There are nonlocal effects in quantum mechanics but I am not sure I would consider quantum teleportation to be one of them. Quantum teleportation may look at first glance to be nonlocal but it can be trivially fit to local hidden variable models, such as Spekkens’ toy model, which makes it at least seem to me to belong in the class of local algorithms.

You have to remember that what is being “transferred” is a statistical description, not something physically tangible, and only observable in a large sample size (an ensemble). Hence, it would be a strange to think that the qubit is like holding a register of its entire quantum state and then that register is disappearing and reappearing on another qubit. The total information in the quantum state only exists in an ensemble.

In an individual run of the experiment, clearly, the joint measurement of 2 bits of information and its transmission over a classical channel is not transmitting the entire quantum state, but the quantum state is not something that exists in an individual run of the experiment anyways. The total information transmitted over an ensemble is much greater can would provide sufficient information to move the statistical description of one of the qubits to another entirely locally.

The complete quantum state is transmitted through the classical channel over the whole ensemble, and not in an individual run of the experiment. Hence, it can be replicated in a local model. It only looks like more than 2 bits of data is moving from one qubit to the other if you treat the quantum state as if it actually is a real physical property of a single qubit, because obviously that is not something that can be specified with 2 bits of information, but an ensemble can indeed encode a continuous distribution.

This is essentially a trivial feature known to any experimentalist, and it needs to be mentioned only because it is stated in many textbooks on quantum mechanics that the wave function is a characteristic of the state of a single particle. If this were so, it would be of interest to perform such a measurement on a single particle (say an electron) which would allow us to determine its own individual wave function. No such measurement is possible.

— Dmitry Blokhintsev

Here’s a trivially simple analogy. We describe a system in a statistical distribution of a single bit with [a; b] where a is the probability of 0 and b is the probability of 1. This is a continuous distribution and thus cannot be specified with just 1 bit of information. But we set up a protocol where I measure this bit and send you the bit’s value, and then you set your own bit to match what you received. The statistics on your bit now will also be guaranteed to be [a; b]. How is it that we transmitted a continuous statistical description that cannot be specified in just 1 bit with only 1 bit of information? Because we didn’t. In every single individual trial, we are always just transmitting 1 single bit. The statistical descriptions refer to an ensemble, and so you have to consider the amount of information actually transmitted over the ensemble.

A qubit’s quantum state has 2 degrees of freedom, as it can it be specified on the Bloch sphere with just an angle and a rotation. The amount of data transmitted over the classical channel is 2 bits. Over an ensemble, those 2 bits would become 2 continuous values, and thus the classical channel over an ensemble contains the exact degrees of freedom needed to describe the complete quantum state of a single qubit.

I got interested in quantum computing as a way to combat quantum mysticism. Quantum mystics love to use quantum mechanics to justify their mystical claims, like quantum immortality, quantum consciousness, quantum healing, etc. Some mystics use quantum mechanics to “prove” things like we all live inside of a big “cosmic consciousness” and there is no objective reality, and they often reference papers published in the actual academic literature.

These papers on quantum foundations are almost universally framed in terms of a quantum circuit, because this deals with quantum information science, giving you a logical argument as to something “weird” about quantum mechanic’s logical structure, as shown in things like Bell’s theorem, the Frauchiger-Renner paradox, the Elitzur-Vaidman paradox, etc.

If a person claims something mystical and sends you a paper, and you can’t understand the paper, how are you supposed to respond? But you can use quantum computing as a tool to help you learn quantum information science so that you can eventually parse the paper, and then you can know how to rebut their mystical claims. But without actually studying the mathematics you will be at a loss.

You have to put some effort into understanding the mathematics. If you just go vaguely off of what you see in YouTube videos then you’re not going to understand what is actually being talked about. You can go through for example IBM’s courses on the basics of quantum computing and read a textbook on quantum computing and it gives you the foundations in quantum information science needed to actually parse the logical arguments in these papers and what they are really trying to say.

Moore’s law died a long time ago. Engineers pretended it was going on for years by abusing the nanometer metric, by saying that if they cleverly find a way to use the space more effectively then it is as if they packed more transistors into the same nanometers of space, and so they would say it’s a smaller nanometer process node, even though quite literal they did not shrink the transistor size and increase the number of transistors on a single node.

This actually started to happen around 2015. These clever tricks were always exaggerated because there isn’t an objective metric to say that a particular trick on a 20nm node really gets you performance equivalent to 14nm node, so it gave you huge leeway for exaggeration. In reality, actual performance gains drastically have started to slow down since then, and the cracks have really started to show when you look at the 5000 series GPUs from Nvidia.

The 5090 is only super powerful because the die size is larger so it fits more transistors on the die, not because they actually fit more per nanometer. If you account for the die size, it’s actually even less efficient than the 4090 and significantly less efficient than the 3090. In order to pretend there have been upgrades, Nvidia has been releasing software for the GPUs for AI frame rendering and artificially locking the AI software behind the newer series GPUs. The program Lossless Scaling proves that you can in theory run AI frame rendering on any GPU, even ones from over a decade ago, and that Nvidia’s locking of it behind a specific GPU is not hardware limitation but them trying to make up for lack of actual improvements in the GPU die.

Chip improvements have drastically slowed done for over a decade now and the industry just keeps trying to paper it over.

At least llama.cpp doesn’t seem to do that by default. If it overruns the context window it just blorps.

This happened to me a lot when I tried to run big models with low context windows. It would effectively run out of memory so each new token wouldn’t actually be added to the context so it would just get stuck in an infinite loop repeating the previous token. It is possible that there was a memory issue on Google’s end.

It’s… literally the opposite. The giant AI models with trillions of parameters are not something you can run without spending many thousands of dollars, and quantum computers cost millions. These are definitely not services that are going to fall into the hands of everyday people. At best you get small AI models.

The reason quantum computers are theoretically faster is because of the non-separable nature of quantum systems.

Imagine you have a classical computer where some logic gates flip bits randomly, and multi-bit logic gates could flip them randomly but in a correlated way. These kinds of computers exist and are called probabilistic computers and you can represent all the bits using a vector and the logic gates with matrices called stochastic matrices.

The vector necessarily is non-separable, meaning, you cannot get the right predictions if you describe the statistics of the computer with a vector assigned to each p-bit separately, but must assign a single vector to all p-bits taken together. This is because the statistics can become correlated with each other, i.e. the statistics of one p-bit depends upon another, and thus if you describe them using separate vectors you will lose information about the correlations between the p-bits.

The p-bit vector grows in complexity exponentially as you add more p-bits to the system (complexity = 2^N where N is the number of p-bits), even though the total states of all the p-bits only grows linearly (complexity = 2N). The reason for this is purely an epistemic one. The physical system only grows in complexity linearly, but because we are ignorant of the actual state of the system (2N), we have to consider all possible configurations of the system (2^N) over an infinite number of experiments.

The exponential complexity arises from considering what physicists call an “ensemble” of individual systems. We are not considering the state of the physical system as it currently exists right now (which only has a complexity of 2N) precisely because we do not know the values of the p-bits, but we are instead considering a statistical distribution which represents repeating the same experiment an infinite number of times and distributing the results, and in such an ensemble the system would take every possible path and thus the ensemble has far more complexity (2^N).

This is a classical computer with p-bits. What about a quantum computer with q-bits? It turns out that you can represent all of quantum mechanics simply by allowing probability theory to have negative numbers. If you introduce negative numbers, you get what are called quasi-probabilities, and this is enough to reproduce the logic of quantum mechanics.

You can imagine that quantum computers consist of q-bits that can be either 0 or 1 and logic gates that randomly flip their states, but rather than representing the q-bit in terms of the probability of being 0 or 1, you can represent the qubit with four numbers, the first two associated with its probability of being 0 (summing them together gives you the real probability of 0) and the second two associated with its probability of being 1 (summing them together gives you the real probability of 1).

Like normal probability theory, the numbers have to all add up to 1, being 100%, but because you have two numbers assigned to each state, you can have some quasi-probabilities be negative while the whole thing still adds up to 100%. (Note: we use two numbers instead of one to describe each state with quasi-probabilities because otherwise the introduction of negative numbers would break L1 normalization, which is a crucial feature to probability theory.)

Indeed, with that simple modification, the rest of the theory just becomes normal probability theory, and you can do everything you would normally do in normal classical probability theory, such as build probability trees and whatever to predict the behavior of the system.

However, this is where it gets interesting.

As we said before, the exponential complexity of classical probability is assumed to merely something epistemic because we are considering an ensemble of systems, even though the physical system in reality only has linear complexity. Yet, it is possible to prove that the exponential complexity of a quasi-probabilistic system cannot be treated as epistemic. There is no classical system with linear complexity where an ensemble of that system will give you quasi-probabilistic behavior.

As you add more q-bits to a quantum computer, its complexity grows exponentially in a way that is irreducible to linear complexity. In order for a classical computer to keep up, every time an additional q-bit is added, if you want to simulate it on a classical computer, you have to increase the number of bits in a way that grows exponentially. Even after 300 q-bits, that means the complexity would be 2^N = 2^300, which means the number of bits you would need to simulate it would exceed the number of atoms in the observable universe.

This is what I mean by quantum systems being inherently “non-separable.” You cannot take an exponentially complex quantum system and imagine it as separable into an ensemble of many individual linearly complex systems. Even if it turns out that quantum mechanics is not fundamental and there are deeper deterministic dynamics, the deeper deterministic dynamics must still have exponential complexity for the physical state of the system.

In practice, this increase in complexity does not mean you can always solve problems faster. The system might be more complex, but it requires clever algorithms to figure out how to actually translate that into problem solving, and currently there are only a handful of known algorithms you can significantly speed up with quantum computers.

For reference: https://arxiv.org/abs/0711.4770

If you have a very noisy quantum communication channel, you can combine a second algorithm called quantum distillation with quantum teleportation to effectively bypass the quantum communication channel and send a qubit over a classical communication channel. That is the main utility I see for it. Basically, very useful for transmitting qubits over a noisy quantum network.

The people who named it “quantum teleportation” had in mind Star Trek teleporters which work by “scanning” the object, destroying it, and then beaming the scanned information to another location where it is then reconstructed.

Quantum teleportation is basically an algorithm that performs a destructive measurement (kind of like “scanning”) of the quantum state of one qubit and then sends the information over a classical communication channel (could even be a beam if you wanted) to another party which can then use that information to reconstruct the quantum state on another qubit.

The point is that there is still the “beaming” step, i.e. you still have to send the measurement information over a classical channel, which cannot exceed the speed of light.