What contribution can a quantum computer make to the financial world?

A quantum computer allows the development of different and, in many respects, more efficient algorithms than ordinary computers that work on a binary (bit) system. The quantum computer also starts from two states 1 and 0, but what makes quantum computers particularly relevant is that the two states can be mixed together through a linear combination in the space of complex numbers, giving rise to a qbit.

Since every complex number is determined by two real quantities, the imaginary part and the real part, the linear combination of two states defines a space with four degrees of freedom. In this space, we must take into account a constraint that derives from the fact that the sum of the probabilities of finding the system in state 0 and in state 1 must be equal to 1, so ultimately the above linear combination is defined by 3 degrees of freedom.

This contrasts with the traditional computer, which works with only two states, opening up enormous possibilities for computation.

Generally, it is not possible to isolate a single spin and make it work as part of a computer, but it is possible to bring the appropriate atoms to extremely low temperatures, so that the electrons behave, within certain limits, as if they were isolated.

However, one factor to take into consideration is that we never reach absolute 0, the lowest possible temperature, so we must consider that quantum computers are subject to measurement errors related to a thermal overheating issue.

There is still a long way to go to be able to solve this problem, and other problems of a strictly technological nature. But in light of all this, why could a quantum computer be useful to us?

As an example, let’s think of a labyrinth where it is necessary to find a path to the exit. In an ordinary computer, the behavior is always binary and the time taken to find the output is proportional to all the output solutions.

Instead, in the case of the quantum computer we can analyze all possible paths at the same time, taking advantage of the fact that a qbit has three degrees of freedom.

With this methodology, in a single shot we find the exit possibility we were looking for.

In finance, the applications are remarkable. It is possible to perform optimizations otherwise unthinkable, to build ever more efficient portfolios. Or create very fast arbitrage systems, able to act almost instantly on multiple markets at the same time.

There are other implications as well. Thanks to their nature, quantum computers have the potential to derive a private key from the public one, so all the technologies associated with the classic public key / private key scheme could be in danger.

In particular, this applies to the traditional encryption methods used by crypto currencies, paving the way for the violation of private wallets, the so-called crypto wallets. Today’s algorithms are not ready to withstand a quantum attack, with the exception of very few blockchains, so if quantum computing were, as we believe, to develop into common use, we would also see a revolution in the world of digital currencies.

by Riccardo Donati
Member of the Scientific Committee