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Big data applications are on the rise, and so is the number of data centers. The ever-increasing massive data pool needs to be periodically backed up in a secure environment. Moreover, a massive amount of securely backed-up data is required for training binary convolutional neural networks for image classification. XOR and XNOR operations are essential for large-scale data copy verification, encryption, and classification algorithms. The disproportionate speed of existing compute and memory units makes the von Neumann architecture inefficient to perform these Boolean operations. Compute-in-memory (CiM) has proved to be an optimum approach for such bulk computations. The existing CiM-based XOR/XNOR techniques either require multiple cycles for computing or add to the complexity of the fabrication process. Here, we propose a CMOS-based hardware topology for single-cycle in-memory XOR/XNOR operations. Our design provides at least $2\times $ improvement in the latency compared with other existing CMOS-compatible solutions. We verify the proposed system through circuit/system-level simulations and evaluate its robustness using a 5000-point Monte Carlo variation analysis. This all-CMOS design paves the way for practical implementation of CiM XOR/XNOR at scaled technology nodes.

Abstract The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired ‘toolbox’ for solving COPs.

Abstract The rich non‐linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While prior work on the stability of the so‐called Oscillator Ising Machines (OIMs) has used the linearization method, in this letter, the authors present a complementary method to analyze stability using the second‐order derivative test of the energy/cost function. The authors establish the equivalence between the two methods, thus augmenting the tool kit for the design and implementation of OIMs.

Context: Government of India launched the Rashtriya Bal Swasthya Karyakram (RBSK) for screening children from 0 to 18 years for 4 D’s (Defects, Diseases, Deficiency and Developmental Delays including disabilities) for timely referral and treatment. There are few studies published evaluating the implementation of this programme. Aims: To evaluate implementation of RBSK programme in Chhattisgarh state, problems in RBSK referral-to-treatment process. Methodology: One good performing district (Raigarh) and one poor performing district (Raipur) were selected, one block was randomly selected by lottery method from one rural and one urban area of each district respectively and all Mobile Health Teams (MHTs) of selected block were included for assessment. Since there are two MHTs allotted in each block, total 8 MHTs were evaluated. A pretested questionnaire was used to assess Knowledge, Attitude and Practice (KAP) of MHT doctors. Evaluation plan included health check-up of randomly selected students, interview with beneficiaries and visit to DEIC. Data analysis was done using Microsoft excel and SPSS. Results: There is shortage of manpower, screening equipment and reporting formats. KAP assessment of MOs shows below average information about paediatric conditions especially group A & D. Limited higher government centres for treatment of group A & D conditions (e.g. CHD, vision impairment, disability, etc.) leads to long waiting list, demotivation and loss to follow up. Conclusions: RBSK programme has its inherent strengths. Troubleshooting of vital issues will help in its smoother implementation. Introduce separate window/desk “CHIRAYU KHIDKI” at Medical College to fast-track service provision to children referred through RBSK. Provide specialised investigations free to beneficiary. Establish referral to centres providing rehabilitation to children with special needs and their care-givers.

Dynamical systems can offer a novel non-Boolean approach to computing. Specifically, the natural minimization of energy in the system is a valuable property for minimizing the objective functions of combinatorial optimization problems, many of which are still challenging to solve using conventional digital solvers. In this work, we design two oscillator-inspired dynamical systems to solve quintessential computationally intractable problems in Boolean satisfiability (SAT). The system dynamics are engineered such that they facilitate solutions to two different flavors of the SAT problem. We formulate the first dynamical system to compute the solution to the 3-SAT problem, while for the second system, we show that its dynamics map to the solution of the Max-not-all-equal (NAE)-3-SAT problem. Our work advances our understanding of how this physics-inspired approach can be used to address challenging problems in computing.

The intrinsic energy minimization in dynamical systems offers a valuable tool for minimizing the objective functions of computationally challenging problems in combinatorial optimization. However, most prior works have focused on mapping such dynamics to combinatorial optimization problems whose objective functions have quadratic degree [e.g., maximum cut (MaxCut)]; such problems can be represented and analyzed using graphs. However, the work on developing such models for problems that need objective functions with degree greater than two, and subsequently, entail the use of hypergraph data structures, is relatively sparse. In this work, we develop dynamical system-inspired computational models for several such problems. Specifically, we define the “energy function” for hypergraph-based combinatorial problems ranging from Boolean Satisfiability (SAT) and its variants to integer factorization, and subsequently, define the resulting system dynamics. We also show that the design approach is applicable to optimization problems with quadratic degree, and use it to develop a new dynamical system formulation for minimizing the Ising Hamiltonian. Our work not only expands on the scope of problems that can be directly mapped to, and solved using physics-inspired models, but also creates new opportunities to design high-performance accelerators for solving combinatorial optimization.

Abstract Realizing compact and scalable Ising machines that are compatible with CMOS-process technology is crucial to the effectiveness and practicality of using such hardware platforms for accelerating computationally intractable problems. Besides the need for realizing compact Ising spins, the implementation of the coupling network, which describes the spin interaction, is also a potential bottleneck in the scalability of such platforms. Therefore, in this work, we propose an Ising machine platform that exploits the novel behavior of compact bi-stable CMOS-latches (cross-coupled inverters) as classical Ising spins interacting through highly scalable and CMOS-process compatible ferroelectric-HfO2-based Ferroelectric FETs (FeFETs) which act as coupling elements. We experimentally demonstrate the prototype building blocks of this system, and evaluate the scaling behavior of the system using simulations. Our work not only provides a pathway to realizing CMOS-compatible designs but also to overcoming their scaling challenges.

Modern computers require an exponential increase in resources when solving computationally hard problems, motivating the need for an alternative computing platform to solve such problems in an energy‐efficient manner. Vertex coloring, a nondeterministic polynomial time (NP‐hard) combinatorial optimization problem, is one such problem. Herein, an experimental demonstration of using cardiac cell‐based bio‐oscillator network coupling dynamics to solve a vertex coloring problem in various scales of graphs using a simple cell patterning method to construct scalable and controlled cardiac cell networks is presented. Although there are limitations to using these cardiac cells as oscillators, such as their low frequency compared to complementary metal–oxide–semiconductor (CMOS) oscillators, that result in longer processing times, the accuracy in large graph instances, the significantly less amount of energy consumption, and the ease of fabrication and potential to extend this system to massively parallel 3D structures make the bio‐oscillators a promising new platform for collective computing applications.

Abstract Ferroelectrics offer a promising material platform to realize energy-efficient non-volatile memory technology with the FeFET-based implementations being one of the most area-efficient ferroelectric memory architectures. However, the FeFET operation entails a fundamental trade-off between the read and the program operations. To overcome this trade-off, we propose in this work, a novel device concept, Mott-FeFET, that aims to replace the Silicon channel of the FeFET with VO2- a material that exhibits an electrically driven insulator–metal phase transition. The Mott-FeFET design, which demonstrates a (ferroelectric) polarization-dependent threshold voltage, enables the read current distinguishability (i.e., the ratio of current sensed when the Mott-FeFET is in state 1 and 0, respectively) to be independent of the program voltage. This enables the device to be programmed at low voltages without affecting the ability to sense/read the state of the device. Our work provides a pathway to realize low-voltage and energy-efficient non-volatile memory solutions.

Abstract Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation-compatible hardware platform to design Ising machines. However, such implementations presently require the injection of an externally generated second-harmonic signal to impose the phase bipartition among the oscillators. In this work, we experimentally demonstrate a new electronic autaptic oscillator (EAO) that uses engineered feedback to eliminate the need for the generation and injection of the external second harmonic signal to minimize the Ising Hamiltonian. Unlike conventional relaxation oscillators that typically decay with a single time constant, the feedback in the EAO is engineered to generate two decay time constants which effectively helps generate the second harmonic signal internally. Using this oscillator design, we show experimentally, that a system of capacitively coupled EAOs exhibits the desired bipartition in the oscillator phases without the need for any external second harmonic injection, and subsequently, demonstrate its application in solving the computationally hard Maximum Cut (MaxCut) problem. Our work not only establishes a new oscillator design aligned to the needs of the oscillator Ising machine but also advances the efforts to creating application specific analog computing platforms.

Abstract Noise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms.

Coupled electronic oscillator networks, under second harmonic injection, have recently been shown to behave as Ising machines capable of solving computationally hard combinatorial optimization problems. In this work, we experimentally investigate the dynamical properties of a reconfigurable network of up to 30 oscillators ( $\equiv $ spins) configured as an Ising machine. Specifically, we analyze the characteristics of the solutions to the Ising model produced by the oscillators and show that as the system evolves towards the ground state through the high-dimensional phase space, it gets trapped in local minima resulting in sub-optimal solutions. Moreover, the exact local minima where the system gets trapped also changes implying that the trajectory of evolution of the system also changes with each trial. Finally, we illustrate experimentally how an appropriately designed annealing scheme can help the coupled oscillators escape a local minimum and attain a lower energy state.

Designing efficient analog dynamical systems for solving hard optimization problems remains a challenge. Here, the authors demonstrate a dynamical system of thirty oscillators with reconfigurable coupling to compute optimal/near-optimal solutions to the hard Maximum Independent Set problem with over 90% accuracy.

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 bipartition that 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 (η). Furthermore, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple postprocessing) 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 seven out of nine measured graphs with η = 0.8. Our work marks a step toward creating an efficient, room-temperature-compatible non-Boolean hardware-based solver for hard combinatorial optimization problems.

Current rate of data generation and the need for real‐time data analytics can benefit from new computational approaches where computation proceeds in a massively parallel way while being scalable and energy efficient. Biological systems arising from interaction of living cells can provide such pathways for sustainable computing. Current designs for biocomputing leveraging the information processing units of the cells, such as DNA, gene, or protein circuitries, are inherently slow (hours to days speed) and, therefore, are primarily being considered for archival storage of information. On the contrary, electrically active cells that can synchronize in milliseconds and can be connected as networks to perform massively parallel tasks can transform biocomputing and lead to novel ways of high throughput information processing. Herein, coupled oscillator networks made of living cardiac muscle cells, or bio‐oscillators, is explored as collective computing components for solving computationally hard problems. An empirically validated circuit compatible macromodel is developed for the bio‐oscillators and the fibroblast cells acting as coupling elements, to faithfully reproduce the synchronization dynamics of the network and it is shown that such bio‐oscillator network can be scaled up to hundreds of nodes and be used to solve computationally hard problems faster than traditional heuristics‐based Boolean algorithms.

The stress induced by the capping electrode is critical to stabilizing the ferroelectric phase in Si-doped HfO2 which is being actively explored for embedded non-volatile memory applications. While TiN is commonly used as the electrode of choice owing to its thermodynamic stability with HfO2, its work function (WF) (=4.8eV) results in reduced memory window (MW), and higher interlayer field (EIL) in bulk Ferroelectric FETs (FeFETs). This is attributed to the built-in electric-field that arises from the WF difference between the metal and the semiconductor. This effectively reduces the ferroelectric hysteresis, and thus, the MW at the read current. Optimizing the MW and the EIL would entail changing the WF, and thus, the capping electrode-essential to retaining the desired ferroelectric properties. We, therefore, propose using the silicon on insulator (SOI)-FeFET architecture which provides an additional knob-back-gate bias (Vbg)-to optimize the MW while reducing the EIL. Further, we show that unlike the bulk FeFET, where a small deviation from the optimal WF dramatically shrinks the MW, the SOIFeFET facilitates a relatively constant MW over a wide range of Vbg. Thus, the SOI-FeFET simplifies the MW & EIL optimization and provides an improved MW versus EIL trade-off in comparison to the bulk FeFET.

Abstract While Boolean logic has been the backbone of digital information processing, there exist classes of computationally hard problems wherein this paradigm is fundamentally inefficient. Vertex coloring of graphs, belonging to the class of combinatorial optimization, represents one such problem. It is well studied for its applications in data sciences, life sciences, social sciences and technology, and hence, motivates alternate, more efficient non-Boolean pathways towards its solution. Here we demonstrate a coupled relaxation oscillator based dynamical system that exploits insulator-metal transition in Vanadium Dioxide (VO2) to efficiently solve vertex coloring of graphs. Pairwise coupled VO2 oscillator circuits have been analyzed before for basic computing operations, but using complex networks of VO2 oscillators, or any other oscillators, for more complex tasks have been challenging in theory as well as in experiments. The proposed VO2 oscillator network harnesses the natural analogue between optimization problems and energy minimization processes in highly parallel, interconnected dynamical systems to approximate optimal coloring of graphs. We further indicate a fundamental connection between spectral properties of linear dynamical systems and spectral algorithms for graph coloring. Our work not only elucidates a physics-based computing approach but also presents tantalizing opportunities for building customized analog co-processors for solving hard problems efficiently.