Decoding Stock Market Behavior with the Topological Quantum Computer

Abstract

A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking into account only the crossing of stocks and fixing a convention defining overcrossings and undercrossings. The braid of stocks prices has a remarkable connection with the topological quantum computer. Using pairs of quasi-particles, called non-abelian anyons, having their trajectories braided in time, topological quantum computer can effectively simulate the stock market behavior encoded in the braiding of stocks. In a typically topological quantum computation process the trajectories of non-abelian anyons are manipulated according to the braiding of stocks and the outcome reflects the probability of the future state of stock market. The probability depends only on the Jones polynomial of the knot formed by plat closing the quantum computation. The Jones polynomial of the knotted stock market acts, making a parallel with the common financial literature, in a topological quantum computation as a counterpart of a classical technical indicator in trading the stock market. The type of knot stock market formed is an indicator of its future tendencies.

Quantum Gates and Quantum Circuits of Stock Portfolio

“…The braid representation of prices time series of stocks in a portfolio prove to be a promising candidate in constructing a basis platform quantum computational methods could be applied on. Present paper extends the findings of the previous work on the quantum computation applications in finance [17] by realizing a series of elementary quantum gates for braided stocks of a portfolio.…”

“…Calculating the delta for all crossings in the figure 1, it result the braid diagram shown in the figure 3. More in depth details on calculating the deltas between prices of stocks in a crossing can be found on [16] and [17]. The colored trajectories of prices are no longer necessary since the only important aspect related to braid diagrams is the over-crossings and under-crossings.…”

“…A series of recent papers [15], [16], [17] formally introduced and developed the braid diagrams of stocks prices time series in a portfolio and sketched their connection with the topological methods of quantum computation.…”