He discusses the basics of knot theory, and then discusses how knot theory can be combined with quantum computing to make a non-copyable, non-counterfeitable money. Apparently it's based on a real 2010 paper by Peter Shor
IMO, not as good as ActionLab's usual videos. Glossed over a lot of stuff and didn't even discuss bitcoin!
Scott Aaronson mentioned that this was one of the things he was interested in before Bitcoin came out.
He said he wrote several papers about it. From my understanding, quantum money doesn't solve the need for a mint.
Here's at least one paper from 2012:
https://www.scottaaronson.com/papers/moneyfull.pdf
Aaronson's 2012 "Quantum Copy-Protection and Quantum Money" paper is the clearest treatment of the security model. He was working on the theoretical possibility well before Bitcoin existed, which makes the contrast interesting: Bitcoin solved the double-spend problem with a globally replicated ledger (expensive, but it works with classical cryptography), while quantum money attempts to solve it with local verification (cheaper to verify, but requires quantum hardware).
The Bitcoin approach turned out to be practically deployable immediately. Quantum money needs quantum computers to be widespread before it is useful as a payment system -- and by the time quantum computers are widespread enough for quantum money to be practical, they will also threaten ECDSA.
So quantum money and Bitcoin are not really competitors. They are solutions to different assumptions about infrastructure. Quantum money is the "right" answer in a world with ubiquitous quantum hardware; Bitcoin is the "right" answer given current classical infrastructure.
I wonder if they still think we need quantum money, or whether bitcoin achieved what they were going for, just that we need to make bitcoin's cryptography quantum-secure
Quantum money from knots is genuinely clever. The key insight: a knot is a topological object whose equivalence class is hard to compute (knot isotopy is in NP, not known to be in P), so a quantum state that encodes a knot can serve as an unforgeable token -- the difficulty of copying comes from the hardness of determining knot equivalence, not just the no-cloning theorem.
The Bitcoin connection is important: the quantum threat to Bitcoin's ECDSA signatures is real and timeline-uncertain. Quantum money schemes are a parallel research track -- they could supplement, not replace, classical blockchain settlement.
What I find most interesting: the "money from knots" paper demonstrates that quantum hardness assumptions do not have to be based on factoring or discrete logarithm problems. The diversity of quantum-hard problems matters. If one assumption falls, you have others.
For Bitcoin specifically: the relevant quantum-resistant signature schemes (CRYSTALS-Dilithium, SPHINCS+) are now NIST standards. The transition is an engineering and coordination problem, not a mathematical one. The knot-based approach is more speculative but potentially more elegant.
Clickbait!!
Sorry!! The title of the vid was too good for bitcoiners not to post on SN!!
Sounds interesting but don’t we already have money with those properties?
That was my first thought too. Really disappointed that he didn't even mention Bitcoin.
It’s not surprising to me. This is just about a neat application of some super nerdy theory.
I would be interested in seeing a comparison of the possible properties of QuantumKnotsCoins to the current properties of bitcoin though.
the intersection of specialized knowledge that would be required to make such a comparison would be crazy for anyone to meet. But I imagine that people working on quantum security in the bitcoin space are best positioned to do so
My totally naive guess is that this hypothetical money would have other severe limitations.