Circuit Complexity Research Articles

Engineering Topological States and Quantum‐Inspired Information Processing Using Classical Circuits

AbstractBased on the correspondence between circuit Laplacian and Schrodinger equations, recent investigations have shown that classical electric circuits can be used to simulate various topological physics and Schrödinger's equation. Furthermore, a series of quantum‐inspired information processing has been implemented by using classical electric circuit networks. In this review, the similarity between the circuit Laplacian and the lattice Hamiltonian is analyzed, with topological physics introduced based on classical circuits. Subsequently, reviews of the research progress in quantum‐inspired information processing based on the electric circuit are provided, including discussions of topological quantum computing with classical circuits, quantum walk based on classical circuits, quantum combinational logics based on classical circuits, electric‐circuit realization of fast quantum search, implementing unitary transforms and so on.

Activation of glutamatergic neurons in the organum vasculosum of the lamina terminalis induces thirst-driven sniffing.

Sniffing is a specialized respiratory behavior that enables rodents to localize and track objects in their environment. The organum vasculosum of the lamina terminalis (OVLT) is critically involved in the regulation of thirst and water intake, yet its role in controlling thirst-driven exploratory sniffing behaviors remains unclear. This study demonstrates that hypertonic stimulation significantly increases sniffing and activates OVLT glutamatergic (OVLTGlut) neurons. Photostimulation of both OVLTGlut neurons and their axon terminals within the paraventricular nucleus of the hypothalamus (PVN) induces robust sniffing. Furthermore, ablation of PVN neurons projecting to the preBötzinger complex not only reduces the sniffing time induced by photostimulation of OVLTGlut neurons projecting to the PVN but also prolongs the drinking latency. These findings identify the OVLTGlut-PVN-preBötzinger complex circuit as a pivotal regulator of thirst-driven sniffing, providing insights into the neural mechanisms underlying thirst and exploratory behavior.

Efficient Learning of Quantum States Prepared With Few Fermionic Non-Gaussian Gates

The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum state from data obtained by measurements. Without prior assumptions on the state, this task is prohibitively hard. Here, we present an efficient algorithm for learning states on n fermion modes prepared by any number of Gaussian and at most t non-Gaussian gates. By Jordan-Wigner mapping, this also includes n-qubit states prepared by nearest-neighbor matchgate circuits with at most t gates. Our algorithm is based exclusively on single-copy measurements and produces a classical representation of a state, guaranteed to be close in trace distance to the target state. The sample and time complexity of our algorithm is poly(n,2t); thus if t=O(log(n)), it is efficient. We also show that, if t scales more than logarithmically, any learning algorithm to solve the same task must be inefficient, under common cryptographic assumptions. We also provide an efficient property-testing algorithm that, given access to copies of a state, determines whether such a state is far or close to the set of states for which our learning algorithm works. In addition to the outputs of quantum circuits, our tomography algorithm is efficient for some physical target states, such as those arising in time dynamics and low-energy physics of impurity models. Beyond tomography, our work sheds light on the structure of states prepared with few non-Gaussian gates and offers an improved upper bound on their circuit complexity, enabling an efficient circuit-compilation method. Published by the American Physical Society 2025

A sensing material-free and simple readout MEMS sensor for detecting Helium

Abstract In this work, we report a method that enables a standard electrostatic MEMS device to perform complex sensing functionalities, such as detecting the presence of helium without a sensing material or a conditioning circuit. Helium is a noble, odorless, non-reactive gas that is very challenging to detect. It is used in critical applications such as storing nuclear fuel waste inside a dry cask. In these applications, its leakage from the dry cask may indicate the cask's safe operation's degradation. A departure from the common practice of exciting the MEMS around its mechanical resonance, the method is based on exciting the MEMS around its electrical resonance circuit. This method shows that the tiny difference between the air dielectric constant (1.00059) and helium (1.000067) corresponding to only a few Femtofarad level capacitances produces a 25 mV difference without a conditioning circuit. Simulation results confirmed those findings and explored the sensor response at different operation conditions. This method eliminates the need for a heated microstructure and the need for absorption material. This method is not limited to gas sensing. It can be applied to other sensing mechanisms, such as acceleration and pressure measurements, and eliminate the complex circuit to read small capacitance in these applications.

A single dorsal vagal complex circuit mediates the aversive and anorectic responses to GLP1R agonists.

GLP-1 receptor agonists (GLP1RAs) effectively reduce feeding to treat obesity, although nausea and other aversive side effects of these drugs can limit their use. Brainstem circuits that promote satiation and that mediate the physiologic control of body weight can be distinguished from those that cause aversion. It remains unclear whether brainstem Glp1r neurons contribute to the normal regulation of energy balance and whether GLP1RAs control appetite via circuits distinct from those that mediate aversive responses, however. Hence, we defined roles for AP and NTS Glp1r -expressing neurons (AP Glp1r and NTS Glp1r neurons, respectively) in the physiologic control of body weight, the GLP1RA-dependent suppression of food intake, and the GLP1RA-mediated stimulation of aversive responses. While silencing non-aversive NTS Glp1r neurons interfered with the physiologic restraint of feeding and body weight, restoring NTS Glp1r neuron Glp1r expression on an otherwise Glp1r -null background failed to enable long-term body weight suppression by GLP1RAs. In contrast, selective Glp1r expression in AP Glp1r neurons restored both aversive responses and long-term body weight suppression by GLP1RAs. Thus, while non-aversive NTS Glp1r neurons control physiologic feeding, aversive AP Glp1r neurons mediate both the anorectic and weight loss effects of GLP1RAs, dictating the functional inseparability of these pharmacologic GLP1RA responses at a circuit level.

Development of robust constitutive synthetic promoter using genetic resources of plant pararetroviruses.

With the advancement of plant synthetic biology, complex genetic engineering circuits are being developed, which require more diverse genetic regulatory elements (promoters) to operate. Constitutive promoters are widely used for such gene engineering projects, but the list of strong, constitutive plant promoters with strength surpassing the widely used promoter, the CaMV35S, is limited. In this work, we attempted to increase the constitutive promoter library by developing efficient synthetic promoters suitable for high-level gene expression. To do that, we selected three strong pararetroviral-based promoters from Mirabilis mosaic virus (MMV), Figwort mosaic virus (FMV), and Horseradish latent virus (HRLV) and rationally designed and combined their promoter elements. We then tested the newly developed promoters in Nicotiana benthamiana and found a highly active tri-hybrid promoter, MuasFuasH17 (MFH17). We further used these promoter elements in generating random mutant promoters by DNA shuffling techniques in an attempt to change/improve the MFH17 promoter. We further evaluated the activity of the MFH17 promoter in Oryza sativa seedlings and studied the effect of as-1 elements present in it. Finally, we tested the efficacy and tissue specificity of the MFH17 promoter in planta by developing transgenic Nicotiana tabacum and Arabidopsis thaliana plants and found it highly constitutive and efficient in driving the gene throughout the plant tissues. Overall, we conclude that this tripartite synthetic promoter MFH17 is a strong, highly constitutive, and dual-species (dicot and monocot) expressing promoter, which can be a valuable addition to the constitutive plant promoter library for plant synthetic biology.

Novel VLSI Architecture for Discrete Wavelet Packet Transform Using Arbitrary Tree Structures

The paper presents a novel pipelined VLSI architec- ture based on an arbitrary wavelet tree for the calculation of the discrete wavelet packet transform (DWPT) of any signal. There are phases of calculating the coefficients for different levels. For each level, there is a bypassed wavelet filter and a circuit for rearranging intermediate coefficients. The recommended lifting- based wavelet filter computes the high and low pass coefficients in series. It either calculates the coefficients or passes the samples such that there is an allowance of the arbitrary tree topology. A subband necessary for the higher-level computation is generated by rearranging the intermediate coefficients. The coefficients are computed progressively, and the circuit complexity diminishes with the reduction of intermediate coefficients other than memory components. A 50 percent decrease in memory components is needed with the pipelined design presented above. Also, data from hardware implementation clearly suggest that the space and power needs have gone reduced by 20% and 33%, respectively. Index Terms—Arbitrary tree structure, bitreordering, discrete wavelet packet transform (DWPT), signal flowgraph (SFG).

Extremal jumps of circuit complexity of unitary evolutions generated by random Hamiltonians

We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles of random generators — the so called Gaussian Unitary Ensemble (GUE) and the ensemble of diagonal Gaussian matrices conjugated by Haar random unitary transformations. In both scenarios we prove that the complexity of exp(–itH) exhibits the following behaviour — with high probability it reaches the maximal allowed value on the same time scale as needed to escape the neighborhood of the identity consisting of unitaries with trivial (zero) complexity. We furthermore observe similar behaviour for quantum states originating from time evolutions generated by above ensembles and for diagonal unitaries generated from the ensemble of diagonal Gaussian Hamiltonians. To establish these results we rely heavily on structural properties of the above ensembles (such as unitary invariance) and concentration of measure techniques. This gives us a much finer control over the time evolution of complexity compared to techniques previously employed in this context: high-degree moments and frame potentials.

Elaborating the connections of a closed-loop forebrain circuit in the rat: Circumscribed evidence for novel topography within a cortico-striato-pallidal triple descending projection, with thalamic feedback, to the anterior lateral hypothalamic area.

We used a bottom-up approach to identify a distinct longitudinal column of dorsomedial nucleus accumbens (ACBdm) that spans its anteroposterior axis. This region projects to medial substantia innominata (SIm) and lateral hypothalamic area (LHA), resembling the "direct" and "indirect" pathways of the classical basal ganglia circuit. We also identified topographically distinct regions in medial prefrontal cortex (strictly delineated here as the cingulate region, CNG), ventral subiculum (SUBv), and basolateral amygdala (BLA) that project to both ACBdm and LHA, further defining the circuit. Finally, we identified an LHA-to-anterior paraventricular thalamic nucleus (PVTa) feedback projection that selectively targets cortical and striatal nodes within the circuit. Our work provides novel detailed maps that bolster the proposal that this "triple descending projection" (cortico-striato-pallidal) and associated thalamic feedback loop play a role in affective and motivational processes.

Combinational Equivalence Checking on AIGs

Combinational Equivalence Checking (CEC) is a critical process in digital circuit design, ensuring that two versions of a circuit are functionally equivalent. Functionally Reduced And-Inverter Graphs (FRAIGs) are a data structure extensively used in CEC, representing Boolean functions as directed acyclic graphs with AND gates and inverters. The main advantage of FRAIGs is their ability to integrate structural hashing with functional reduction, allowing for the elimination of functionally equivalent nodes during graph construction. However, conventional FRAIG approaches face challenges with scalability in complex circuits. To overcome these limitations, we propose three novel methods: improved sampling techniques that refine random simulation and SAT-based methods for early identification of equivalent nodes; advanced graph partitioning strategies that enable parallel processing and localized equivalence checking to accelerate computation; and support node analysis combined with probability distribution modeling to reduce unnecessary checks. Extensive experiments show the effectiveness and efficiency of our proposed methods

Efficient Quantum Circuit Design with a Standard Cell Approach, with an Application to Neutral Atom Quantum Computers

We design quantum circuits by using the standard cell approach borrowed from classical circuit design, which can speed up the layout of circuits with a regular structure. Our standard cells are general and can be used for all types of quantum circuits: error-corrected or not. The standard cell approach enables the formulation of layout-aware routing algorithms. Our method is directly applicable to neutral atom quantum computers supporting qubit shuttling. Such computers enable zoned architectures for memory, processing and measurement, and we design circuits using qubit storage (memory and measurement zones) and standard cells (processing zones). Herein, we use cubic standard cells for Toffoli gates and, starting from a 3D architecture, we design a multiplication circuit. We present evidence that, when compared with automatic routing methods, our layout-aware routers are significantly faster and achieve shallower 3D circuits (by at least 2.5×), while also reducing routing costs. Additionally, our co-design approach can be used to estimate the resources necessary for a quantum computation without using complex compilation methods. We conclude that standard cells, with the support of layout-aware routing, pave the way to very-large-scale methods for quantum circuit compilation.

Transistor Frequency-Response Analysis: Recursive Shunt-Circuit Transformations

Frequency-response analysis is critical in circuit design. Frequency response encodes crucial information, like gain, accuracy, bandwidth, response time, phase shift, stability, and more. Unfortunately, existing methods are either algebraic and obscure or approximations with inaccuracies. So applying them to more complex circuits is often arduous or unreliable. This paper proposes recursive shunt-circuit transformations: a simple, rigorous, and insightful analytical method for conceptualizing and designing electronic circuits. The method asserts that (a) each equivalent capacitance shunts away its parallel resistance past its RC frequency. This (b) decreases the gain (induces a pole) and (c) changes the circuit. (d) The next dominant capacitance shunts its parallel resistance past the next pole and so on until all remaining capacitances shunt their parallel resistances past the poles they establish. The method also asserts that (e) bypass capacitances increase gain (induce zeros) and (f) cross-amp capacitances couple stages and poles. By applying this method and concepts, designers can (i) simplify an arbitrarily complex circuit into simpler coupled/decoupled stages and (ii) determine and manage poles and zeros with insight. This method was applied to design and analyze single- and multi- stage amplifier circuits and results were benchmarked against traditional methods and NGSPICE simulations, demonstrating its accuracy and broad applicability.

Memory engram synapse 3D molecular architecture visualized by cryoCLEM-guided cryoET.

Memory is incorporated into the brain as physicochemical changes to engram cells. These are neuronal populations that form complex neuroanatomical circuits, are modified by experiences to store information, and allow for memory recall. At the molecular level, learning modifies synaptic communication to rewire engram circuits, a mechanism known as synaptic plasticity. However, despite its functional role on memory formation, the 3D molecular architecture of synapses within engram circuits is unknown. Here, we demonstrate the use of engram labelling technology and cryogenic correlated light and electron microscopy (cryoCLEM)-guided cryogenic electron tomography (cryoET) to visualize the in-tissue 3D molecular architecture of engram synapses of a contextual fear memory within the CA1 region of the mouse hippocampus. Engram cells exhibited structural diversity of macromolecular constituents and organelles in both pre- and postsynaptic compartments and within the synaptic cleft, including in clusters of membrane proteins, synaptic vesicle occupancy, and F-actin copy number. This "engram to tomogram" approach, harnessing in vivo functional neuroscience and structural biology, provides a methodological framework for testing fundamental molecular plasticity mechanisms within engram circuits during memory encoding, storage and recall.

High-performance ternary logic circuits and neural networks based on carbon nanotube source-gating transistors.

Multi-valued logics (MVLs) offer higher information density, reduced circuit and interconnect complexity, lower power dissipation, and faster speed over conventional binary logic system. Recent advancement in MVL research, particularly with emerging low-dimensional materials, suggests that breakthroughs may be imminent if multistates transistors can be fabricated controllably for large-scale integration. Here, a concept of source-gating transistors (SGTs) is developed and realized using carbon nanotubes (CNTs). By extending the source electrode into the channel of conventional CNT transistors, a controllable p-n homojunction is formed, allowing CNT-SGTs to reliably switch between three distinct states. Capitalizing on the straightforward fabrication process of CNT-SGTs, ternary inverters, NMIN and NMAX logic gates, ternary SRAM cells, and a ternary neural network achieving 100% image classification accuracy have been successfully implemented. This study represents the most advanced and highest-performing ternary circuits realized with low-dimensional materials to date. This progress highlights the potential of CNT-SGTs in driving the future of MVL architectures.

Current‐Mirror Based Filters With Reduced Circuit Complexity

Current‐Mirror Based Filters With Reduced Circuit Complexity

Light-eye-body axis: exploring the network from retinal illumination to systemic regulation.

The human body is an intricate system, where diverse and complex signaling among different organs sustains physiological activities. The eye, as a primary organ for information acquisition, not only plays a crucial role in visual perception but also, as increasing evidence suggests, exerts a broad influence on the entire body through complex circuits upon receiving light signals which is called non-image-forming vision. However, the extent and mechanisms of light's impact on the body through the eyes remain insufficiently explored. There is also a dearth of comprehensive reviews elucidating the intricate interplay between light, the eye, and the systemic connections to the entire body. Herein, we propose the concept of the light-eye-body axis to systematically encapsulate the extensive non-image-forming effects of light signals received by the retina on the entire body. We reviewed the visual-neural structure basis of the light-eye-body axis, summarized the mechanism by which the eyes regulate the whole body and the current research status and challenges within the physiological and pathological processes involved in the light-eye-body axis. Future research should aim to expand the influence of the light-eye-body axis and explore its deeper mechanisms. Understanding and investigating the light-eye-body axis will contribute to improving lighting conditions to optimize health and guide the establishment of phototherapy standards in clinical practice.

Design and Testing of MEMS Component for Electromagnetic Pulse Protection.

With the demand for high-safety, high-integration, and lightweight micro- and nano-electronic components, an MEMS electromagnetic energy-releasing component was innovatively designed based on the corona discharge theory. The device subverted the traditional device-level protection method for electromagnetic energy, realizing the innovation of adding a complex circuit system to the integrated chip through micro-nanometer processing technology and enhancing the chip's size from the centimeter level to the micron level. In this paper, the working performance of the MEMS electromagnetic energy-releasing component was verified through a combination of a simulation, a static experiment, and a dynamic test, and a characterization test of the tested MEMS electromagnetic energy-releasing component was carried out to thoroughly analyze the effect of the MEMS electromagnetic energy-releasing component. The results showed that after the strong electromagnetic pulse injection, the pulse breakdown voltage of the MEMS electromagnetic energy-releasing component increased exponentially in terms of the pulse injection voltage, and the residual pulse current decreased significantly from one-third to one-half of the original, representing a significant protective effect. In a DC environment, the breakdown voltage of the needle-needle structure of the MEMS electromagnetic energy-releasing component was 144 V, and the on-time was about 0.5 ms.

FPGA acceleration of tensor network computing for quantum spin models.

Increasing the degree of freedom for quantum entanglement within tensor networks can enhance the depiction of the essence in many-body systems. However, this enhancement comes with a significant increase in computational complexity and critical slowing down, which drastically increases time consumption. This work converts a quantum tensor network algorithm into a classical circuit on the Field Programmable Gate Arrays (FPGAs) and arranges the computing unit with a dense parallel design, efficiently optimizing the time consumption. Test results show that the FPGA-based design achieves a computational speed 1.7 times greater than that of the central processing unit and is comparable to the graphics processing unit. This work explores a scalable and reusable approach suitable for parallel tensor operations implemented on FPGA, advancing research in quantum physics for many-body computing and quantum technologies.

Design of Multilayered XOR Gate Using Quantum Dot Cellular Automata

The rapid advancement of microelectronics technology necessitates the development of high-speed, low-power devices. Quantum Cellular Automaton (QCA) is emerging as a promising technology enabling logic circuits with exceptional operating speeds. The XOR gate is crucial in nanocomputing applications, such as nano-processors and nano-communication units, and requires innovative design approaches. This paper presents a novel design of an XOR gate using a multilayered layout methodology within the QCA framework. The circuit’s design and validation are performed using QCADesigner 2.0.3, while energy dissipation analysis is conducted with QCADesigner-E, resulting in an energy dissipation of 15 meV. Comprehensive parameter analysis, including cost functions, highlights the superiority of the proposed design. A comparative analysis with similar existing multilayered designs shows a 55% improvement in QCA-specific quantum cost. Notably, the proposed design eliminates the need for internal nodes within the layout, enhancing the methodology’s applicability to higher-order and more complex circuits.

Automated polynomial formal verification using generalized binary decision diagram patterns.

With the ongoing digitization, digital circuits have become increasingly present in everyday life. However, as circuits can be faulty, their verification poses a challenging but essential challenge. In contrast to formal verification techniques, simulation techniques fail to fully guarantee the correctness of a circuit. However, due to the exponential complexity of the verification problem, formal verification can fail due to time or space constraints. To overcome this challenge, recently Polynomial Formal Verification (PFV) has been introduced. Here, it has been shown that several circuits and circuit classes can be formally verified in polynomial time and space. In general, these proofs have to be conducted manually, requiring a lot of time. However, in recent research, a method for automated PFV has been proposed, where a proof engine automatically generates human-readable proofs that show the polynomial size of a Binary Decision Diagram (BDD) for a given function. The engine analyses the BDD and finds a pattern, which is then proven by induction. In this article, we formalize the previously presented BDD patterns and propose algorithms for the pattern detection, establishing new possibilities for the automated proof generation for more complex functions. Furthermore, we show an exemplary proof that can be generated using the presented methods.This article is part of the theme issue 'Emerging technologies for future secure computing platforms'.