HN Theater @HNTheaterMonth

> one can literally write down a matrix of numbers in a program to define a new mathematical function, and later use that function to manipulate the contents of the computer's RAM[1].

This "Quantum Computing for Computer Scientists" video https://youtu.be/F_Riqjdh2oM explains classical and quantum operators as just matrices. What are other good references?

Quantum state: https://en.wikipedia.org/wiki/Quantum_state

Quantum logic; quantum logical operators: https://en.wikipedia.org/wiki/Quantum_logic

> All this business about energy levels, evolution, etc. are distractions, just as the electrodynamics of a transistor are distractions from what it means to program a computer.

But a classical simulator - like e.g. qiskit - for a quantum circuit/experiment/function must run the experiment very^very^very many times to even probabilistically approximate a sufficient quantum system; because of the combinatorial probabilistic explosion that results from adding just one more basis state.

What are the fundamental limitations of quantum simulators? Maybe it's possible.

Quantum simulator: https://en.wikipedia.org/wiki/Quantum_simulator

- [ ] Maybe Twistor theory has insight into a classical geometrical formulation that could be run on a non-QC?

Amplituhedron: https://en.wikipedia.org/wiki/Amplituhedron

[Photon] wave-particle constructive superpositions approximate which operators, which may form a neat topology like this:

- [ ] > A research question for a new school year:

> The classical logical operators form a neat topology. Should we expect there to be such symmetry and structure amongst the quantum operators as well? https://commons.m.wikimedia.org/wiki/File:Logical_connective...

⬐ reikonomusha

Your assessment of how a quantum simulator works is not quite right. These simulators represent the entire probability distribution of basis states succinctly as an array. This array grows very large (exponentially) in the number of qubits.

A simulator only needs to run a computation once (which is multiplication of matrices in a tensor product space) and look at the resulting state. You don't need to run anything multiple times to approximate a quantum state.

The questions you're asking are the whole point of the field of quantum information science. On an ordinary quantum computer where quantum state will collapse to a basis state upon readout, indeed you might need to gather statistics to determine the answer to whatever you've asked your computer. However, "very many times" is mathematically bounded in some way for an ideal quantum computer. It's like saying "we need to do many^many^many^many comparisons to do quicksort". Well yes, but we have a relationship between the size of the input (N) and the average number of comparisons needed (N log N), which makes the algorithm feasible in practice. This is the same with quantum algorithms.

There are also different kinds of quantum algorithms. Some are more probabilistic in nature. Others are—again in purely ideal circumstances—give you the right answer in one go.

As a side note: It is very hard for me to read, understand, and respond to your comments. They seem like random buzzword soups and aren't very coherently put together, mixed with random links and references.

⬐ westurner

Re: error in simulators and actual QC hardware, which we do need for a reason: Quantum Error Correction # General_codes https://en.wikipedia.org/wiki/Quantum_error_correction#Gener...

How to best quantize reals into matrices (~= tensors)? https://en.wikipedia.org/wiki/Quantization_(signal_processin...

> Peter Shor first discovered this method of formulating a quantum error correcting code by storing the information of one qubit onto a highly entangled state of nine qubits. A quantum error correcting code protects quantum information against errors of a limited form.

Here's "Quantum Algorithm Zoo" by Microsoft Quantum: https://quantumalgorithmzoo.org/

And "Timeline of quantum computing and communication" https://en.wikipedia.org/wiki/Timeline_of_quantum_computing_...

I have a hard time with the idea that the outcome of the ultimate quantum simulation is a collapsed float.

Quantum Monte Carlo: https://en.wikipedia.org/wiki/Quantum_Monte_Carlo :

> Quantum Monte Carlo encompasses a large family of computational methods whose common aim is the study of complex quantum systems. One of the major goals of these approaches is to provide a reliable solution (or an accurate approximation) of the quantum many-body problem. [...] The difficulty is however that solving the Schrödinger equation requires the knowledge of the many-body wave function in the many-body Hilbert space, which typically has an exponentially large size in the number of particles. Its solution for a reasonably large number of particles is therefore typically impossible,

What sorts of independent states can or should we map onto error-corrected qubits in an approximating system?

Propagation of Uncertainty ... Numerical stability ... Chaotic convergence, ultimately, apparently: https://en.wikipedia.org/wiki/Propagation_of_uncertainty

For those who are interested, this lecture was sent to me as an overview of quantum computation for people like me: people who know how to code and know some basic linear algebra.

It goes deeper than the pop-sci articles about "doing all combinations at once" but remains accessible and by the end you understand entanglement and can read some Q# code.

https://www.youtube.com/watch?v=F_Riqjdh2oM

I think this talk is an excellent 'foot in the door' intro.

Should provide a solid foundation, and plenty of insider jargon to follow up on!

https://www.youtube.com/watch?v=F_Riqjdh2oM

⬐ dj00d

Apologies, made a mistake when creating the link. Now starts somewhere towards the end of the talk... Still, I think this is the best introduction to Quantum Computing I've seen in my short life!

I made a lecture aimed at such people (I was such a person!), which has proven popular: https://youtu.be/F_Riqjdh2oM

With a follow-up blog post focusing on entanglement: https://ahelwer.ca/post/2018-12-07-chsh/

⬐ juancn

Thanks! Commenting so I don’t lose this.

⬐ wskinner

You can use the “favorite” button on comments to save them to your profile.

⬐ juancn

I didn't know you could do it on a comment. It's not on the normal UI. Thanks.

⬐ nyc

Andrew, that lecture you gave was fantastic. The Deutsch oracle example in the lecture was especially helpful -- I'm surprised it doesn't get used more frequently in other explanations of QC. I think one of the most interesting moments in the video was when the audience (me included) jumped to the conclusion that the QC was more powerful than it actually was and you helpfully brought everyone back to reality.

⬐ ahelwer

Glad you enjoyed! I do think the Deutsch Oracle problem is the closest thing to a "hello world" problem in quantum computing, or maybe more analogous to the "sum every value in a list of integers" problem in GPU programming. Of course you can shoot holes in it, and a lot of people have trouble with the "rewire the black box to use two wires" thing and think it's cheating. But such an objection would disappear if you just look at the N-bit Deutsch Oracle problem, which is unfortunately too complicated to be the first problem one encounters.

There is absolutely no way to understand quantum mechanics without learning the math. All metaphors are faulty and will lead you to incorrect conclusions. Fortunately the advent of quantum computing has made the math quite easy - it's just linear algebra of the type one would pick up within the first week of an undergraduate course. I made a video aimed at computer scientists which you might find useful: https://www.youtube.com/watch?v=F_Riqjdh2oM

⬐ qbutt

This talk is excellent. Thank you for that.

I think an issue with communicating the lack of information transmission is that the statement usually fails to acknowledge two aspects:

1) We are unable to reliably force any one entangled particle to a specified state prior to measurement. ( You mention this more passively in a gp >"First of all, we don't know which color is in which envelope at the start." )

2) After measuring we have now entangled our particle to our measurement. So, if after our measurement we change the state of our particle the previously entangled particle fails to reliably correlate.

Information is transmitted; it's useful information that we are unable to communicate.

If I give you instructions saying if the envelope contains this then do this or if it contains that then do that, you can use the information from the particle's entanglement to make that decision, but because of 2) you can only use it to make that decision reliably once, and because of 1) those two outcomes will have to be equally desirable for this form of communication; making it useless. Just roll a dice.

⬐ zelphirkalt

Couldn't one argue, that in some situations coordination via previously agreed upon criteria is worth more than which one of two decisions is made?

If A and B agree upon, that B will know what A is doing in either case of discovery, then B needs only to look at their observation and will know what A's observation is (the opposite). Then B can know how A will act, because A decides what to do based on what they observe. Then B can act in a coordinated way. Even though it is only a roll of a die, it can still be helpful.

For Sci-Fi example: Some alien spaceship fleet (bare with me!) wants to attack another civilization from 2 sides across wast distances. They split up waaay before that and each keeps an entangled particle. They agree upon which observation means what detail in the first fleet's attack plan. Depending on that, the second fleet will act differently on the other side. But the first fleet only decide which of the 2 strategies to use, when they are already split up, based on the observation of the entangled particle. The second fleet has to act accordingly, or the strategy will fail.

Is this impossible? Or is this simply not seen as useful information in some specific definition?

⬐ ahelwer

You can accomplish the same thing with a PRNG initialized to the same seed.

⬐ qbutt

> Or is this simply not seen as useful information in some specific definition?

You are adding another conditional but nested conditionals still all rely on the first.

We are getting 1 bit of data:0|1; from this entrangled pair.

Fleet1 has Strategy0 in case their measurement reads 0.

Strategy0 requires Fleet2 to act using Strategy2 for the highest probability of success.

Fleet1 also has Strategy1 in case their measurement reads 1.

If Strategy1 also requires Fleet2 to act using Strategy2 for highest probability of success then Fleet1's measurement is useless as Fleet2 can just use Strategy2 in both events.

If instead Strategy1 requires a new Strategy3, and even though you could communicate which of these strategies to choose faster than we know how to communicate that electromagnetically, our 1 bit of information is still useless because you would still have to prepare for both eventualities.

Both pairs: Strategies02 and Strategies13; would equally have to have the same probability of success because if one is favoured over another then using this technique to decide your fleet movements could result in your allowing the possibility for the measurement to order you in a strategy you know is less likely to be successful.

This is what I was trying to get at by using the word 'desirable'.

Fleet2 may appear to be waiting on Fleet1 for orders, but in fact both fleets are waiting on their orders from the first measurement.

Here is a long-ish video that explains quantum computers without using pop-science hand-wavy terminology

https://www.youtube.com/watch?v=F_Riqjdh2oM

If anyone is interested I've also created a short 1.5 hour lecture on quantum computing aimed specifically at software engineers & computer scientists, which has proven popular: https://youtu.be/F_Riqjdh2oM

I'd love to answer any questions people have. In quantum computation, state behaves like a vector and logic gates behave like matrices that multiply the vector to get a new state value. It doesn't get too much more complicated than that.

⬐ asb3st0s

Just wanted to say I watched your lecture on YouTube a while back and thought it was very well-done and informative. I learned a lot. Thank you!

⬐ ahelwer

Glad you enjoyed! I also wrote a couple of follow-up blog posts which examine quantum entanglement & quantum chemistry simulation, respectively:

https://ahelwer.ca/post/2018-12-07-chsh/

https://ahelwer.ca/post/2019-12-21-quantum-chemistry/

⬐ DevX101

Nice! This seems to fit my learning style well. I prefer to understand why something matters, than progressively probe backwards into the theory.

⬐ thijsb

That was incredibly insightful! Thank you sharing this!

⬐ mendeza

Any advice on breaking into the industry? Would be really neat to work as a quantum research engineer, or software engineer on quantum computers!

⬐ virattara

For research you should go for a PhD. UCB/SB, UWaterloo, Duke (to count a few) have some nice Quantum centered programs/labs. Though the choice of program heavily depends upon the specific aspect of QC that you want to investigate. If you are thinking of working as a software engineer in this field then I believe you can do it without any formal higher eduction beyond bachelor's in engineering.

Since the field is very much experimental going into research would be a good choice as compared to software engineering, QC is unlikely to see full fledged corporate software engineer type roles in the near future.

⬐ erej

ETH Zurich has a quantum engineering masters: https://master-qe.ethz.ch/

⬐ deeeeplearning

In that Vein, so does USC. MSc in Quantum Information Science https://viterbigradadmission.usc.edu/programs/masters/msprog...

⬐ whimsicalism

Probably a PhD

⬐ ahelwer

Google, Amazon, IBM, and Microsoft all have quantum programs which use "regular" software engineers in various roles - for example, writing software to support researchers working in the labs. That's what I did for Microsoft. If you want to work on actual research yourself though, you'll probably need a PhD. There are some non-PhD positions that do research-adjacent work like simulating, implementing & refining researcher findings for the specific hardware the company is developing, but those are quite competitive/difficult to get (I tried!)

Microsoft also has a fairly large team working on Q# and the Microsoft Quantum Development Kit. That would also involve research-adjacent things like efficiently compiling programs to specific quantum device layouts with appropriate error correction schemes, etc.

Learning Quantum Computing based on skill level (math is the biggest friction point, suggested pdf should save you lots of time) (Recc is personal recommendations, Hi-Recc is look at ASAP)

# QC Main Ideas

    - Rotate, Compute, Rotate
    - Think in Amplitude Interference

# Beginner:

    -(Hi-Recc) Quantum Computing Primer (1.5hr) : https://www.youtube.com/watch?v=F_Riqjdh2oM
    -(Hi-Recc) Math Primer for Quantum Computing (easiest intro/primer I found on the topic; Highly Recommend   ) : https://cds.cern.ch/record/1522001/files/978-1-4614-6336-8_BookBackMatter.pdf
        -- understand Bra Ket notation [<Bra|Ket>]  (Ket as Column vector, Bra (Row vector) as Complex Conjugate of Ket (denoted as dagger) )
        -- understand Kronecker product  ( for multi-qubit systems) 
    - Quantum Computing for Computer Scientists book - https://www.amazon.com/Quantum-Computing-Computer-Scientists-Yanofsky/dp/0521879965
    - Quantum Math Primer (Faculty of Khan) (found a bit hard the first time around, pretty dense) : https://www.youtube.com/playlist?list=PLdgVBOaXkb9AtG88OsK_c8FDEBDLCC6_9

# Intermediate

    -(Recc) Ryan O'Donnell CMU course [is the best if you want to really understand the capabilities of quantum computing, get practice with math, intuition] (algos connection to Fourier, Quantum Complexity Theory, Math best practices, learning multi-quibit systems) 
        -- Quantum Computation and Information at CMU : https://www.youtube.com/playlist?list=PLm3J0oaFux3YL5qLskC6xQ24JpMwOAeJz
        -- Lecture Notes (use as reference in case video is not clear, or camera shot lags/changes) https://www.cs.cmu.edu/~odonnell/quantum18/  
    - Mermin's Textbook https://www.goodreads.com/book/show/1959623.Quantum_Computer_Science
    - Nielsen & Chuang's Textbook https://www.amazon.com/Quantum-Computation-Information-10th-Anniversary/dp/1107002176
        -- Nielsen's Lectures https://www.youtube.com/playlist?list=PL1826E60FD05B44E4

# Advanced

    -(Recc) Scott Aaronson Graduate Course http://stellar.mit.edu/S/course/6/fa14/6.845/materials.html
    -(Recc) Scott Aaronson Papers (really interesting) https://scottaaronson.com/papers/
    - Complexity Zoo - List of Algorithms https://complexityzoo.uwaterloo.ca/Complexity_Zoo
    -(Recc) Machine Learning https://www.amazon.com/Quantum-Machine-Learning-Computing-Mining/dp/0128100400

# Reference:

    -(Recc) https://qiskit.org/textbook/preface.html   ToC for different algorithms ( easy to follow, do it for quick basic algo math implementation lookup)
    - 'Suggested texts, notes, and videos to look at' section at bottom of page https://www.cs.cmu.edu/~odonnell/quantum18/

( I found this skill level format useful when learning Haskell/Functional Programming Paradigm. This is what I found useful for getting started with minimal friction; if more of a textbook learner Nielsen/Chuang textbook or Quantum Computing for Computer Scientist's)

I will answer this question in two ways: one, I will tell you how I learned, and two I will tell you how I would have liked to have learned with the benefit of hindsight. Different people will value one more than the other, but both are more valuable than a giant list of resources with zero guidance where to start.

How I learned:

I started out like you, in possession of an undergraduate education in computer science. I began reading Quantum Computer Science: An Introduction[0] by N. David Mermin. This is a very good textbook, but I absolutely could not skim it. I had to ensure I understood every single line before moving onto the next. I had the impression I wasn't learning very quickly, when in fact (due to the textbook's density) I was taking in a huge amount of information.

After a few weeks with the Mermin textbook, I bought Quantum Computing for Computer Scientists[1] by Yanofsky & Mannucci. This is a much softer introduction than Mermin, almost too soft: I skipped the first few chapters on linear algebra and complex numbers. However, in combination with the Mermin textbook, I acquired a good understanding of quantum computing basics. It was at this point I reached my own personal threshold for feeling I "understood" quantum computing.

People often recommend Quantum Computation and Quantum Information by Nielsen & Chuang (also called "Mike & Ike") for beginners. I believe this is not good advice. Had I tried to learn from that textbook, I would have failed. However, it is an excellent textbook after you already understand the basics. Anecdotally, I knew two people who tried to learn quantum computing at the same time as me: one used Mike & Ike, and the other used a book called Quantum Computing: A Gentle Introduction. Neither of those people understand quantum computing today.

How I wish I had learned:

My experience learning quantum computing required a huge amount of mental effort, and in the end what I learned wasn't actually complicated! So, I created a lecture called Quantum Computing for Computer Scientists[2] which is the lecture I wish I'd had access to before trying to read any textbooks. The lecture is popular and well-received, and I think it covers all the stuff that's really conceptually tricky; once you're over those conceptual hurdles, you can apply your regular computer science skills to learn everything else about quantum computing you need (how specific algorithms work, etc.) Thus my "hindsight" study guide is as follows:

1. Watch the lecture I created.

2. Watch Professor Umesh Vazirani's lectures on quantum computing; they flesh out my lecture and he is a tremendously effective explainer of concepts (these are scattered around YouTube but you can find a full playlist at [3])

3. Concurrently, work through the first few chapters of either the Mermin or Yanofsky textbooks

4. After you feel you understand the quantum computing basics, pick topics which interest you from the Nielsen & Chuang textbook

5. Stick around quantumcomputing.stackexchange, reading questions & answers, asking your own, and maybe eventually answering your own!

Good luck!

P.S. I've also heard good things about the Quantum Katas: https://docs.microsoft.com/en-us/quantum/tutorials/intro-to-...

[0] https://www.amazon.com/Quantum-Computer-Science-David-Mermin...

[1] https://www.amazon.com/Quantum-Computing-Computer-Scientists...

[2] https://youtu.be/F_Riqjdh2oM + slides https://speakerdeck.com/ahelwer/quantum-computing-for-comput...

[3] https://www.youtube.com/playlist?list=PLDAjb_zu5aoFazE31_8yT...

I’ve begun to put together useful resources for learning more here: https://quantumjavascript.app/resources.html

I’d like to really flesh out that page; I’ve now come across so many folks that are amazing at explaining this stuff... It’s just a time crunch to juggle all this as you might imagine ;)

These two videos in particular helped me get started:

1. What is a physical quantum computer? https://www.youtube.com/watch?v=OWJCfOvochA

2. How might one compute using it? https://www.youtube.com/watch?v=F_Riqjdh2oM

Here is a video of a researcher at Microsoft Quantum lecturing on this: https://www.youtube.com/watch?v=F_Riqjdh2oM "Quantum Computing for Computer Scientists.".

However, even with understanding how a Quantum Computer works at its most basic level I still have difficulty understanding the more useful Quantum Algorithms:

https://en.wikipedia.org/wiki/Shor%27s_algorithm

https://en.wikipedia.org/wiki/Grover%27s_algorithm

The Quantum Computing for Computer Scientists video by Microsoft Research (https://www.youtube.com/watch?v=F_Riqjdh2oM) really hammered it home for me. It goes slowly and the presenter, in his own words "shuts up and does the math".

I'll try to give here a crash course on how simulating quantum systems on a quantum computer works - not for the actual computer type in the article (D-Wave's quantum annealer) but on a traditional gate-based quantum computer.

So, we have this thing called the Schrodinger equation. For our purposes, all you need to know is that it's an equation which can perfectly describe the behavior of a quantum system as it evolves in time. Examples of quantum systems include a single electron sitting in a magnetic field, photons going through closely-placed slits, or entire biomolecules doing biomolecule things.

Simulating things on computers is great because of how darn easy & cheap it is compared to running the same scenario in the real world. We want to simulate quantum systems on computers. We simulate quantum systems by trying to mimic the action of the Schrodinger equation on the quantum system. However, (as Feynman famously pointed out in Simulating Physics with Computers[0]), classical computers are very bad at this. They take exponential resources to simulate a quantum system. Now, if you have a computer that obeys the same physical laws as the quantum system it's simulating - a quantum computer - we might be able to simulate the system with only linear resources.

Let's take a very simple quantum system. Consider a single electron, sitting in a magnetic field. Electrons have a property called spin which is affected by magnetic fields. Electrons can have their spin be up, down, or some superposition thereof. We want to know how the spin of the electron changes over time as it sits inside the field.

There are three steps involved in simulating this quantum system:

1. Encode the system's start state in a form understood by a quantum computer - a qbit, which is a 2-vector [a, b] of complex numbers where |a|^2 + |b|^2 = 1. We'll say the qbit [1, 0] represents spin up, and [0, 1] represents spin down. Other states [a, b] where both a and b are nonzero mean the electron spin is in superposition of up & down. Here, let's say we start in spin up - so [1, 0].

2. Compile the Schrodinger equation into a series of quantum logic gates for execution on a quantum computer. This is the real meat of the problem, more on that later.

3. Decode the end state back into the physical world. After the start state has been put through all the logic gates, we want to decode the result to the same spin state we would've had if we'd set up a real electron in a real magnetic field and let it actually evolve over time (within some acceptable error).

Pretty simple so far, right? All the magic happens in step 2 - how do we compile the Schrodinger equation into logic gates? It revolves around something called the Hamiltonian. The Hamiltonian is a component of the Schrodinger equation, and is a matrix which represents the energy of the system. That brings up a lot of questions around how exactly a matrix corresponds to the energy of a system, but it's a (fascinating!) rabbit hole we'll sadly have to avoid. Let's just look at an example.

Consider again our plucky electron in a magnetic field. Suppose the magnetic field points upward along the Z axis. This means the Schrodinger equation for our system is e^(-i H t), where e is Euler's constant, i is the square root of -1, t is a scalar variable representing time, and H is the Hamiltonian matrix - here, the 2x2 Pauli-Z matrix in column form Z = [[1, 0],[0,-1]]. How can we compile this equation into a quantum logic gate?

Turns out you can do it through basic algebraic manipulation. There are some tricky intermediate steps involving expanding e^x into the Taylor series[1] and back into trig functions[2] but at the end of the day you have:

e^(-i Z t) = cos(t) 1 - i sin(t) Z

where 1 is the 2x2 identity matrix and Z is the 2x2 Pauli-Z matrix from above. This just so happens to be a common primitive gate on a quantum computer, called the Rz(t) operator[3] which performs a rotation of the quantum state vector about the Z axis (actually what we use is Rz(2t)). So, we can apply this single quantum gate to our encoded start state, end up with our end state, and decode it back to a real physical spin state!

Now, of course this is a very simple example with a single qbit, but you can build up from there. I'll be writing a much longer guide on this which I hope to release at the end of next week. If you're interested in quantum computation in general and not just quantum simulation, I have a 1.5 hour talk on the topic aimed at computer scientists here[4]!

[0] https://people.eecs.berkeley.edu/~christos/classics/Feynman....

[1] https://en.wikipedia.org/wiki/Taylor_series#Exponential_func...

[2] https://en.wikipedia.org/wiki/Taylor_series#Trigonometric_fu...

[3] https://docs.microsoft.com/en-us/qsharp/api/prelude/microsof...

[4] https://www.youtube.com/watch?v=F_Riqjdh2oM

Crash course in entanglement:

The state of each qbit is represented by a state vector of two complex numbers [a, b] where |a|^2 + |b|^2 = 1. There are two special qbit values called the classical basis: [1, 0] which is the classical bit 0, and [0, 1] which is the classical bit 1. If a qbit is not in one of the two classical states, we say it is in superposition. When a qbit is in superposition, we can measure it[0] and it will collapse probabilistically to 0 or 1; for a qbit [a, b], the probability that it collapses to 0 is |a|^2 and the probability that it collapses to 1 is |b|^2.

Things get more interesting when we have multiple qbits. If we have two qbits [a, b] and [c, d], we define their product state as their tensor product [ac, ad, bc, bd]. For example, if we have two qbits both in state [1/sqrt(2), 1/sqrt(2)], their product state would be [1/2, 1/2, 1/2, 1/2]. We use the product state to calculate the action of a quantum logic gate that operates on multiple qbits - for a gate which operates on two qbits, we can always represent its action as a 4x4 matrix.

Usually we can move back and forth between the product state representation and writing out the individual qbits states. However, in certain scenarios something very special happens: we cannot factor the product state back into the individual state representation! Consider the product state [1/sqrt(2), 0, 0, 1/sqrt(2)]. If you try to write this as a tensor product of two states [a, b] and [c, d], you cannot! It cannot be factored; the qbits have no individual value, and we say they are entangled.

Well, what does this mean? It means when you measure one qbit, even if the qbits are very far apart, you instantly know the value of the other qbit. So if I entangled two qbits in the state [1/sqrt(2), 0, 0, 1/sqrt(2)], give you one, then we go to opposite ends of the universe, if I measure my qbit and see a 0 I'll know your qbit instantly also collapsed to 0 (or collapsed to 1 if I measured 1). This phenomenon has been experimentally-verified to occur faster than light. It is instantaneous, as far as we can tell. So, local realism is wrong! Spooky action at a distance is real!

There is an important caveat: while the qbits seem to coordinate in some faster-than-light way, you cannot use this to communicate in a faster-than-light way. All we have is a shared random number generator. I can't send some chosen bit from my reference frame to yours. This is called the no-communication theorem.

If you found this interesting, I have a full video on quantum computing for computer scientists here: https://youtu.be/F_Riqjdh2oM

[0] IDGAF about your chosen quantum mechanics interpretation, don't @ me

⬐ divan

I think this video deserves much more attention by HN readers, it's truly great introduction into quantum computing.

⬐ 3pt14159

Since speed warps spacetime, does the relative speed of the qubits change this? Can they go out of sync if one is moved much faster than the other for a prolonged period of time? If not, could this property be used for a universal clock?

⬐ Florin_Andrei

"Much faster than the other" relative to what?

There is no absolute motion or speed. There is only relative motion or speed.

⬐ bdamm

The part I don't understand is the "spooky action at a distance." Isn't this just the same as if the qbits were already in whatever their final state was as soon as they were entangled? Or in other words, is there any experimental basis for determining that the "cat" stayed alive at all? It seems a lot less magical when we just determine that in fact the value is the same no matter when or where you measure it, although it may not be predictable. And since the "entangled" qbit always had the same value, no matter when you measured it, then there is no "spooky action at a distance". The action occurred when d=0, and what you actually have is two copies of the same ROM.

⬐ stouset

The explanation you're supposing for the "spooky action at a distance" is called a hidden variable theory, and as others have said, this explanation has been disproven. You might be wondering how, and I'll tell you the scenario (adapted from The Elegant Universe) that helped me understand.

Imagine you and I each have a device: a small box with one openable window on the top, one on the front, and one on the back. When one of these windows is opened, it shows either white or black. Further, I tell you that these boxes are entangled: if we both open the same window, the same color will be displayed on both boxes. This only works for the first window opened and only if we both open the same window: if a second window is opened or if we open two different windows, the colors shown will no longer be correlated in any way.

I actually have many of these pairs of boxes, each pair numbered uniquely to identify its matching twin, and we run the experiment for an arbitrarily large number of them until you're satisfied that my claim holds true. You see nothing special about these boxes and argue that they're simply preprogrammed from the factory to display a set of colors the first time a window is opened (for example, BWB or WWB). I counter that entanglement is special and the boxes are not preprogrammed from the factory. In fact, they decide at random which color to show right at the moment one of the boxes' windows is opened!

My claim seems crazy and at first glance possibly even unprovable! But it turns out with a bit of cleverness we can test this.

We take an arbitrarily large number of boxes and begin independently opening their windows at random (without consulting or coordinating with each other when deciding which window to open), recording box numbers, window choices, and the resulting colors. When finished, we compare notes. Sure enough, when we both open the same window on entangled boxes, the colors match as expected. Upon a closer look at the data, we discover something surprising. Ignoring which window we opened, each pair of entangled boxes showed the same color exactly 50% of the time. How is this surprising? A little bit of probabilistic analysis conclusively demonstrates that such a result is fundamentally incompatible with any hidden variable theory.

Assume for the sake of argument that the boxes are preprogrammed. The only possible programming for each box is some form of XXX or XXY. Consider: if both boxes are programmed WWW (or BBB) and we both open a window at random, it will show the same color 100% of the time. If both are programmed WWB (or BWB, or BWW, or any equivalent variant), 2/3 of the time there's a 2/3 chance of displaying the same color when choosing windows at random and 1/3rd of the time there's a 1/3 chance. Combined, whenever the colors are in an XXY configuration, there's a 5/9 chance of showing the same color when windows are chosen at random. Note that in both scenarios the odds of seeing the same color from randomly-chosen windows are greater than 50%! Assuming the preprogrammed colors are chosen at random, some form of XXX will be chosen 2/8 of the time and XXY will be chosen 6/8 of the time, we see that the total odds of seeing the same color if the boxes were preprogrammed should be 2/8 * 100% + 6/8 * 5/9 = 2/3. In theory, our data should have shown a 66% agreement in color, but our experiment consistently shows colors matching 50% of the time.

A hidden variable theory—any hidden variable theory—runs into this probabilistic hurdle.

⬐ bdamm

What I draw from this is that polarized light doesn't quite work the way we think, and the investigation should be into the modes of polarity.

⬐ stouset

Are you seriously dismissing offhand theoretically sound and experimentally-verified core tenets of quantum mechanics?

It's not like they're making this stuff up. It falls very straightforwardly out of the mathematics underpinning quantum mechanics, we have tested these things, and we have conclusively disproven the existence of any type of hidden variable theory.

That's not to say quantum mechanics is faultless and complete, but any new theory is going to have to incorporate these results rather than throw them out entirely (much like how Newtonian physics "falls out" of general relativity at low speeds and small masses.

⬐ ahelwer

The idea that the qbits choose which value they'll collapse to at time of entanglement is called local hidden variable theory, which John Bell disproved in 1964: https://en.wikipedia.org/wiki/Local_hidden_variable_theory

In more practical terms, the theory also falls apart when you start doing more complicated things with entangled qbits than just measuring them, like quantum teleportation or error correction.

⬐ donutte

It’s also worth noting that as of 2015[0], this has been experimentally verified.

We’ve made real-world measurements here that correlate with measurements made at the exact same time over there in a way that mathematically cannot be accounted for without some species of intuition-violating spookiness. It’s all very real.

0: https://en.wikipedia.org/wiki/Bell_test_experiments#Hensen_e...

⬐ madeuptempacct

So, it's kind of like closures in JavaScript?

"A Bell test experiment or Bell's inequality experiment, also simply a Bell test, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to two other concepts: the principle of locality and Einstein's concept of "local realism". The experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons. According to Bell's theorem, if nature actually operates in accord with any theory of local hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. If a Bell test is performed in a laboratory and the results are not thus constrained, then they are inconsistent with the hypothesis that local hidden variables exist."

Spooky private method scope is spooky.

⬐ moosinho

Can someone tell me if I understand this correctly. So Bell famously proved that it is not the case that the correlation we see between 2 entangled particles A and B is because of some common cause C. Therefore we concluded that it must be that A => B or B => A and we called it a spooky action at a distance. But aren't we forgetting that there's a one more way to get a correlation between A and B without resorting to spooky action at a distance - conditioning on a common effect, aka collider: http://www.the100.ci/2017/03/14/that-one-weird-third-variabl... Has anyone proven that this is not the case?

⬐ abecedarius

What you're proposing is essentially what Bell's inequalities contradict. That's why they're surprising.

I think the many-worlds picture is a clearer way to think about this than "spooky action at a distance".

⬐ mundo

Yes, this is more or less what Bell's theorem disproves, although it's kind of a poor metaphor, because entanglement deals with indeterminate states, not just unknown ones.

⬐ avip

Bell inequality proves (or is used to show) that the shared/correlated state of "entangled" particles cannot be fixed before the act of measurement. It has nothing to say about "A => B" or the likes. If there exists a third "C" it'll still have to set the state of A and B, at the moment of measurement, regardless of distance.

⬐ None

None

⬐ crumpington

Big deal. There's nothing shocking or spooky about two billiard balls being made to spin in arbitrarily opposing directions, selecting only one (omg! without discovering which way it spins, you guys), then separating them, and then noticing the spin of one, in order to reliably grasp that the other is the reversal.

I have two guitars. I place the guitars facing one another, such that plucking the HIGH E string on one, also plucks the LOW E string on the other. We put ear plugs in our ears, such that I can separate the two guitars, without us ever hearing them. I pluck the guitars, give you one, and take the other one and travel far away. I then listen to my guitar. It is the HIGH E guitar. Now I know you have the LOW E guitar. Wow. Incredibly unspooky. Not teleportration.

⬐ mundo

> There's nothing shocking or spooky about two billiard balls being made to spin in arbitrarily opposing directions, selecting only one, then separating them, and then noticing the spin of one, in order to reliably grasp that the other is the reversal.

Okay. So now, make two billiard balls so that they're spinning opposite directions, and separate them to opposite sides of the table. Then, go to ball A and do something to it that reverses its spin. Then observe the spins of the two balls. Are they the same?

For billiard balls, yes. If ball A is spinning clockwise and ball B is spinning counter-clockwise, and you reverse the spin of ball A, then you will observe both balls to be spinning counter-clockwise.

For quantum particles, no. If we manufacture two entangled electrons such that observing them will reveal them to have opposite spin, you can reverse the spin of one of them, and then observe them, and they will both still have opposite spin.

⬐ zackmorris

Unfortunately I don't think this is true. The moment you observe them, they are no longer entangled. So they have opposite spin at that point, but if you reverse one, it behaves classically and both electrons then have the same spin.

I'm still trying to wrap my head around why there isn't some hidden variable though which determines which spin they'll have. Like with Bayes' theorum, I keep learning it but for whatever reason my brain won't remember it and I have to look it up again hahah.

⬐ mundo

Correct, this only works if you can reverse the particle's spin without observing it. This is a descriptive example - the real experiment is slightly more complicated - but it was experimentally verified by Alain Aspect in 1982. If you want a more detailed explanation I recommend http://scienceblogs.com/principles/2007/02/22/spooky-action-...

⬐ ChrisClark

https://en.wikipedia.org/wiki/Local_hidden_variable_theory

https://en.wikipedia.org/wiki/Bell_test_experiments#Hensen_e...

⬐ crumpington

These links are intended to suggest something contrary to what I've said, but they do not suggest any contradiction.

⬐ bazinga56

Im not an expert so from my outside viewpoint

I think by taking the guitar far away you are implying possibility of faster than light communication, which is thought to be not possible, so his links address that? Hard for me to understand so I'm just saying my thoughts out loud to get clarified, thanks

⬐ crumpington

The quantum state of interest is induced when plucking the conjoined "guitars". (analog for particles)

That state is induced at the moment the guitars share "locality" because entanglement requires locality for initialization of polarization.

So then, we say we are as yet unaware of the qualities of the polarization we, ourselves, induced. Very mysterious.

So spooky, yes? We do not measure, because we choose not to, so we do not yet know.

Even if we prevent ourselves from having the capacity to measure, the results hold true, but so what? And so what, if we ask others to do the same. Imagine that we ask two waiters to tape two coins together in the kitchen, flip the linked coins, peel the coins apart while preserving the outcome of the coin flip, then take one coin to your table, and one to mine. Now I know which side of the coin you are looking at, without walking over to your table. So what. Nothing about this claims transmit information superluminously.

In reality, with instrumentation, carrier signals relay an electromagnetic transmission in such a way that one cannot peek or tamper (the waiters can't change the coin flip, we cannot hear the ringing guitar), but this does not invalidate the premise of the analog. For the purposes of the analogous guitar example, we say that our couriers (electromagnetism itself) are prevented from touching or listening to the ringing guitars, or disclosing what they might sense.

With the guitars, we say the guitars move away from the place where they were entangled. We'll say that our instrumentation rang the guitars at the grand canyon. Our couriers then transported the guitars to you, at the top of the Empire State Building in New York, and me on the Golden Gate Bridge in San Francisco. I receive the guitar, and discover that the LOW E string is ringing, it can only mean that you guitar's HIGH E string in ringing in New York.

There are no local hidden variables in this example. The premise of polarity as a corollary for guitar strings is modeled in the exact same manner. Six strings on a guitar maps to the same essential parameters of each of two directions for all three axes of spin.

⬐ pishpash

It's not about getting correlated outcomes when the measurements are made, that would be unsurprising. It's that the correlations (or more precisely, the distributions) of the outcomes conditioned on seemingly random measurement choices suggest that the outcomes are not from independent measurements.

Now there are several ways you can interpret that: 1) the measurement choice at one site is superluminously conveyed to the other site and causes an effect; 2) the measurement choices are not independent and random despite the best attempts of the experimenters; 3) the wavefunction over the two sites is physically real and both measurement choices are necessary to sample it.

⬐ None

None

⬐ danbruc

You are missing the point of Bell test experiments. Such experiments demonstrate that which guitar is the high E one and which is the low E one is not decided when they are still together. It is not that you and everyone else just don't know which way it is until someone listens to one of them, it is actually not yet decided until someone listens to one of them.

⬐ crumpington

It's just an expression of the conservation of energy. Much in the same way the double slit experiment conflates a particle transporting itself through two windows at once, so too, do these experiments conflate the polarizers as causing the effect.

Ask yourself: if you construct a gun, with two diametrically opposed barrels, with exactly opposed rifling twists, and you aim the gun at two opposing (but identical) abrasive knurled metal rasp targets, such that if the bullet spins one way, the ricochet off rasp target will send it to a blue target, but if the bullet spins the other way, the grain of the rasp target is such that the bullet is sent to an orange target, will you be surprised to find that the behavior of the projectiles remains consistent?

Fire those bullets out of that gun, and as the bullets leave the opposing twists of the barrel, and the spin of the bullets encounters the friction of the knurled surface, they will consistently be sent in whichever direction the spin of the barrels rifling puts them. When one side sends spins the bullet to hit the blue target, the other barrel's twist always puts the other corresponding bullet onto the orange target, by bouncing it off the polarizer rasp.

So, now, to shrink downward to the realm of particle physics, what we find is that the ballistic particle guns are such that the emitter source is an array of many guns with varying rifling twists, but like pulling a lever on a slot machine, we cannot know which of the guns embedded in the radiation source will fire next.

We won't know the turn of the rifling of the gun's barrel prior to whichever one happens to go off. We stick out our rasp target to have it send the bullet to a colored target, and we declare that the polarizer rasp directed the bullet particle, but not really. The emitting source's gun barrel imparted the spin. The polarizers induced behavior on particles that would have behaved as reciprocals anyway.

⬐ danbruc

No, no, no. There is almost half a century of experimental evidence against you. The experimental results of Bell test experiments are incompatible with the assumption that the states of both particles are fixed when the pair is generated and are only classically correlated because of the way their states are fixed. All your analogy attempts are flawed and bound to fail exactly because entangled pairs of quantum particles do not behave like pairs of classical particles. You are making up classical experiment and assume that quantum particles will behave in the same way, but they don't. And that's the entire point.

EDIT: I just came across an illustration which might be helpful. I will place three coins on a table and cover them so that you can not see whether they are heads or tails. You get to pick two of them and I will reveal them for you but you can never look at the third one. Your task is to figure out by which rule I am placing the coins on the table.

In the first round you pick coins one and two, I reveal them to be heads and tails. In the second round you pick coins one and two again, now they are tails and heads. You continue picking coins one and two for a few thousand rounds and always see heads and tails or tails and heads, they are never the same.

Then you switch to picking coins two and three for a few thousand rounds and again they are always heads and tails or tails and heads, they are also never the same. Now you have figured out what I am doing, I am randomly choosing between heads, tails, heads and tails, heads, tails for coins one, two, and three.

So in the next round you pick coins one and three and I reveal them to you. Heads and tails. WtF?!? They should have been the same if I always choose between heads, tails, heads and tails, heads, tails. You try again. Heads and tails. Again. Tails and heads.

No matter what you try, you never get to see two coins with the same side up. That's ridiculous, you think. There are only two sides to a coin but three coins on the table. At least two of the coins have to have the same side up in each round and if you select the two coins to reveal at random, then you should at least sometimes get to see two coins with the same side up no matter which rule I use to place them. But you don't.

Assuming that I choose heads and tails for each of the coins when I placed them on the table and before you make your choice is incompatible with your observation that you never see two coins with the same side up. But if you assume that I can magically turn the coins around at the moment you tell me which two coins to reveal, then you can explain your observation. It may however trouble you because your explanation now involves magic.

And that is roughly how entangled pairs in Bell test experiments behave. Or more formally, classically P(1=2) + P(2=3) + P(3=1) >= 1, at least two coins always have the same side up no matter what the underlying distribution is. Entangled pairs in Bell test experiments violate this inequality, the probability of two coins having the same side up is less than 1. Not 0 as I portrayed it but 0.75.

⬐ bomberFighter

Except you can't tell me what the spin is without polarizers. This is like telling me I have to measure the orientation of a fidget spinner with a fitness club's treadmill set to the brisk pace of an uphill jog.

None of the experiments don't use polarizing lenses to make a determination of results on both sides. This is where the experiments are fundamentally flawed and propose weak evidence.

To simply read about the fundamentals of light polarization is to understand that quantum wave function collapse is much ado about nothing, and it becomes obvious that all this contention is total bullshit, and none of it is magic.

https://en.wikipedia.org/wiki/Polarizer

https://en.wikipedia.org/wiki/Polarizing_filter_(photography...

https://en.wikipedia.org/wiki/Photon_polarization

⬐ breadAndWater

Except you can't tell me what the spin is without polarizers. This is like telling me I have to measure the orientation of a fidget spinner with a fitness club's treadmill set to the brisk pace of an uphill jog.

None of the experiments don't use polarizing lenses to make a determination of results on both sides. This is where the experiments are fundamentally flawed and propose weak evidence.

To simply read about the fundamentals of light polarization is to understand that quantum wave function collapse is much ado about nothing, and it becomes obvious that all this contention is total bullshit, and none of it is magic.

https://en.wikipedia.org/wiki/Polarizer

https://en.wikipedia.org/wiki/Polarizing_filter_(photography...

https://en.wikipedia.org/wiki/Photon_polarization

⬐ danbruc

If you read through the list of Bell test experiments [1], you will discover that not all of them are done with photons, for example »Violation of Bell’s inequality in Josephson phase qubits« [2].

[1] https://en.wikipedia.org/wiki/Bell_test_experiments#Notable_...

[2] https://web.physics.ucsb.edu/~martinisgroup/papers/Ansmann20...

⬐ breadAndWater

https://en.wikipedia.org/wiki/Inconsistent_comparison

Josephson phase qubits aren't even utilizing the same fundamental concepts to examine the qualities of the mediums that quantum uncertainty affects.

https://en.wikipedia.org/wiki/Phase_qubit

https://en.wikipedia.org/wiki/Josephson_effect

https://en.wikipedia.org/wiki/Josephson_voltage_standard

⬐ donutte

Just to be clear, these are experimental results that are statistically impossible assuming a classical physics. Are you actually worried that they are somehow studying the wrong self-evidently non-classical thing, or what?

⬐ breadAndWater

Quote from the "Phase_qubit" Wikipedia article:

"The zero voltage state describes one of the two distinct dynamic behaviors displayed by the phase particle, and corresponds to when the particle is trapped in one of the local minima in the washboard potential. [...] With the phase particle trapped in a minimum, it has zero average velocity and therefore zero average voltage. [...] The voltage state is the other dynamic behavior displayed by a Josephson junction, and corresponds to the phase particle free-running down the slope of the potential, with a non-zero average velocity and therefore non-zero voltage."

So, we're not even talking about actual fundamental subatomic particles anymore. We're talking about phase oscillations, and renaming that as if it were a "particle" because, hey, particle/wave duality, so why not?

Hand-wavey math permits us to equivocate that a current induced on a wire, by way of the transfer of many actual electrons across substrates, can serve to prove the premise of a "teleportation device" also.

See? If we play our game of three-card monte, change phase oscillations, wiggle our noses, and tilt our heads a little, it's all very obvious that faster-than-light information transfer can be generalized to fit in the same picture, because this tuning fork makes that tuning fork ring in harmony, but only when we choose to notice.

⬐ donutte

I’m not sure I follow your argument, but if I understand you right, I don’t believe what you’re quoting is relevant. From the article you are (I think?) criticizing:

We measure a Bell signal S of 2.0732 ± 0.0003, exceeding the maximum value |S| = 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the “detection loophole”[11]. Since the Bell inequality was designed to test for non-classical behavior without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system [7]. https://web.physics.ucsb.edu/~martinisgroup/papers/Ansmann20...

That says in plain English that they have not assumed that this system behaves according to quantum principles. In fact, it is precisely the opposite: the quantum nature of this system is a conclusion of their results. It would be statistically impossible for any system following classical rules to produce the same data.

(It bears repeating that the math underlying that conclusion is truly not very complex, and it is very, very well studied. If you can show that it’s flawed somehow, don’t bother publishing— just post your proof here and I’ll, uh... pick up the Nobel for you.)

The only caveat is that this experiment closes the detection loophole, but not the locality loophole; it is theoretically possible that a classical signal could be sent from one qubit to the other quickly enough to fabricate this data. There’s no particular reason to suspect a secret signal is in play, but it isn’t theoretically prohibited.

Assuming you haven’t found a flaw in their mathematics, and that you aren’t alleging that the researchers deliberately fabricated their data, the locality loophole is your best (and likely only) avenue to dispute their conclusions. However, if you wish to pursue that, you should keep in mind that there are many other experiments which close the locality loophole but not the detection loophole, and, since 2015, several that close both. Three-card monte may be a better investment of your time.

⬐ breadAndWater

Uh, wow, at no point have I made the claim that an electrical circuit is not a quantum system. Nor have I claimed that they are incapable of simulating quantum phenomena. Quite the very opposite.

What I did clearly state, and insist as quite relevant, is that entanglement and double slit experiments are hocus pocus and irrelevant distractions. In fact, I stated that this experiment says basically nothing because it merely simulates quantum phenomena within a circuit.

Hello? Yes. Electrons are quantum entities, and assuredly interact with photons which are also quantum entities. This is demonstrated by the photo-electric effect, which we can all notice by placing tin foil in a microwave. Therefore a circuit is indeed a quantum system, since it assuredly deals in electrons.

Wow! Didn't even need to publish a paper about qubits to draw that conclusion! Amazing!

The implication here is that Bell is waste of time, and so is his theorum: such that emission doesn't determine state, especially when you don't look at it.

Great, thanks Bell. I'll be sure to not look at anything until I want to know what it is. True genius at work.

⬐ donutte

The experiment demonstrates quantum entanglement. I gather you don’t believe this. So how about this: I don’t believe you.

I don’t believe that you could, even theoretically, produce the data from a loophole-free Bell test without invoking superdeterminism, superluminality, or quantum entanglement.

Can you describe how this would be theoretically possible?

⬐ breadAndWater

The experiment certainly demonstrates "something" in terms of how not to "measure" relativistic effects with macroscopic tools...

And yet, with relativistic particles, the wild claims are made that splitting photons through a substrate, and then passing them through the wall of a polarizing lens, means we can declare ourselves capable of rewriting and erasing history. Eh, not quite.

But hey, where there's smoke, there's fire, so something must be true, right? Let's just make up whatever.

⬐ danbruc

1. Do you think all Bell test experiments ever done were flawed, i.e. none of the observed Bell inequality violations were real?

2. If so, do you think a non-flawed Bell test experiment could be done?

3. If so, do you have a definite opinion about whether or not it would yield a Bell inequality violation?

4. If so, would it yield a Bell inequality violation or not.

5. If you think all Bell test experiments ever done were flawed, can you pick one, preferably one commonly considered a good one, and point out what exactly you think the flaw in the experiment is?

6. If you think Bell inequality violations are or could be real, how do you want to explain them?

Note that those are all yes no questions, well, at least all but the last two. I don't need and want more than a yes or no for the first four because from your comments alone it is not clear, at least to me, what your position actually is.

⬐ danbruc

You complained - without providing any substantive arguments why this might be an issue - that all Bell test experiments use polarizers, I pointed out that you are wrong. I have no idea what you are complaining about now, what is »[...] qualities of the mediums that quantum uncertainty affects [...]« even supposed to mean? You are obviously far outside of your area of competence. If not, just do the experiment, write the paper, and collect your Nobel Prize, no need to argue with clueless people on the web.

⬐ breadAndWater

A Josephson junction doesn't even trap any single actual physical particle. It's just a standing wave of electrical current trapped in a bounded array of geometrically crafted slabs of superconductors and insulators. It's a phenomenon that arises from the construction of the device.

Unlike fundamental particles such as photons and electrons, there is nothing substantial about the state represented by the standing wave qubit trapped in a circuit operated by a Josephson junction device. Destroy the device (or nevermind that, just never place it in a dewar flask chilled to 4 degrees kelvin, to activate it) and the phenomenon doesn't even exist. So much for whether or not matter or energy can never be created nor destroyed.

To sit there and state that, on paper, this is the same thing as an individual electron emitted as beta decay is, well... fundamentally flawed.

⬐ None

None

⬐ lisper

Something else worth noting: an entangled state is itself a superposition of two non-entangled states. This is obvious when you look at the math: the entangled state |10> + |01> is the superposition of the factorizable (non-entangled) states |10> and |01>. But physically what this means is that entanglement is intimately related to interference. Interference happens when a photon "goes both ways". Entanglement happens when a pair of photons go in such a way that you can't tell which photon went which way. (There's more to it than that, but the point is that entanglement and interference are closely related phenomena. This fact is often overlooked, particularly when it comes to explanations of entanglement directed at lay audiences.)

Also, the idea that collapse is a physical phenomenon that propagates faster than light is not universally accepted. There are other ways to interpret these results. None of them take a toll on your intuition, but personally I like this one:

http://www.flownet.com/ron/QM.pdf

(There's a video too: https://www.youtube.com/watch?v=dEaecUuEqfc)

Hey, Scott! Love your book, Quantum Computing Since Democritus. There is one section which confused me, in the Quantum chapter (https://www.scottaaronson.com/democritus/lec9.html). I have two questions:

1) You say applying the unitary operation is the quantum analogue of "taking a coin and flipping it" - what do you mean by this? Could we think of, for example, a pair of slits as applying this transformation on a photon qbit being sent through them, so it's now in superposition with regard to which slit it went through?

2) What does it mean when you say there are two paths to |1>? I understand this section is getting at the physical underpinnings of this mathematical model, but I can't quite wrap my head around how there are two "paths". My mind is stuck thinking of the Bloch sphere as a state machine you can deterministically hop around by applying unitary transformations.

P.S. I did a talk called Quantum Computing for Computer Science which covers everything up to the one-bit Deutsch Oracle problem in 1.5 hours; I found that presenting quantum algorithms as running on a "unit circle state machine" (basically 2d Bloch sphere by restricting states to real numbers) was a very effective way to explain the subject to software engineers! (https://www.youtube.com/watch?v=F_Riqjdh2oM)

⬐ ScottAaronson

1) Yes, a unitary transformation like the Hadamard gate maps the state |0> to |0>+|1>, while mapping |1> to |0>-|1>. In either case, if you then just measured immediately in the {|0>,|1>} basis without doing anything else, you'd see |0> or |1> with equal probabilities, so it would have the effect of a coin flip. But of course, in other cases---e.g., if you measured in a different basis, or if you applied the Hadamard to a state that wasn't just a |0> or |1> basis state---you could see that Hadamard is not just a coin-flipping transformation, because it's able to produce interference.

2) When we talk about the different "paths" that contribute to a given amplitude, it's just a fancy way of saying that we can organize the matrix multiplications in such a way that the amplitude we want is a giant sum. So for example, suppose we apply Hadamard twice in sequence to the initial state |0>. The first Hadamard maps |0> to (|0>+|1>)/sqrt(2). The second Hadamard maps |0> to (|0>+|1>)/sqrt(2) and |1> to (|0>-|1>)/sqrt(2). So by linearity, it maps (|0>+|1>)/sqrt(2) to

((|0>+|1>)/sqrt(2) + (|0>-|1>)/sqrt(2))/sqrt(2) = (1/2+1/2)|0> + (1/2-1/2)|1>.

So in this case, we could say that there are "two paths leading to |0>," both of which contribute 1/2 to its final amplitude (so that the amplitude is 1). There are also "two paths leading to |1>," but one contributes 1/2 to its amplitude and the other contributes -1/2, so the two contributions interfere destructively and the final amplitude of |1> is 0.

This is sometimes called the "Feynman" or "sum-over-paths" picture of quantum mechanics. As you can see, though, it's just a different way of looking at exactly the same math, namely multiplication of matrices and vectors.

So then why use the sum-over-paths picture at all? Well, a few reasons: physicists like it because it often gives them more insight into what's going on, into what are the more and less important contributions to a given process, and it can also make calculations easier. Meanwhile, computer scientists like the picture because it lets us simulate a quantum computer by a classical computer, still using exponential time but now using only a linear amount of memory, rather than the exponential amount of memory we'd need if we tried to store all 2^n amplitudes at once.

⬐ i-blis

The cleanest explanation I read of information / state linearity properties of quantum operators. Thanks! (Working through Brian Hall's Quantum Theory for Mathematicians and Frederic Schuller's course at the moment, both highly recommended).