Dimensional Reduction in Quantum-Enhanced Stochastic Modelling*

In data analytics, the curse of dimensionality is a well-acquainted adversary. As we seek to make predictions from time-series data drawn from processes of ever-growing complexity, modelling the possible future effects from all possible past observations becomes quickly intractable. Even when the time-series data is binary, the cost of accounting for temporal correlations in the last n time-steps grows as 2ⁿ – making the exact simulation of highly non-Markovian processes computationally infeasible. In this talk, we describe how quantum models – machines the store relevant past information in quantum memory - has the potential to significantly outperform their classical counterparts. Notably:

1. Given models of a fixed memory dimension, quantum models can achieve superior accuracy than their classical counterpart

2.  There exist families of progressively more non-Markovian processes that require increasing classical memory dimensionality to model, and yet can be modelled by a quantum machine of bounded dimension.

We illustrate such quantum models discovered directly from time-series data, and how they can display provable accuracy advantage within today’s noisy quantum processors. We discuss how such models can also generate future predictions in a quantum superposition, providing a key sub-routine for various quantum algorithms that enable the enhanced analysis of stochastic processes (e.g., quantum amplitude estimation, risk analysis, importance sampling).