Engineering superpositions over all possible futures through quantum stochastic simulation*

Stochastic simulation plays an important role in quantitative science, enabling future predictions based on past observations. However many of the most important systems that we wish to understand and simulate are complex. Predicting and simulating such systems can involve tracking a prohibitive amount of data, evincing a pressing need for more efficient tools in algorithmic modelling and simulation.

Quantum technologies have shown the potential to dramatically reduce the amount of working memory required to simulate stochastic processes [1]. This enables quantum computers to accurately predict a complex system's future behaviour, while reducing the amount of past information that must be tracked beyond classical limits. The key to achieving such memory compression advantages, is maintaining coherence of the quantum memory during the simulation process.

Here we introduce the first experimental demonstration of a quantum simulator using time-bin encoding in an optical system [2]. A key feature of the processor is that it creates quantum superpositions over all possible future trajectories a stochastic system can evolve into. These superpositions enable the comparison of the statistical futures of two classical processes via quantum interference. We present experimental results from the interference of two 16-dimensional quantum states, representing comparison of two different potential statistical futures of a process, and report visibilities of up to 0.96±0.02. Our results suggest that quantum computers may provide compelling methods for enhancing stochastic simulation and time serries analysis.

[1] Gu, M., Wiesner, K., Rieper, E., & Vedral, V. Nat. Comms. 3, 1 (2012).
[2] Ghafari, F., Tischler, N., Di Franco, C., Thompson, J. & Gu, M. Pryde, G. Nat. Comms. 10, 1630 (2019)