Thread by @HangukQuant

1\ Thread:

A Quantum Revolution is Looming.

Why should you care?
Is it going to “break Bitcoin”?

A Trader’s Overview of the Quantum World

2\ You probably have heard of quantum teleportation. No, it is not going to make your girlfriend appear on your bed whilst your parents are sleeping. Whilst it cannot currently destroy your digital coins, it might just be able to do that, sometime soon.

3\ So, what is Quantum Mechanics? It is a fundamental theory in physics that provides a description of the physical properties of nature. The branch of quantum theory dealing with manipulation and computation of quantum bits (qubits) is known as quantum computational theory.

4\ It is known to popular culture and media as some “holy grail”, and much like AI suffers from the buzzword syndrome, no thanks to Einstein and The Big Bang Theory. It also has a long history of overpromising and underdelivering.

5\ Theoretical advances far outpace physical engineering capacities, leaving much to be desired in terms of hardware. It turns out that quantum computers are susceptible to interactions with surroundings (decoherence), and other problems exist.

6\ Error correcting mechanisms are needed, and “circuit depth” is a real challenge for implementing useful algorithms that have already been proposed. Basically, let’s leave the hardware issue discussion for the thread as “it be tough”; quantum theorists have charged ahead.

7\ But, it seems that in recent years that efforts and advances is accelerating towards usability. So, what exactly can these do? Let’s handwave over general classes of “Quantum Solutions”, and then maybe dive deeper into one of them.

8\ Some of the problem they can solve (theoretically) for trading include quantum optimization problems (quantum annealing), optimal trading path, identifying arbitrage paths, quantum machine learning, quantum neural nets, quantum monte carlo et cetera.

9\ Note that we have not even tackled its potential boons in other facets of finance. So, let’s maybe try to explain Quantum Monte Carlo (QMC). How is it different? One of the properties of quantum states, as opposed to classical states is the “superposition” phenomena.

10\ Instead of being discrete states 00, 01 et cetera, quantum states can exist in a combination of these basis states. You probably also heard of “entanglement”, and things like “schrodinger's cat”.

11\ Well, the interesting this is that observing/measurement of quantum states collapses this superposition into one of just one of the states. If measurement of qubits were just arbitrary in measurement, one would think that such a measurement would contain little information

12\ The trick is that the probability of measurements is non-uniform, and the distribution depends on their relative amplitudes. This is where things get exciting. You can measure a state, but it turns out you can use some clever tricks called “Quantum Amplitude Estimation”

13\ Now suppose you quantum bits, and you can query some oracle to manipulate these bits such that the outcome is encoded in the amplitudes. If the oracle were simulating some path (like in Monte Carlo), you can now estimate all sorts of statistical distributions.

14\ The slam dunk is, you only “query the oracle” once to obtain your sampling distribution along a sampling axis. In the classical space, obtaining N independent samples require N units of time, but quantumly you do it “all at once”; a near quadratic speedup can be obtained.

15\ The consequences of these are significant, particularly for derivatives desks, who price their books heavily using Monte Carlo engines. More paths, mean higher accuracy.

16\ For large portfolios containing exotic derivatives with complex payoffs now can be “marked-to-marked” a lot faster than they currently are. Imagine a HFT that can identify optimal trading paths for an arb faster than their counterparts. The flash boys just got faster.

17\ For the “Bitcoin bros”, quantum prime factorization is a real headache, due to Shor’s algorithm. Many blockchain cryptographic principles will be rendered useless via the evolution of quantum computers.

18\ When such an era shall arrive, not all is lost. Cryptography can also exist in quantum channels, and Quantum Cryptography will rear its head.

FIN