks.
Luckily there are encryption algorithms (like elliptic curve encryption, e.g. ECDSA) that have no known quantum algorithm to crack them. And if you’re paranoid that one day we will crack those algorithms too, quantum comes to the rescue with quantum encryption, which makes the encryption key generation fundamentally secure (as in, proven by physics that no third party could possibly listen in on the key generation). Quantum encryption is luckily much more easy to realize than quantum computing and it’s starting to become commercially available already (if you have a couple 10k dollars per link you want to secure).
Thanks mate. I really appreciate your time. I hope I get to see quantum computing be in practical use in my lifetime.
It’ll be insane to see where “AI” and quantum computing lead us. Folding at home was always really interesting to me, and I could imagine a machine learning platform combined with the massive increase in compute power could solve so many biomedical problems.
It’s great you learned about entanglement! There’s a bit more to it though :) (also sorry, this got long, I got a bit carried away)
Have you had any linear algebra at all? It’s the best way I can explain it without introducing any “quantum” terminology.
Basically, with our normal digital computers we operate on bits that are 0 or 1. We read those bits, store those bits, shift them, flip them, etc. Quantum computers, on the other hand, are more like analog computers, but with a twist.
Quantum bits (qubits) are not represented by a single binary digit. Instead, they are represented by two complex numbers (a vector)
[a, b]with|a|^2 + |b|^2 == 1. You can represent this visually as a point on the surface a sphere with radius 1. A qubit’s state can be any point on that sphere. That’s the notion of superposition. When measuring a qubit’s state however, nature forces us to choose just one axis along which the qubit can point. So let’s say we choose the up/down axis, and we make the qubit point somewhere perpendicular to that, we will measure either a 0 or a 1 with 50% probability.Entanglement means two (or more) qubits are strongly correlated. To represent the state of two qubits, let’s extend our vector to four complex numbers
[a, b, c, d](still with norm 1).[1, 0, 0, 0]means “qubit A and qubit B are both pointing up on their spheres”,[0, 0, 0, 1]means “A and B are pointing down”.[0, 1, 0, 0]means “A points up and B points down”[0, 0, 1, 0]means “A points down and B points up”And any combination of those is possible. This state for example:
[1/√2, 0, 0, 1/√2]means: “A and B point up together and A and B point down together”. A and B are entangled. Nature doesn’t let us observe this directly, but we can measure it statistically by repeating an experiment over and over. And the measurement results should show that A and B always point in the same direction (in a perfect world, that is). And while we can’t ever observe entanglement directly, we know that these states are possible and that we can use them.**So how do we use these qubits? We rotate them and make their rotations correlate and then rotate them some more and… we measure. And repeat this a bunch of times. In mathematics world this means we multiply these vectors above with so-called unitary matrices. In the physics world this means we send microwaves and/or RF waves and/or laser light at the qubits.
What’s the use of all this? Well, for one it’s much closer to how nature actually works and we can use it e.g. to simulate complex chemicals. Plenty of use-cases in machine learning are also being researched (as you can imagine, large matrices with floating point numbers map quite well to qubits).
As for what this article means though… to non-researchers, not much. Qubits are analog and thus they (and operations on them) have errors. Especially today’s qubits. This means you need 1000s of qubits that still must be of much higher quality than today’s qubits to do anything remotely practically useful (and we try not to think about this too much…).
** Side-note: I should also mention the small mistake in your explanation. Changing one qubit’s state doesn’t change it’s entangled counterpart. Let’s stick with the example entangled state. If I rotate A to point, let’s say, along the “left/right” axis, then the state could be “left/up and right/down”. I.e., only A’s state rotates. If this were otherwise, faster-than-light communication would be possible.
Amazing. Thank you.
Don’t ever apologise for getting carried away. Sharing something you’re passionate about is a gift for your audience!
Can you also explain quantum advantage for me?
And share your thoughts on what you think the timeline will look like for the development of quantum computing?
Also I’m sorry but I have one more question for you, Being a bit of a tech nerd I’ve had a few conversations with people about quantum computing and encryption. Obviously there’s concerns that current cyphers will be obsolete, but I’ve always wondered is this not a problem that we could easily solve by just drastically ramping up entropy?
I haven’t delved too much into the theory side of this, but so far “quantum advantage” has meant that researchers found a particular algorithm (doesn’t need to be practically useful) that their quantum processor can execute, but a “classical” computer cannot feasibly do (it would cost too much memory or too much time). Different research groups put different nuances on the term “quantum advantage” so it’s hard to give a straightforward answer.
Difficult to say. There was a paper by Microsoft that showed what it would take to realize one of the first real practical applications (simulating chemical reactions for nitrogen fixation in fertilizers). On page 22 there is a table. When it comes to “clifford error rate”, the best qubits today can reach
10^-5or so, and our control electronics are actually too noisy to get below ~10^-7-10^-8if everything else were perfect. The best we can do on “required code distance” in practice up to now is 5.TL;DR, 3 decades to get there would be a very optimistic estimate if we continue improving our current technology.
But, the “current technology” (the ones that all these papers by IBM, Google, etc. are about) is superconducting qubits. Many other platforms are being researched and show promise to be higher quality, but are simply not scalable yet. Microsoft is betting on the most stable, high-quality qubits we can think of (“Majorana qubits”), but they are so early in the research stage they haven’t even proven that you can actually make qubits that way.
Quantum computers will be able to break asymmetric encryption that rely on prime factorization, like RSA, which happens to be by far the most widely used encryption algorithm today. Increasing the cipher length is not going to help you much since the quantum computer can scale much faster. Action should be taken now for critical environments (e.g. government, military) because of store now, decrypt later attacks.
Luckily there are encryption algorithms (like elliptic curve encryption, e.g. ECDSA) that have no known quantum algorithm to crack them. And if you’re paranoid that one day we will crack those algorithms too, quantum comes to the rescue with quantum encryption, which makes the encryption key generation fundamentally secure (as in, proven by physics that no third party could possibly listen in on the key generation). Quantum encryption is luckily much more easy to realize than quantum computing and it’s starting to become commercially available already (if you have a couple 10k dollars per link you want to secure).
Thanks mate. I really appreciate your time. I hope I get to see quantum computing be in practical use in my lifetime.
It’ll be insane to see where “AI” and quantum computing lead us. Folding at home was always really interesting to me, and I could imagine a machine learning platform combined with the massive increase in compute power could solve so many biomedical problems.