Not all computing problems are created equal. The inherent complexity of processing certain classes of problems using digital computers has inspired the exploration of alternate computing paradigms. Coupled oscillators exhibiting rich spatio-temporal dynamics have been proposed for solving hard optimization problems. However, the physical implementation of such systems has been constrained to small prototypes. Consequently, the computational properties of this paradigm remain inadequately explored. Here, we demonstrate an integrated circuit of thirty oscillators with highly reconfigurable coupling to compute optimal/near-optimal solutions to the archetypally hard Maximum Independent Set problem with over 90% accuracy. This platform uniquely enables us to characterize the dynamical and computational properties of this hardware approach. We show that the Maximum Independent Set is more challenging to compute in sparser graphs than in denser ones. Finally, using simulations we evaluate the scalability of the proposed approach. Our work marks an important step towards enabling application-specific analog computing platforms to solve computationally hard problems.

We present a quasi-analytical model for Tunnel Field Effect Transistors (TFETs) that includes the microscopic physics and chemistry of interfaces and non-idealities. The ballistic band-to-band tunneling current is calculated by modifying the well known Simmons equation for oxide tunneling, where we integrate the Wentzel-Kramers-Brillouin (WKB) tunneling current over the transverse modes. We extend the Simmons equation to finite temperature and non-rectangular barriers using a two-band model for the channel material and an analytical channel potential profile obtained from Poisson's equation. The two-band model is parametrized first principles by calibrating with hybrid Density Functional Theory calculations, and extended to random alloys with a band unfolding technique. Our quasi-analytical model shows quantitative agreement with ballistic quantum transport calculations. On top of the ballistic tunnel current we incorporate higher order processes arising at junctions coupling the bands, specifically interface trap assisted tunneling and Auger generation processes. Our results suggest that both processes significantly impact the off-state characteristics of the TFETs -Auger in particular being present even for perfect interfaces. We show that our microscopic model can be used to quantify the TFET performance on the atomistic interface quality. Finally, we use our simulations to quantify circuit level metrics such as energy consumption. arXiv:1806.06331v3 [cond-mat.mtrl-sci]

In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard Maximum Cut (Max-Cut) problem. We show that under the influence of an external second-harmonic injection signal, the oscillator phases exhibit a bi-partition which can be used to calculate a high quality approximate Max-Cut solution. Leveraging the all-to-all reconfigurable coupling architecture, we experimentally evaluate the computational properties of the oscillators using randomly generated graph instances of varying size and edge density (ƞ). Further, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple post-processing) produce a Max-Cut that is within 99% of the optimal value in 28 of the 36 measured graphs; importantly, the oscillators are particularly effective in dense graphs with the Max-Cut being optimal in 7 out of 9 measured graphs with ƞ=0.8. Our work marks a step towards creating an efficient, room-temperature-compatible non-Boolean hardwarebased solver for hard combinatorial optimization problems.

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