A Quantum Revolution in Finance — Part I
The formulation of Quantum Mechanics in the early 20th century by erudites such as Schrodinger and Heisenberg left an indelible mark on all of Computer Science. When the probabilistic nature of matter was revealed, it left behind a fascinating trail of possibilities in computing — one that would let us harness the power of exponential calculations — to solve algorithms thought impossible by classical means.
Quantum mechanics is dictated by probabilities. Its most fundamental postulate is that nothing is completely certain — nothing at all. Even the location of a particle that we can observe is only known to a specific precision. This logically follows from the Uncertainty principle, which states that the momentum and position of a particle is uncertain to at least some infinitesimal amount.
Soon after, in 1935, Schrodinger’s experiment came to the forefront, which demonstrated that a particle can simultaneously exist in an infinite number of states. Such a condition is known as a linear superposition of states.
|ψ| = p(A) + q(B) + r(C)…
where A, B and C are three possible states. The absolute square of the coefficients of the states (p, q, r…) represent the probabilities of finding the particle in that particular state. It must be noted that these coefficients may be complex functions— they have no ‘real’ interpretation unless squared.
|p|² + |q|² + |r|² …. = 1
This superposition of states is the foundation of the mammoth project that we call ‘Quantum Computing’.
Computers use ‘bits’ — arbitrary strings of binary — to perform operations. Each bit occupies one of two states, o or 1. To create a 3-digit string, 2³ bits are needed to cover each of the possibilities — 000, 001, 010, 100, 101, 110, 011, 111.
Quantum computing makes use of the same principle of superposition to be exponentially more efficient. Instead of taking on one discrete value as a classical bit does, a quantum bit — or ‘qubit’ — occupies both those states simultaneously.
A qubit is both 0 and 1, unlike a classical bit, which is o or 1.
So, to display our 3-digit string, we need only 3 qubits, since each can occupy either the 0 or 1 state at will. This can easily be generalized:
To display a n-digit string, classical computers require 2^n strings, while quantum computers require only n bits.
Given the sheer complexity of binary structures in computers today, one can only marvel at the possibility of quantum computing. Estimates suggest that a computer with 49 qubits achieves quantum supremacy — that is, it possesses the same processing power as today’s supercomputers. Add a few qubits, and we are heralded into an age where even the most complex simulations can be performed in a matter of seconds.
3 days ago, on the 5th of July, 2017, the supercomputer Cori II at the National Energy Research Scientific Computing Center (NERSC), broke the record for quantum computing by utilizing 45 qubits — just 4 short of the magic number.
Indeed, quantum computing can be applied to a vast spectrum of fields, most notably physical science and finance, where they may be used in performing high frequency trading dictated by algorithmic systems. Corporations such as Google and IBM are pouring billions of dollars into such computing systems — in the hopes of revolutionizing the world. Applications of Quantum Computing to finance shall be discussed in subsequent posts.
