s1dev

When maintaining a quantum memory, you measure parity checks of the quantum error correcting code. These parity checks don't contain any information about the logical state, just (partial) information about the error, so the logical quantum information remains coherent through the process (i.e. the logical part of the state is not collapsed).

These measurements are classical data, and a computation is required in order to infer the most likely error that led to the measured syndrome. This process is known as decoding.

This work is a model that acts as a decoding algorithm for a very common quantum code -- the surface code. The surface code is somewhat like the quantum analog of a repetition code in a sense.

I often wondered why MIMO was such an investigated topic. It would make sense if the Shannon limit is higher for this channel. Is there a foundational paper or review that shows this?

I believe that a classical radio receiver is measuring a coherent state. This is a much lower level notion than people normally think about in QEC since the physical DoF are usually already fixed (and assumed to be a qubit!) in QEC. The closest analogue might be different choices of qubit encodings in a bosonic code.

In general, I'm not sure that the classical information theory toolkit allows us to compare a coherent state with some average occupation number N to say, M (not necessarily coherent) states with average occupation number N' such that N' * M = N. For example, you could use a state that is definitely not "classical" / a coherent state or you could use photon number resolving measurements.

A tangential remark: The classical information theory field uses this notion of "energy per bit" to be able to compare more universally between information transmission schemes. So they would ask something like "How many bits can I transmit with X bandwidth and Y transmission power?"

Are Q-switched / pulsed lasers common in industrial applications?

What bank is this and are they available nationwide?

For a circuit of size C, the size of a fault tolerant circuit to compute the same thing is O(C polylog C)

https://arxiv.org/abs/quant-ph/9906129

I’m generally in agreement with the anti-bash camp, but I can name about that many :)

- Mutating default arguments to functions, so subsequent calls have different behavior

- Somewhat particular rules around creating references vs copies

- Things that look like lambda captures but aren’t quite

A few things come to mind from more modern aircraft like the 787/A350: Fly by wire (flight envelope protection), electronically actuated control surfaces (less hydraulics / reduced complexity), bleedless engines (greater efficiency), greater use of composites (less weight), modern wing design using computational modeling/optimization (possibly more efficient), and essentially as large of a turbofan fan as you would like

I want to point out that the experiment was at Harvard in the Lukin group. There is a proposal for constant-rate encodings using large quantum low-density parity check codes via atom rearrangement which could in principle achieve such high encoding rate. That said, it's certainly not mainstream yet. https://arxiv.org/abs/2308.08648

This is pretty neat! I think it's worth doing more analysis on the entropy cells separately from the entropy extractor. For example, the von Neumann extractor requires exchangeability of the input bits. Does this hold? In the setting where there is no phase noise from the entropy cells (and hence no entropy), does the TRNG give any output? Assuming some basic model (maybe measure this?) about gate delays, how much entropy should be generated by each entropy cell?

Is there some good intuition why P-complete problems are difficult to parallelize? This is the first I've heard of it (but then again, I'm usually interested in more obscure complexity classes)

This is not quite true. You only need to keep the qubits at a fixed temperature as you scale the system, so the resources required to add additional qubits grow only polynomially with the system size. Once you have many qubits with a sufficiently low (but constant) error rate, you can do quantum error correction which also only has polynomial overhead.

I hear good things about this book “how to prove it”

I also like Knuth’s art of computer programming book which is more about proving correctness of algorithms

In general, stuff like combinatorics, algorithms, etc I find to have a low barrier to entry, so it’s a nice playground

https://www.cambridge.org/highereducation/books/how-to-prove...

Yes. Breaking things in aviation frequently results in a body count

The correction card is legally required equipment and there are a few maintenance items that trigger a requirement to update it

What experimental evidence of quantum gravity is there? I like to argue for theoretical evidence of quantum gravity, but afaik there hasn’t been any experiments to rule out classical GR coupled to a quantum matter sector

It is worth noting that all known classical algorithms to solve this problem scale exponentially with the problem size, and fundamentally there is no reason why putting 60 or 70 qubits in the fridge is particularly more difficult than 53. The point is that while classical algorithm advances can take off orders of magnitude off the runtime, this has to be done _every_ time there is a small increase in the size of the quantum computing device in order to kill a supremacy claim.

(To clarify, I personally think optimization is not a remotely near-term application)

I once ran across an application that had a heap footprint for which the size was fixed at runtime. The data locality loss from the indirection killed the performance. In principle, JIT could fairly transparently unbox this and have no heap footprint

More or less, we're just before the finish line. About 20% lower noise and we'll be there. For every little bit past that, the overhead gets reduced immensely

https://arxiv.org/abs/2207.06431

Quantum error correction is a key ingredient for future realizations of fault-tolerant quantum computers.

Physics is local, so errors in far separated regions of the device are only slightly correlated. In this setting, threshold theorems can be proved to show that as long as the device is below some constant amount of noise at the physical level, the noise can be suppressed arbitrarily (exponentially) at the logical level.

From a theoretical point of view, this is evidence that quantum computing is a more powerful model of computation. I think it would be hard to argue that a model of computation that can solve more problems is any less useful. Applications like quantum simulation do appear to be difficult on a classical computer yet efficiently computable on a quantum computer

I don’t think anyone does grad school expecting that it’s going to be a good investment. Most people I know do it because they can’t imagine themselves doing anything other than research. Is it a waste if afterwards you just get some 9-5 software or finance gig? Definitely. That said, there’s few other ways you get to spend several years becoming a world expert *in a topic of your choice*

There is an extremely broad range of scaling between linear and exponential…

Even in architectures with nearest neighbor gates, the (multiplicative) overhead stemming from error correction will only need to be logarithmic in the size of the computation. The constants may be unfavorable, but a log is still a log. See for example https://arxiv.org/abs/1208.0928 and https://arxiv.org/abs/1310.2984

Here's a few references

https://doi.org/10.1145/2492101.1555372

https://doi.org/10.1145/2786763.2694348

https://doi.org/10.1109/DSN.2015.57

A consumer PC should see a single bit error roughly once a week. That’s hardly non-existent

That's not quite true. The dimension of the ambient space is constrained to be exactly 10 (in strings, 11 in M-theory) by consistency considerations.

The important question is what is the geometry of the extra dimensions, if they exist. You need a large amount of energy to probe the extra dimensions, so it would appear just like some extra particles in the theory to a low energy observer. (Of course, the observer has to have enough energy to find even those particles).

The standard model also has seemingly arbitrary particle content and interactions without much to constrain it. A majority of the particle content was put in the theory by hand after seeing a failure of the theory. In strings, this choice has been moved from the theory to the initial data (choice of geometry of the extra dimensions).

It's generally expected that the spacetime geometry is emergent as some coherent state of gravitons

Unpacking that statement a bit:

- In quantum mechanics there is a procedure called "quantization" that takes in a classical theory and gives you a quantum theory.

- The things (excitations) that follow your classical intuition are waves [*] and when you quantize them, you get excitations that carry discrete quanta of energy (ex. photons / gravitons / <particle name of choice>)

- It's convenient to talk about states with a definite number of particles because of the way the math works out.

- To get back to something that follows your classical intuition (waves) you have to consider superpositions of the states with definite particle number. These particular states are known as "coherent states" and very much look like your normal notion of a classical wave which is something with a definite phase and amplitude

As an example: you can recover something that looks like a classical radio wave in quantum electrodynamics by taking a particular superposition of states with a definite number of photons. Since it's in superposition, the number of photons in the state isn't well defined. By well defined here, I mean if you measure the number of particles, you can get different answers due to Heisenberg uncertainty.

You can even get standing waves in a cavity (like a microwave oven) which is an oscillator and the state has a definite phase and amplitude that you can measure. Everything looks nice and classical but if you look hard enough you find that actually you can't put in an infinitesimally small amount of energy, you can only add it in multiples of some constant (h-bar).

Now replace the electromagnetic field with a field that represents the curvature of spacetime and away you go, your theory works with small excitation quanta (gravitons) but the actual things in everyday life that you see are complicated superpositions of these things [**].

So the geometry (spacetime) is some superposition of states with definite graviton numbers that have no classical description. Much like how the electric field around an electron or an oscillating electromagnetic field inside of a microwave oven is a superposition of states with definite photon number. Sidenote: it’s also easy to talk about a single graviton in isolation sitting on top of that emergent geometry

[*] This is "backwards" from pop-sci / intro physics because we are talking about electromagnetism which shares some superficial similarities with gravity

[**] For some technical reasons this viewpoint doesn't apply to particles which aren't "force-carriers" ex. electrons, protons, etc

Of course you wouldn't actually put them in Texas, but since this seems to be missed a lot: It hails reasonably frequently in the Midwest (incl. Texas)

it's one instruction in the generated code and we can reasonably expect the branch predictor to do the right thing, but branches and error handling can inhibit vectorization which is a much higher performance cost. While in this particular case you probably aren't vectorizing much, it is not always the case that error handling is almost free

The A72 has speculative execution so I don’t think that’s strictly speaking true