"Memory is a precious commodity across many different areas—from the ever-growing worldwide demand on storage capacity driven by social media use, to the importance of memory as a possible limiting factor in simulation and quantum computation. In this talk, I will present two recently demonstrated ways in which quantum devices can lower memory requirements.

The first application lies in the simulation of classical stochastic processes. Stochastic process models serve to describe a wide variety of natural and social phenomena, such as the weather and traffic congestions. The simulation of stochastic processes provides valuable information about the dynamics of complex systems. However, for highly complex processes, a large amount of information about the system’s past needs to be stored in order to simulate its future. This translates to a large memory requirement, which may limit the feasibility of such a simulation. Here, quantum mechanics promises an advantage: simulators that process quantum information can outperform classical simulators, by reducing the memory requirement significantly below the ultimate classical limits [1].

In Geoff Pryde's lab, we have recently achieved the first experimental realizations of such quantum-enhanced simulation of classical stochastic processes [2–4]. Using photonic quantum information processing, we simulated up to three steps of a stochastic process [3]. This involved producing 16-dimensional quantum states that contain a superposition of the process’s different possible futures. In addition to an asymptotic memory advantage achievable via Schumacher compression, we have demonstrated that even individual simulators can have a lower-dimensional memory register than their best classical counterparts [4].

The second type of quantum device I will discuss is a quantum autoencoder, which autonomously learns how to compress quantum data. We have developed and experimentally realized a photonic quantum autoencoder that is trained based on sets of quantum states [5]. We demonstrated that when the inherent structure of the dataset allows lossless compression, our autoencoder reduces qutrits to qubits with low error levels. The device is able to perform with minimal prior information about the quantum data or physical system and is robust to perturbations during its optimization routine.

References:

[1] M. Gu, K. Wiesner, E. Rieper, and V. Vedral, Nat. Commun. 3, 762 (2012).

[2] M. S. Palsson, M. Gu, J. Ho, H. M. Wiseman, and G. J. Pryde, Science Advances 3, e1601302 (2017).

[3] F. Ghafari, N. Tischler, C. Di Franco, J. Thompson, M. Gu, and G. J. Pryde, Nature Commun. 10, 1630 (2019).

[4] F. Ghafari, N. Tischler, J. Thompson, M. Gu, L. K. Shalm, V. B. Verma, S.-W. Nam, R. B. Patel, H. M. Wiseman, and G. J. Pryde, arXiv:1812.04251 (2018).

[5] A. Pepper, N. Tischler, and G. J. Pryde, Phys. Rev. Lett. 122, 060501 (2019).

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