Circuit Complexity Research Articles

Single-flux-quantum circuits utilizing self-shunted NbN/TaN/NbN Josephson junctions grown on silicon substrates

Abstract We report on the electrical properties of NbN/TaN/NbN Josephson junctions grown on thermally oxidized silicon substrates, along with the design and fabrication of superconducting single-flux-quantum (SFQ) circuits based on these NbN superconductor/normal metal/superconductor (SNS) junctions. The critical current density (J c) of the junctions was found to be relatively sensitive to the barrier thickness, decreasing from 108.0 ± 8.1 kA cm−2 for a 15 nm barrier to 12.8 ± 1.9 kA cm−2 for a 30 nm barrier. For a J c of approximately 24.5 ± 2.1 kA cm−2 and a barrier thickness of 25 nm, the NbN SNS junctions are self-shunted and exhibit nonhysteretic current–voltage (I–V) characteristics. Especially for junctions with diameter (φ) ranging from 0.8 to 1.6 μm, their critical current (I c) falls within the range of 110–450 μA, making them suitable for SFQ circuits. By considering the impact of excess current and incorporating it as an additional term in the conventional resistively and capacitively shunted junction model, the I–V curves of NbN SNS junctions can be precisely described, successfully minimizing the deviation between simulations and test results. The DC-SFQ and SFQ-DC interface circuits can both operate normally, and the bias margins of cell circuits such as Josephson transmission line, confluence buffer, D flip-flop, and splitter are greater than 40%. Compared to Nb superconductor/insulator/superconductor junctions, their self-shunting characteristics and relatively thick 25 nm barriers can also enhance the integration of circuits and increase the yield to complex circuits.

Microscopic deconstruction of cortical circuit stimulation by transcranial ultrasound.

Transcranial Ultrasound Stimulation (TUS) can noninvasively and reversibly perturb neuronal activity, but the mechanisms by which ultrasound engages brain circuits to induce functional effects remain unclear. To elucidate these interactions, we applied TUS to the cortex of awake mice and concurrently monitored local neural activity at the acoustic focus with two-photon calcium imaging. We show that TUS evokes highly focal responses in three canonical neuronal populations, with cell-type-specific dose dependencies. Through independent parametric variations, we demonstrate that evoked responses collectively scale with the time-average intensity of the stimulus. Finally, using computational unmixing we propose a physiologically realistic cortical circuit model that predicts TUS-evoked responses as a result of both direct effects and local network interactions. Our results provide a first direct evidence of TUS's focal effects on cortical activity and shed light on the complex circuit mechanisms underlying these effects, paving the way for TUS's deployment in clinical settings.

Spiking Neural Network Pressure Sensor.

Von Neumann architecture requires information to be encoded as numerical values. For that reason, artificial neural networks running on computers require the data coming from sensors to be discretized. Other network architectures that more closely mimic biological neural networks (e.g., spiking neural networks) can be simulated on von Neumann architecture, but more important, they can also be executed on dedicated electrical circuits having orders of magnitude less power consumption. Unfortunately, input signal conditioning and encoding are usually not supported by such circuits, so a separate module consisting of an analog-to-digital converter, encoder, and transmitter is required. The aim of this article is to propose a sensor architecture, the output signal of which can be directly connected to the input of a spiking neural network. We demonstrate that the output signal is a valid spike source for the Izhikevich model neurons, ensuring the proper operation of a number of neurocomputational features. The advantages are clear: much lower power consumption, smaller area, and a less complex electronic circuit. The main disadvantage is that sensor characteristics somehow limit the parameters of applicable spiking neurons. The proposed architecture is illustrated by a case study involving a capacitive pressure sensor circuit, which is compatible with most of the neurocomputational properties of the Izhikevich neuron model. The sensor itself is characterized by very low power consumption: it draws only 3.49 μA at 3.3 V.

Universal early-time growth in quantum circuit complexity

We show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric. Deviations from linear early-time growth arise from the commutation algebra of the gates and are manifestly negative for any circuit, decreasing the linear growth rate and leading to a bound on the growth rate of complexity of a circuit at early times. We illustrate this general result by applying it to qubit and harmonic oscillator systems, including the coupled and anharmonic oscillator. By discretizing free and interacting scalar field theories on a lattice, we are also able to extract the early-time behavior and dependence on the lattice spacing of complexity of these field theories in the continuum limit, demonstrating how this approach applies to systems that have been previously difficult to study using existing techniques for quantum circuit complexity.

Plaquette models, cellular automata, and measurement-induced criticality

Abstract We present a class of two-dimensional randomized plaquette models, where the multi-spin interaction term, referred to as the plaquette term, is replaced by a single-site spin term with a probability of $1-p$. By varying $p$, we observe a ground state phase transition, or equivalently, a phase transition of the symmetry operator. We find that as we vary $p$, the symmetry operator changes from being extensive to being localized in space. These models can be equivalently understood as 1+1D randomized cellular automaton dynamics, allowing the 2D transition to be interpreted as a 1+1D dynamical absorbing phase transition. In this paper, our primary focus is on the plaquette term with three or five-body interactions, where we explore the universality classes of the transitions. Specifically, for the model with five-body interaction, we demonstrate that it belongs to the same universality class as the measurement-induced entanglement phase transition observed in 1+1D Clifford dynamics, as well as the boundary entanglement transition of the 2D cluster state induced by random bulk Pauli measurements. This work establishes a connection between transitions in classical spin models, cellular automata, and hybrid random circuits.


Review of recent trends of advancements in multilevel inverter topologies with reduced power switches and control techniques

AbstractCurrently, multilevel inverters (MLI) are comprehensively used to integrate renewable energy sources with the grid or high‐power applications. MLI has outstanding properties such as high‐level output voltage with tremendous power quality and negligible harmonics distortion. General MLI topologies have a more complex circuit, high overall cost and installation area. Due to a large number of power switches and isolation of control circuit, fewer power electronic switches and DC source along with its suitable control logic is the need of the hour. Therefore, a lot of research scope exists in this area. Here, some of the topologies with a fewer number of power switches are reviewed and scrutinized. An extensive analysis of the topologies, control strategy and applications are presented here, suggesting suitable multilevel inverter solutions to the known industrial application or new research.

Data-driven discovery of a model equation describing self-oscillations of direct current discharge

Data-driven techniques developed in recent years for the discovery of equations describing complex physical phenomena open unique opportunities for plasma physics. These methods allow getting insights into the processes difficult for analytical description. Since gas discharges can be represented as complex electrical circuits consisting of impedances and capacitances, it looks natural to use the data-driven techniques to study their complex dynamics. In the present paper, the sparse identification of nonlinear dynamics (SINDy) method is applied to analyze the self-oscillations of direct current discharge in argon. It is obtained that the third order polynomials describe best the oscillations of the discharge voltage and current. They allow an accurate capturing of the oscillations amplitudes as well as the harmonics of these oscillations. To understand the physical meaning of each term, an analytical model is presented which describes the discharge self-oscillations.

Increased leg muscle power and arm muscle strength of basketball athletes: through complex training method and circuit body weight training

Increased leg muscle power and arm muscle strength of basketball athletes: through complex training method and circuit body weight training

Building Krylov complexity from circuit complexity

Krylov complexity has emerged as a probe of operator growth in a wide range of nonequilibrium quantum dynamics. However, a fundamental issue remains in such studies: the definition of the distance between basis states in Krylov space is ambiguous. Here we show that Krylov complexity can be rigorously established from circuit complexity when dynamical symmetries exist. Whereas circuit complexity characterizes the geodesic distance in a multidimensional operator space, Krylov complexity measures the height of the final operator in a particular direction. The geometric representation of circuit complexity thus unambiguously designates the distance between basis states in Krylov space. This geometric approach also applies to time-dependent Liouvillian superoperators, where a single Krylov complexity is no longer sufficient. Multiple Krylov complexity may be exploited jointly to fully describe operator dynamics. Published by the American Physical Society 2024

Simulation-based effective comparative analysis of neuron circuits for neuromorphic computation systems

The spiking neural networks (SNN) which are inspired by the human brain offers wider scope for application in the growth of neuromorphic computing systems due to their brain level computational capabilities, reduced power consumption, minimal data movement cost, and among other advantages. Spike-based neurons and synapses are the essential building blocks of SNN, and their efficient implementation is vital to its performance enhancement. In this regard, the design and implementation of spiking neurons have been the major focus among the researchers. In this paper, functioning of different leaky integrate fire (LIF)-based spiking neuron circuits like frequency adaptable CMOS-based LIF, resistor-capacitor-based (RC) LIF, and volatile memristor-based LIF are subjected to comparison. The work mainly focuses on revealing analysis of spike duration and amplitude, number of spikes produced during excitation period, threshold operation, field of application, and various other significant parameters of aforementioned neuron circuits. Extensive simulations of these circuits are carried out utilizing the Cadence Virtuoso simulation environment in order to validate their behavior. Further, a brief comparative analysis is executed considering into account the attributes like circuit complexity, supply voltage, firing rate, membrane capacitance, nature of input/output, refractory mechanism, and energy consumption per spike. This work seeks to assist researchers in selecting an appropriate LIF model to efficiently construct memristors and/or non-memristors based SNN for certain application.

A Switching Memory-Based Event-Trigger Scheme for Synchronization of Lur'e Systems With Actuator Saturation: A Hybrid Lyapunov Method.

This article is concerned with the event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization results.

Simulation and fabrication of a 20 kHz single-beam transducer

Abstract With the vigorous development of underwater acoustic technology in China, underwater acoustic transducers are constantly moving towards broadband, low-frequency, and high-power directions. How to obtain piezoelectric transducers with lower frequencies is still a research direction that scholars from various countries are striving to study. This article mainly studies and manufactures a 20 kHz single-beam piezoelectric transducer, using the classic Tonpilz transducer structure. Firstly, the Tonpilz transducer is theoretically analyzed using the classical equivalent circuit method. Secondly, the transducer is analyzed using ANSYS finite element analysis software to study the influence of piezoelectric ceramics on the frequency of the transducer, and the size of the piezoelectric ceramics is optimized to determine the size of the piezoelectric ceramic structure of the transducer. The working frequency of the transducer was calculated using software, and it was determined that the working frequency was approximately 20 kHz.

Investigation of the TaOx unipolar switching memory on high efficiency computing

Memristor has shown great potential application for data storage, neuromorphic computing chip, and memory logic, but its bi-directional operation from setting in positive bias voltage region to resetting in a negative bias voltage region would introduce a complex control circuit. Herein, a memristor with the structure of Au/TaOx/F-doped SnO2 presents unipolar switching behavior, enabling the memristor to operate the set and reset processing in a single voltage direction. By comparison with bipolar switching memristor, using this unipolar switching memristor to operate the logic expression of the letter “D” based on American standard code for information interchange (ASCII) can reduce power consumption by 55.56% while switching the logic state from “0” to “1” and then back to “0” can save up to 48% of power consumption. This work provides a feasible method for the low power consumption computing as well as a road to simplify circuit design.

High efficiency AOT-controlled boost converter with pseudo-constant switching frequency

An on-time generator for boost converters is proposed to achieve an adaptive on-time (AOT) control with pseudo-constant frequency in continuous conduction mode (CCM). Since the first-order parasitic effect of the components and devices is considered in the design of the on-time generator, the switching frequency (fsw) variation of the boost converter in CCM can be better suppressed with the load current (ILOAD), input voltage (VIN) and output voltage (VOUT) changes, which can effectively solve the EMI noise problem. In addition, the idea of capacitor pre-charging is applied to simplifying circuit complexity. Meanwhile, an on-demand modulation strategy is applied to improve the conversion efficiency. Simulation results show that the boost converter based on the proposed on-time generator can realize the fsw variation of 0.4 % in case of 200 mA ILOAD change. Moreover, the VIN may range from 0.8 to 1.5 V, the VOUT is set to 1.8 V, and the peak efficiency of the simulation is 96.9 %.

Hardware Implementation of Fully Controlled Bridge Rectifier with Rapid Control Prototyping Approach

In industrial applications, rapid prototyping of digital controls is important in terms of time, cost, and getting easier design steps. Especially the complexity of different power electronic converter circuits and their necessity of providing various operating conditions make digital control inevitable. However, developing a digital control system has many unknown details. In-the-loop simulation techniques evolved to simplify this stage during the last few decades. In this paper, a fully controlled bridge rectifier is designed and implemented by using a rapid control prototyping approach; its steps are accelerated with processor-in-the-loop and hardware-in-the-loop tests. Launchpad F28379D from Texas Instruments is used as an interface between the designed rectifier hardware circuit and MATLAB/Simulink Embedded Coder platform. Additionally, a driver control board is developed to provide switching signals and analog to digital measurements. The performance of the system is experimentally tested on a 500W rectifier prototype with a closed loop PI controller for voltage regulation at different parametric variations.

CMOS-Compatible High-Performance Silicon Nanowire Array Natural Light Electronic Detection System.

In this article, we propose a novel natural light detector based on high-performance silicon nanowire (SiNW) arrays. We achieved a highly controllable and low-cost fabrication of SiNW natural light detectors by using only a conventional micromachined CMOS process. The high activity of SiNWs leads to the poor long-term stability of the SiNW device, and for this reason, we have designed a fully wrapped structure for SiNWs. SiNWs are wrapped in transparent silicon nitride and silicon oxide films, which greatly improves the long-term stability of the detector; at the same time, this structure protects the SiNWs from breakage. In addition, the SiNW arrays are regularly distributed on the top of the detector, which can quickly respond to natural light. The response time of the detector is about 0.015 s. Under the illumination of 1 W·m-2 light intensity, multiple SiNWs were detected together. The signal strength of the detector reached 1.82 μA, the signal-to-noise ratio was 47.6 dB, and the power consumption was only 0.91 μW. The high-intensity and highly reliable initial signal reduces the cost and complexity of the backend signal processing circuit. A low-cost and high-performance STM32 microcontroller can realize the signal processing task. Therefore, we built a high-performance SiNW natural optoelectronic detection system based on an STM32 microcontroller, which achieved the real-time detection of natural light intensity, with an accuracy of ±0.1 W·m-2. These excellent test performances indicate that the SiNW array natural light detector in this article meey the requirements of practicality and has broad potential for application.

Exploiting Spatial Ionic Dynamics in Solid-State Organic Electrochemical Transistors for Multi-Tactile Sensing and Processing.

The human nervous system inspires the next generation of sensory and communication systems for robotics, human-machine interfaces (HMIs), biomedical applications, and artificial intelligence. Neuromorphic approaches address processing challenges; however, the vast number of sensors and their large-scale distribution complicate analog data manipulation. Conventional digital multiplexers are limited by complex circuit architecture and high supply voltage. Large sensory arrays further complicate wiring. An 'in-electrolyte computing' platform is presented by integrating organic electrochemical transistors (OECTs) with a solid-state polymer electrolyte. These devices use synapse-like signal transport and spatially dependent bulk ionic doping, achieving over 400 times modulation in channel conductance, allowing discrimination of locally random-access events without peripheral circuitry or address assignment. It demonstrates information processing from 12 tactile sensors with a single OECT output, showing clear advantages in circuit simplicity over existing all-electronic, all-digital implementations. This self-multiplexer platform offers exciting prospects for circuit-free integration with sensory arrays for high-quality, large-volume analog signal processing.

Large circuit models: opportunities and challenges

Within the electronic design automation (EDA) domain, artificial intelligence (AI)-driven solutions have emerged as formidable tools, yet they typically augment rather than redefine existing methodologies. These solutions often repurpose deep learning models from other domains, such as vision, text, and graph analytics, applying them to circuit design without tailoring to the unique complexities of electronic circuits. Such an “AI4EDA” approach falls short of achieving a holistic design synthesis and understanding, overlooking the intricate interplay of electrical, logical, and physical facets of circuit data. This study argues for a paradigm shift from AI4EDA towards AI-rooted EDA from the ground up, integrating AI at the core of the design process. Pivotal to this vision is the development of a multimodal circuit representation learning technique, poised to provide a comprehensive understanding by harmonizing and extracting insights from varied data sources, such as functional specifications, register-transfer level (RTL) designs, circuit netlists, and physical layouts. We champion the creation of large circuit models (LCMs) that are inherently multimodal, crafted to decode and express the rich semantics and structures of circuit data, thus fostering more resilient, efficient, and inventive design methodologies. Embracing this AI-rooted philosophy, we foresee a trajectory that transcends the current innovation plateau in EDA, igniting a profound “shift-left” in electronic design methodology. The envisioned advancements herald not just an evolution of existing EDA tools but a revolution, giving rise to novel instruments of design-tools that promise to radically enhance design productivity and inaugurate a new epoch where the optimization of circuit performance, power, and area (PPA) is achieved not incrementally, but through leaps that redefine the benchmarks of electronic systems’ capabilities.

Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits

The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known to arise in various ways. However, a caveat of most existing gradient bound results is the requirement of t-design circuit assumptions that are typically not satisfied in practice. In this work, we loosen these assumptions altogether and derive tight upper and lower bounds on loss and gradient concentration for a large class of parameterized quantum circuits and arbitrary observables, which are significantly stronger than prior work. Moreover, we show that these bounds, as well as the variance of the loss itself, can be estimated efficiently and classically-providing practical tools to study the loss landscapes of VQA models, including verifying whether or not a circuit/observable induces barren plateaus. In particular, our results can readily be leveraged to rule out barren plateaus for a realistic class of ansätze and mixed observables, namely, observables containing a non-vanishing local term. This insight has direct implications for hybrid Quantum Generative Adversarial Networks (qGANs). We prove that designing the discriminator appropriately leads to 1-local weights that stay constant in the number of qubits, regardless of discriminator depth. This implies that qGANs with appropriately chosen generators do not suffer from barren plateaus even at scale-making them a promising candidate for applications in generative quantum machine learning. We demonstrate this result by training a qGAN to learn a 2D mixture of Gaussian distributions with up to 16 qubits, and provide numerical evidence that global contributions to the gradient, while initially exponentially small, may kick in substantially over the course of training.

On the Exploration of Quantum Polar Stabilizer Codes and Quantum Stabilizer Codes with High Coding Rate.

Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors.