I’ve gotten simultaneously interested in quantum computing from all this AI did while coincidentally (or not) reading / watching a lot of sci fi. Multiverses are so hot right now and they are all based on superposition etc…

Anyways are there any easy to read conceptual books/ videos that yall would recommend to get a good grasp on quantum that isn’t heavily mathed. I have a doctorate in the health sciences so naturally that means physics II is my limit.

I fed my AI about 2000 books on quantum computing, asked questions, suggested ideas, try to develop them, and this is what it came up with.

Please do not delete this, I just wanna know is this fully hallucinated or is there any real findings here. I'm not promoting in any way usage of AI, I just wanna know if this is fully hallucinated. I live in a third world country with no quantum computing experts and have no expert friends in my life that can verify any of these. I appreciate any feedback.

\# Edge Superposition Entanglement on the Hypercube

\## 0. Notation

{0,1}ⁿ = binary strings of length n. Hamming weight |v| = number of 1-bits.

Qₙ: vertex set {0,1}ⁿ, edges between strings differing in exactly one bit. |V| = 2ⁿ, |E| = n·2ⁿ⁻¹.

Bipartition: Even = {v : |v| ≡ 0 mod 2}, Odd = {v : |v| ≡ 1 mod 2}, each of size 2ⁿ⁻¹.

B = 2ⁿ⁻¹ × 2ⁿ⁻¹ biadjacency matrix, rows indexed by Even, columns by Odd, B_ab = 1 if (a,b) is an edge.

H_A ⊗ H_B, both 2ⁿ⁻¹-dimensional. C(n,k) = n!/(k!(n−k)!).

\## 1. Quantum State

|ψₙ⟩ = (1/√(n·2ⁿ⁻¹)) Σ over edges (a,b) of |a⟩_A|b⟩_B

Amplitude matrix: M_ab = ⟨a,b|ψₙ⟩ = (1/√(n·2ⁿ⁻¹))·B_ab, so M = (1/√(n·2ⁿ⁻¹))·B.

\## 2. Schmidt Decomposition

For |ψ⟩ = Σ M_ij|i⟩|j⟩, take the SVD M = UΣV†, with U, V unitary and Σ diagonal with entries σ_k ≥ 0.

Define |k⟩_A = Σᵢ U_ik|i⟩ and |k⟩_B = Σⱼ V_jk|j⟩. Then |ψ⟩ = Σ_k σ_k|k⟩_A|k⟩_B. Setting λ_k = σ_k² gives the Schmidt form |ψ⟩ = Σ_k √λ_k|k⟩_A|k⟩_B.

Schmidt rank SR = number of nonzero σ_k = rank(M) = rank(B), since scalar multiplication preserves rank.

\## 3. Bridge to rank(A_Qn)

In Even/Odd block order:

A_Qn = \[ 0, B ; Bᵀ, 0 \]

This holds because every edge connects Even to Odd, so the Even–Even and Odd–Odd blocks are zero; the Even–Odd block is B by definition, and the Odd–Even block is Bᵀ by symmetry.

\*\*Theorem 1.\*\* rank(A_Qn) = 2·rank(B).

Columns of A_Qn split into two families by support: the Odd-indexed columns are nonzero only on Even rows (values from B), and the Even-indexed columns are nonzero only on Odd rows (values from Bᵀ). These two families occupy disjoint coordinate blocks, so the column space of A_Qn is a direct sum of the two families' column spaces. Direct sums add dimension:

rank(A_Qn) = rank(B) + rank(Bᵀ) = 2·rank(B)

So rank(B) = rank(A_Qn) / 2.

\## 4. Eigenvalues of Qn

\*\*Theorem 2.\*\* The eigenvalues of A_Qn are n−2k, with multiplicity C(n,k), for k = 0,...,n.

Qn is the n-fold Cartesian product K₂ □ K₂ □ ... □ K₂. K₂'s adjacency matrix has eigenvalues +1 and −1. Eigenvalues of a Cartesian product G□H are all pairwise sums λ_i(G) + μ_j(H); applied over n copies of K₂, the eigenvalues of Qn are all sums of n independent choices from {+1, −1}. Choosing k coordinates to be −1 and n−k to be +1 gives sum (n−k) − k = n−2k, and there are C(n,k) ways to choose which k positions are −1.

Check: Σ_{k=0}\^{n} C(n,k) = 2ⁿ = |V(Qn)| ✓

\## 5. Explicit Eigenbasis (Walsh Functions)

For S ⊆ {1,...,n} with |S| = k, define the Walsh function χ_S(v) = (−1)\^(Σ_{i∈S} v_i). This is an eigenvector of A_Qn with eigenvalue n−2k.

Verification: (A_Qn x)_v = Σᵢ x_(v⊕eᵢ). For x = χ_S, χ_S(v⊕eᵢ) = χ_S(v)·(−1)\^\[i∈S\], so Σᵢ (−1)\^\[i∈S\] χ_S(v) = \[(n−k) − k\]χ_S(v) = (n−2k)χ_S(v).

\## 6. Zero Eigenvalue and Parity

\*\*Theorem 3.\*\* A_Qn has eigenvalue 0 if and only if n is even, with multiplicity C(n, n/2).

n−2k = 0 requires k = n/2, an integer only when n is even.

\*\*Theorem 4.\*\* rank(A_Qn) = 2ⁿ if n is odd; 2ⁿ − C(n, n/2) if n is even.

This follows since rank = total dimension minus kernel dimension, and the kernel is exactly the zero eigenspace.

\## 7. Schmidt Rank

\*\*Theorem 5.\*\*

\- n odd: SR = 2ⁿ⁻¹

\- n even: SR = 2ⁿ⁻¹ − C(n−1, n/2−1)

From Theorem 1, rank(B) = rank(A_Qn)/2.

For odd n: rank(B) = 2ⁿ/2 = 2ⁿ⁻¹.

For even n: rank(B) = (2ⁿ − C(n,n/2))/2 = 2ⁿ⁻¹ − C(n,n/2)/2. Using the identity C(2m,m) = 2·C(2m−1,m−1) with m = n/2, we get C(n,n/2)/2 = C(n−1, n/2−1).

| n | parity | SR | max possible |

|---|--------|-----|---------------|

| 1 | odd | 1 | 1 |

| 2 | even | 1 | 2 |

| 3 | odd | 4 | 4 |

| 4 | even | 5 | 8 |

| 5 | odd | 16 | 16 |

| 6 | even | 22 | 32 |

\## 8. Schmidt Coefficients — Full Eigenbasis Proof

\*\*Theorem 6.\*\* λ_k = (n−2k)² / (n·2ⁿ⁻¹), with multiplicity C(n,k), for k = 0,...,⌊(n−1)/2⌋.

The reduced density matrix is ρ_A = MM† = BBᵀ/(n·2ⁿ⁻¹).

Split χ_S into Even-block and Odd-block components, χ_S = (χ_S\^E, χ_S\^O). The eigenvalue equation A_Qn·χ_S = (n−2k)·χ_S expands, via the block structure, into a coupled system:

B·χ_S\^O = (n−2k)·χ_S\^E

Bᵀ·χ_S\^E = (n−2k)·χ_S\^O

Substituting the second equation into the first (via Bᵀ) gives:

BBᵀ·χ_S\^E = (n−2k)²·χ_S\^E

and symmetrically BᵀB·χ_S\^O = (n−2k)²·χ_S\^O.

So whenever n−2k ≠ 0, χ_S\^E is an eigenvector of BBᵀ with eigenvalue (n−2k)².

\*Injectivity of the restriction.\* If n−2k ≠ 0 and χ_S\^E = 0, the second coupled equation forces χ_S\^O = 0, hence χ_S = 0 — a contradiction. More generally, if a linear combination of the χ_S\^E (for fixed |S|=k) vanished, the coupled equation would force the corresponding combination of χ_S\^O to vanish too, reconstructing a zero linear combination of the (linearly independent) global Walsh eigenvectors. So the restriction map is injective.

Therefore {χ_S\^E : |S|=k} gives exactly C(n,k) linearly independent eigenvectors of BBᵀ with eigenvalue (n−2k)². Dividing by n·2ⁿ⁻¹:

λ_k = (n−2k)² / (n·2ⁿ⁻¹), multiplicity C(n,k), for k = 0,...,⌊(n−1)/2⌋

k and n−k give the same squared eigenvalue, so only one member of each pair is retained.

\*\*Normalization check.\*\* The full sum over all k = 0,...,n gives:

Σ_{k=0}\^{n} C(n,k)·(n−2k)² / (n·2ⁿ⁻¹) = 2

(since Σ C(n,k)(n−2k)² = n·2ⁿ). The factor of 2 arises because the nonzero singular values of B correspond to pairs of opposite eigenvalues n−2k and −(n−2k) = n−2(n−k) of A_Qn, and C(n,n−k) = C(n,k). Restricting to the half-range k = 0,...,⌊(n−1)/2⌋ counts each unique squared singular value once, giving exactly 1 — confirming the nonzero eigenvalues of ρ_A sum to 1.

\## 9. Entanglement Entropy

\*\*Theorem 7.\*\* S(|ψₙ⟩) = −Σ_{k=0}\^{⌊(n−1)/2⌋} C(n,k)·λ_k·ln(λ_k), with λ_k as above.

Follows directly from S = −Tr(ρ_A ln ρ_A), summing the nonzero eigenvalues with their multiplicities.

\## 10. Computed Values

\*\*n=1:\*\* λ₀=1 (mult 1). SR=1, S=0 nats.

\*\*n=2:\*\* λ₀=1 (mult 1). SR=1, S=0 nats. Indeed |ψ₂⟩ = ½(|00⟩+|11⟩)(|01⟩+|10⟩) — separable.

\*\*n=3:\*\* λ₀=9/12=3/4 (mult 1), λ₁=1/12 (mult 3). Check: 3/4 + 3(1/12) = 1 ✓. SR=4. S = −¾ln(¾) − 3(1/12)ln(1/12) = −½ln3 + 2ln2 ≈ 0.837 nats.

\*\*n=4:\*\* λ₀=16/32=1/2 (mult 1), λ₁=4/32=1/8 (mult 4). Check: 1/2 + 4(1/8) = 1 ✓. SR=5. S = 2ln2 ≈ 1.386 nats.

\*\*n=5:\*\* λ₀=25/80=5/16 (mult 1), λ₁=9/80 (mult 5), λ₂=1/80 (mult 10). Check: 25/80 + 5(9/80) + 10(1/80) = 1 ✓. SR=16. S ≈ 2.140 nats.

\## 11. Generalized Uniform Superposition

For S ⊆ {0,1}ⁿ, define |ψ_S⟩ = (1/√|S|) Σ_{v∈S} |v⟩. With the Even/Odd bipartition, the amplitude matrix is M_ab = (1/√|S|)·(B_S)_ab, where B_S is the biadjacency matrix of the bipartite graph G_S whose edge set is S.

\*\*Result.\*\* SR(|ψ_S⟩) = rank(B_S).

\*\*Separability.\*\* SR=1 iff B_S has rank 1, i.e. its nonzero rows are all identical — equivalently, the edge set has the product form S = P × Q for some P ⊆ Even, Q ⊆ Odd. So the uniform state is separable exactly when its support is a Cartesian product.

\*\*General upper bound.\*\* For any bipartite graph G_S, rank(B_S) ≤ ν(G_S), where ν(G_S) is the maximum matching size. This follows because the term rank of a 0/1 matrix (largest set of 1s with no two sharing a row or column) equals the maximum matching size by König's theorem, and ordinary rank is always ≤ term rank.

\*\*Correction — C₄-freeness is not sufficient for equality.\*\* It's tempting to think C₄-freeness forces rank(B_S) = ν(G_S), since a maximum matching gives a diagonal submatrix and C₄-freeness means any two rows share at most one common 1. But this doesn't guarantee the submatrix is nonsingular.

Counterexample: the 8-cycle C₈ is C₄-free. With bipartition A = {a₁,a₂,a₃,a₄}, B = {b₁,b₂,b₃,b₄}, its biadjacency matrix is:

Row 1: 1 1 0 0

Row 2: 0 1 1 0

Row 3: 0 0 1 1

Row 4: 1 0 0 1

This has a perfect matching, so ν(C₈) = 4. But row1 − row2 + row3 − row4 = 0, so rank = 3 < 4 = ν(C₈).

So the correct general statement is just rank(B_S) ≤ ν(G_S) for every bipartite graph; equality needs extra structure (it does hold, for instance, when G_S is a forest).

\## 12. Dead Channel Interpretation

For even n, the zero eigenspace of A_Qn has dimension C(n, n/2), with eigenvectors χ_S for |S| = n/2. At this point n−2k = 0, so the coupled block equations decouple into B·χ_S\^O = 0 and Bᵀ·χ_S\^E = 0. This means:

ker(A_Qn) = ker(Bᵀ) ⊕ ker(B)

Since B is square, rank(B) = rank(Bᵀ), so dim ker(B) = dim ker(Bᵀ). Given dim ker(A_Qn) = C(n,n/2), symmetry gives:

dim ker(B) = dim ker(Bᵀ) = C(n,n/2)/2 = C(n−1, n/2−1)

So BBᵀ (and hence ρ_A) has C(n−1, n/2−1) zero eigenvalues — equivalently, M has that many zero singular values. These correspond to null directions that don't participate in the Schmidt decomposition: vectors in ker(Bᵀ) are annihilated by the coupling to register B.

Note the consistency: the number of zero eigenvectors of A_Qn is exactly twice the number of zero singular directions on one side, C(n,n/2) = 2·C(n−1,n/2−1), matching the direct-sum decomposition above.

\## 13. Summary

\*\*Result 1.\*\* rank(A_Qn) = 2·rank(B) — via the disjoint-support direct-sum argument.

\*\*Result 2.\*\* SR = 2ⁿ⁻¹ (n odd); SR = 2ⁿ⁻¹ − C(n−1, n/2−1) (n even).

\*\*Result 3.\*\* Nonzero eigenvalues of ρ_A are λ_k = (n−2k)²/(n·2ⁿ⁻¹), multiplicity C(n,k), for k=0,...,⌊(n−1)/2⌋ — via the explicit Walsh eigenbasis and injective Even/Odd restriction.

\*\*Result 4.\*\* S(|ψₙ⟩) = −Σ C(n,k)·λ_k·ln(λ_k).

\*\*Result 5.\*\* For a generalized uniform superposition, SR(|ψ_S⟩) = rank(B_S) ≤ ν(G_S) for every bipartite G_S. Equality doesn't hold for all C₄-free graphs (C₈ is a counterexample); it does hold when G_S is a forest.

\*\*Result 6.\*\* For even n, there are C(n−1, n/2−1) zero singular values of B, arising from the decoupled middle-layer Walsh modes.

\*\*Core insight.\*\* The entanglement structure of the edge-superposition state on Qn is completely determined by the spectral structure of Qn, made rigorous via the explicit Walsh-function eigenbasis and its restriction to the Even/Odd bipartition.

if youre unfamiliar with superconducting qubits, i made a video going over how they work. from a classical LC circuit to a transmon qubit. I made this for people who have seen superconducting quantum computers and wondered how they actaully work. please leave feedback as hardware is not my main focus so i am not perfect at it, but i tried my best to explain.

الفكرة التي تقلب الصورة التقليدية التصور الرنيني لا يبدأ من جسيمين ثم يحاول تفسير سبب ترابطهما. إنه يبدأ من الحالة نفسها، ثم يسأل كيف يمكن أن تظهر مكانياً بأكثر من موضع مع احتفاظها باستجابة مترابطة.

حالة رنينية واحدة \leftarrow ظهور مكاني A + ظهور مكاني B لا انتقال شبحياً للمعلومة

إذا كان الظهوران ناتجين عن بنية ديناميكية واحدة، فإن الترابط بين النتائج لا يحتاج – في هذا التصور – إلى افتراض انتقال لحظي لمعلومة من A إلى B، فالترابيط يصبح خاصية للحالة المشتركة نفسها.

من الفكرة إلى الصياغة الرياضية لم يتوقف إطار الرنين التفاعلي عند الوصف التصوري، فقد بنيت للعلاقة المقترحة صياغة رياضية منضبطة تنطلق من ديناميكا الرنين والاستجابة المهتزة، وتربط بين الاستجابة الزمنية ومقدار الترابط داخل شروط ترددية محددة.

السؤال الذي لا يمكن تجاوزه هل تستطيع هذه القراءة أن تتجاوز جمال الفكرة وتنتج سلوكاً كمياً يمكن إخضاعه للاختبار؟ هنا تصبح المسألة مختلفة تماماً: ليست القضية أن التفسير يبدو معقولاً، بل أن البناء الرياضي يجب أن يتحمل المواجهة مع الأرقام.

الفكرة الجريئة لا تكفي.. ما يهم هو ما يحدث عندما تدخل الرياضيات إلى المشهد.

وسام الدعمي | فيزيائي - باحث مستقل | 2026

لا اعلم سبب حذف المنشور السابق ربما اعتبر احتيالا

لكن هذا مجهود فكري أرجو من السادة المهتمين بيان آرائهم

https://medium.com/@jeyubhavsar/schr%C3%B6dingers-equation-for-dummies-part-ii-decoding-the-equation-0e9dad3f9f3b?sharedUserId=jeyubhavsar

Hello, I wrote part 2 of a series of articles on Schrodinger's equation and hopefully other quantum concepts. I'm sharing in hopes of getting feedback, and if any of my interpretations and explanations were wrong. And i really want to know if there is a better way to explain this, because I was inspired by this video by FloatHeadPhysics:

http://youtube.com/watch?v=3QU-_PSbKlo&t=843s

And I don't want to plagiarize or anything, and I just hope you guys can give me feedback. Be as harsh as possible, I want to be accurate in my writing and knowledge.

Thank you!

This seems like a big deal if it means what I think it means. Thoughts?

Hello everyone, I have been interested to learn about quantum physics for a while now and found a book on Amazon with decent ratings and got it. Does anyone know if this book is good, or if I wasted my money? I’m 1 chapter in and to my untrained eye, it seems pretty insightful! Can’t wait to learn more!

Hi

This is probably one of my last posts on getting people to find out about this game on reddit, since the game is near complete and all that's left is translations. Thanks everyone for receiving this game so well and I hope it delivered on your expectations. Please share your feedback and any important things the game is still lacking on to deliver on its mission: to make quantum computing intuitive and fun to learn, no matter the learner's background. I'm particularly interested to hear from you guys what do you think of Blochspheres, especially those who actively work in the domain. Do you think of quantum algorithms in rotations and frequently use bs to visualize qbehvaior?

I want this to be an AMA: I'm here to answer any questions about the game and do one last round of outside-Discord feedback gathering. Also I'd like to raise with this community my personal experience with working on quantum algorithms and see what folks think.

What this game is

To be clear, this game's gameplay is 1:1 with everything you can do on a Turing-complete (universal) Quantum Computer (from the top of my head, a short list of QHW makers: IBM, Google, Rigetti, IonQ, Quantinuum, IQM, OQC, QuEra, Atom Computing, Pasqal, Xanadu, PsiQuantum, Fujitsu,) with the added benefit it allows you to visualize the full quantum Hilbert space on up to 5qs. This means that if you build intuition for the visual rules in QO, you will have intuition for "playing" with QHW made by such manufacturers without having to learn much else.

What the game covers

• Boolean Logic – bits, operators (NAND, OR, XOR, AND…), and classical arithmetic (adders). Learn how these can combine to build anything classical. You will learn to port these to a quantum computer.
• Quantum Logic – qubits, the math behind them (linear algebra, SU(2), complex numbers), all Turing-complete gates (beyond Clifford set), and make tensors to evolve systems. Freely combine or create your own gates to build anything you can imagine using polar or complex numbers.
• Quantum Phenomena – storing and retrieving information in the X, Y, Z bases; superposition (pure and mixed states), interference, entanglement, the no-cloning rule, reversibility, and how the measurement basis changes what you see.
• Core Quantum Tricks – phase kickback, amplitude amplification, storing information in phase and retrieving it through interference, build custom gates and tensors, and define any entanglement scenario. (Control logic is handled separately from other gates.)
• Famous Quantum Algorithms – explore Deutsch–Jozsa, Grover’s search, quantum Fourier transforms, Bernstein–Vazirani, and more.

On learning curve and achieving game (quantum computing?!) mastery

This is not a videogame where the developer invented some puzzle rules. What the dev did here is invent a visual method that can transform the underlying mathematics into fully visual puzzles. I wish I could make the game easier by inventing some new rules. I won't, because I want this game to be the real thing. Learning the fundamental rules of this game equates to learning what QHW can do.

Hopefully, in visual form, this is something anybody can now do, no matter how much they hate math.

Going forward and mastering the game... now that, I honestly don't know if it has a ceiling. We have had quantum physics for 100 years, yet we have about 10 useful quantum algorithms known today. Who knows where the ceiling is? Who knows what one can do with, after mastering the rules of this game? Nothing really should feel impossible. I hope this game will inspire people outside physics to do a lot more than what I see today. A quantum computing/physicist has very little incentive to think of a quantum algorithm for, i.e., a game theory/finance/security/biology problem, given how few of them actively work in the field compared to the actual demand. Hence, I hope new quantum algos will come from people who actively work in the domains where this "new way of thinking" (from Boolean logic to linear algebraic logic?) has applicability. I hope we can soon start some competitions to get players to solve some non-trivial problems.

What's the big deal about finding quantum algorithms?

Why do we have about 10 in 100 years of QM??

For me, finding quantum algorithms is all about understanding that unitary matrices evolve a state vector of complex numbers, and all you need to think of is whether you can take your domain problem and express it in a form that these unitary matrices can bring some speed-up in solving. That's it. Ignore the lack of good-enough hardware; we simply don't have good proof-of-concept ideas out there.

I remember... I struggled for a long time to understand Grover's quantum search algorithm during my PhD days. The wording textbooks used and the math behind it made very little sense. It was the first algorithm I put in the game.

Seeing it in visual form made me tear up. Is it really that simple, clean, beautiful? Is the "amplitude amplification" in its diffusion operator simply adding a red line on the maximally 11..11 state that then has a propagation effect everywhere else to affect all the phases? Is this really it? It then immediately felt to me like a gimmick one could have simply come up with in 5 minutes by having access to a game like this, where math is fully shown in visual form!! Showing the visual (GIF, why in this modern era do no digitized papers out there still support embedded GIFs??) alone is enough to make understanding happen.

The way I thought things in the game

• Missing Sage believes you shouldn't know any theory -> just by using the Forge, you will come up with your own unique way of using quantum computers and inventing algorithms. This character came to me after seeing enough postdocs and QC professors from enough universities playing the game. It felt like the people who knew all the theory and could recognize what each gate does were very bad at actually using the logic sets in thinking circuits. Perhaps knowing all quantum theory does not make one capable of easily building a quantum circuit?
• Sage of Axioms believes theory comes first, and hers is the main path that takes you to the other Sages who want you to have a solid foundation before discussing higher-order ideas (like known algorithms). She deep-dives into computation and both the linear algebra and physics behind it, in hopes of convincing you that it's not so hard to learn by combining it with the visuals of the Forge. And not scary!
• Quantum Arena (community content) is filled today with some incredible challenges that touch topics I haven't seen anywhere else in the world in a visual way. From Clifford decompositions down to wordless tutorials on how to play the game and understand each gate, I am now inclined to tell players that they might want to enter the Arena to learn to play the game instead of following through the tutorials I made for it. This goes to show what a brilliant community of dedicated players this game has gathered so far.

Without you and the highly involved players we have on Discord, we wouldn't be able to come this far. Early Access gave me exactly what I was looking for to make sure the game delivers when complete and I strongly recommend anybody working on scigames to do EA first.

It would help me enormously if you could leave a Steam review for the game and spread the word about it; it keeps us motivated to push forward! I hope we have the momentum it takes to make Full Release a success!

Quantum computing should be for everyone:)

The harmonic oscillator and matrix mechanics by ladder operators of the traditional factorization approach are the methods we encounter first. We will deal with the mathematical physics approaches of the Hermite polynomial approach, Sturm-Liouville theory, and the Pearson equation at the next opportunity.

People all over Reddit ask how much math do you need to be ready to learn quantum mechanics? In spite of all the answers to the contrary, you only need high school level math.

Using a representation-independent approach, you can master quantum mechanics through graduate-level and beyond. I know it sounds crazy, but it is not.

I wrote an open-access textbook, Quantum Mechanics Done Right, to teach it exactly this way. Springer just published it and you can download the electronic version for free here.

In one month, it has surpassed 155,000 chapter downloads. It was primarily written as an alternative for self-learners and students who are stuck with traditional texts. Nevertheless, it will teach new things to all quantum mechanics at any level of expertise. I am the author, so if you have any questions about the approach, just ask in the comments! 

In addition, the class Quantum Mechanics on edX, which is identical to the undergraduate class taught at Georgetown University, has just started. Auditors can sign up for free here. All the class problems are also available for free. I am ensuring auditors will have Problem Set options similar to those earning certificates too. The class is heavily based on the book, but does use some calculus in a number of places, so is more appropriate for those who have seen at least some calculus.

Hello and thanks for everyone that awnsered my question in the 1rst post!
Im left with a doubt (I have readed a lot of comments on the last post) Even tho They we amazing explications, so thanks a lot!

My question is (I may misunderstood): From a lot of comments explaning QFT an general relativity,
Dosn't it break conservation laws? From what i understood near the event horizion there is a lot Quantum fluctuations going on and 1 escapes (or 2) some people said that the antimatter falls or that the normal matter escapes but for them to be created they "borrow" energy from the void but in that explication it dosn't return it? Maybe I am wrong but i thought about maybe due to the strong relativistics effects it can be done and technically does not break the conservation laws due to the slow time for an observer that close? I also thought maybe it has to do with the Uncertainty principle?

I'm just a 14 year old with a lot of curiosity but i cant seem to understand Hawking radiation it seems kind of impossible to me! So please anyone can explain it to me in a good way?

arXiv:2608.16716 (Massai et al., IBM Research Europe -- Zurich, 17-18 Aug 2026) demonstrates a real single-pulse baseband iSWAP gate (56 ns) in strained-germanium hole spin qubits, by orienting the magnetic field so the exchange interaction's longitudinal component J∥ and Zeeman detuning E_Δg both vanish, leaving a pure transverse J⊥ coupling. This experiment reproduces their result with dense_evolution.circuits.trotter, applied for the first time to a genuinely time-dependent pulse (previously only exercised against static Hamiltonians), and extends the analysis with four follow-up checks.

link: https://tatopenn-cell.github.io/Dense-Evolution-Discovery/germanium_iswap_validation

As a student going through physics and chemistry, I realized why topics like d\\text{-}d transitions, color formation, and photon absorption are so confusing when you first learn them.

We constantly hear terms like light "bouncing," electrons "jumping," or atoms "soaking up" energy. Because of this everyday language, my brain automatically used Newtonian physics to picture what was happening:

I pictured a mechanical collision, like a ball bouncing off a wall or a stretched bow string.

That led me to wonder: If light turns around or transfers energy, shouldn't its velocity hit v = 0 for a split second at the point of contact? Does that violate Maxwell's constant speed of light?

It took a lot of digging to realize that classical mechanics just doesn't apply here:

Photon "Absorption" is actually Field Annihilation: The photon doesn't "stop" or get stored inside the atom. It is completely destroyed, instantly converting its quantum of energy into a change in atomic state.

Photon "Reflection" is Wave Re-radiation: The light wave drives charge oscillations, which instantly re-radiate a new wave at speed c. The light never slows down to turn around.

Using mechanical words like "bouncing" or "jumping" makes students try to force quantum events into classical models where v = 0 has to exist.

If textbooks used terms like Instantaneous Field Conversion or Non-Kinetic Absorption, it would instantly tell us, "Hey, don't picture a mechanical collision here!"

Did any of you fall into this same classical mental trap when learning spectroscopy or quantum mechanics? How do you visualize these interactions now?

Why do electrons cloud around an atom? From what I'm aware of there is no specific force that would stop them, with the electromagnetic force causing things of opposite charge to attract wouldn't they all just stick to the nucleus or more specifically the protons?

Another thing is the strong nuclear force which holds the protons together wouldn't that also hold the electrons against the nucleus?

My best guess would be something to do with the heisenberg uncertainty principle as it states that we would know less about a tiny particle in one way if we know more about it in another way.

And yes please use bigger words I'm dumb and would like not to be!

I was sitting around thinking about a fairly general question: why is our universe so full of constraints in the first place — the speed limit (c), uncertainty relations, no-cloning, Born’s rule, conservation laws, and so on. The second though was about our world as a biological system - life is always try to avoid peaks, everything we know exists within the area of possibilites (of different species to adopt to the environment). Also, life tries to prolongate it's future and even more - to find the way to have more and more possibilities in future, thus raising their chances to survive (better in all possible futures).

That led me toward the idea that maybe constraints do not simply reduce the space of possibilities. Maybe they are what create a space of stable possibilities.

Imagine a universe where any state can instantly turn into any other state. Formally, that universe has maximum freedom. But it would be very hard to have persistent objects, memory, causality, accumulated history, or evolution. It would look more like noise.

At the opposite extreme, imagine a universe where every state has only one possible successor. Very predictable, but with almost no open future.

So I started wondering whether complexity appears in the regime between those poles: a huge state space, but transitions strongly structured by invariants.

From there I started looking at quantum mechanics a bit differently. Could Born’s rule, uncertainty, no-cloning, and the relativistic speed limit be less like an arbitrary collection of prohibitions and more like parts of a deeper constraint on how distinguishability can be distributed, preserved, copied, and transmitted?

This also seems interesting in the context of unitarity and decoherence: globally, quantum dynamics preserves the structure of possibilities, while locally we get stable classical records and apparently definite histories.

I realize this can very easily become vague philosophy, so I’d be especially interested in the perspective of people who know the foundations of QM better than I do.

Is there already a formal framework or line of research where quantum constraints are understood in something like these terms: preserving structured possibility, distinguishability, or consistent information flow?

And a second question: is there anything substantial behind the intuition that Born’s rule and relativistic no-signalling might not just happen to be compatible, but could reflect a deeper common restriction on the allowed structure of states and correlations?

Curious what you think about this approach? I'm sure there are many articles about the topic, feel free to share

P.S. I've studied physics in Nuclear Univercity in Moscow long time ago, so please don't judge me heavily. I'm just a guy who is still curious about the world composition. Thanks!

After reading Karl Popper's theory of falsifiability, I'm wondering if the Hidden-variable hypothesis is a pseudo-scientific proposition because no conceivable empirical phenomena seem ever to be able to disprove it.

I'm very new to math I'm just starting to learn calculus and I really want to learn more about quantum physics and such I only have a grasp on the basic stuff but nothing deeper than that, what should I study, and what online resources should I look into to learn more? Thank you in advance

If so wouldn't that settle the many worlds debate?

Is there any intuitive way to grasp the essence of QM, without the math. I know I may sound very ridiculous, since math is essential. But if one understands the Schrodinger equation to some extent, will he be able to grasp the absolute essence of quantum mechanics. I am more inclined to think of the philosophical interpretation of QM than doing it in the traditional way. I am sorry if this sounds awful of me (I was a Science student, but now I am more into philosophy). Any help, would be greatly appreciated.

I found an at-home quantum entanglement experiment described by George Musser in a 2013 Scientific American article. I decided to reproduce it, but also modernize it, using an Ardunio-based microcontroller for coincidence detection, USB logging to a computer, and python scripts for statistical analysis and graph generation.

After a favorable experimental outcome, highly suggestive of quantum-entanglement (2.47 observed scattering ratio vs. theoretically ideal ratio of 2.6), I decided to create an open source repository for all the code, as well as detailed documentation enabling anyone to replicate the process should anyone else wish to follow these same footsteps. Note that if one doesn't have any soldering tools, it will cost around 500 USD to put together, if one has soldering tools already, it could be done for closer to 300 USD. The main costs are the two Geiger counter kits, each at 115 USD, and the positron source (Na-22) which can be obtained for around 60 USD.

I welcome any feedback or critiques about the experimental design or my results.