Minimum Circuit Research Articles

Accuracy recovery: A decomposition procedure for the synthesis of partially-specified Boolean functions

Logic Synthesis From Partial Specifications (LSFPS) is the problem of finding the hardware implementation of a Boolean function from a partial knowledge of its care set. The elements missing from the specifications are named don’t knows. The exact solution of LSFPS is the minimum size circuit of the corresponding problem in which the don’t knows set is void. Hence, in addition to the traditional objective of size minimization, the goal is to maximize the test accuracy, i.e., the accuracy of the circuit when evaluated over a subset of the don’t knows. This problem is relevant because efficient solutions can lead to hardware friendly machine learning models, not relying on black-box approaches. Indeed, LSFPS maps directly to the problem of the automatic generation of optimized topologies for Binarized Neural Networks. Furthermore, combining the exact solution with modern logic synthesis techniques would unlock unprecedented optimization capabilities. Previous works proved the effectiveness of approximate logic synthesis (ALS) for designing circuits with high test accuracy. Nonetheless, these methods sacrifice accuracy on the specifications, which banishes them from the legitimate candidates for LSFPS. In this paper, we propose accuracy recovery, a procedure to map an approximate version of the circuit to a new one that satisfies the exact functionality of the specifications. The proposed approach relies on an extension of a disjoint support decomposition algorithm. Relative experiments on the IWLS2020 benchmarks show that, on average, the addition of the designed decomposition to a synthesis flow reduces by 17.38% the number of gates and by 12.02% the depth. The usage of accuracy recovery, based on such a decomposition, yields a 95.73% accuracy in the binary MNIST problem, beating the state-of-the-art in ALS of 92.76%.

An Efficient Power Optimization Approach for Fixed Polarity Reed–Muller Logic Circuits Based on Metaheuristic Optimization Algorithm

With the emergence of the multicore architecture and the increase of chip operating frequency, power optimization has become a key step of circuit logic synthesis. Aiming at the XNOR/OR circuits, with the goal of minimizing power, construct the optimal polarity fixed-polarity Reed–Muller (FPRM) circuits power optimization scheme. However, the power optimization for FPRM circuits is a multipeak combinatorial optimization problem, we first propose a metaheuristic optimization algorithm (MOA), which includes the global exploration optimizer, local deep exploitation optimizer, and initial population and uses the proposed differential evolution optimization, fierce wolf siege algorithm-based tabu search, and improved skew tent map to make the population evolve. Based on the proposed Huffman tree construction algorithm and MOA, we propose an efficient power optimization approach (EPOA) to find the minimum power FPRM circuit. Experimental results on the benchmark circuits confirm the effectiveness of EPOA.

Identification of Key Areas for Ecosystem Restoration Based on Ecological Security Pattern

Ecosystem degradation and conversion are leading to a widespread reduction in the provision of ecosystem services. It is crucial for the governance of regional land spaces to rapidly identify key areas for ecosystem restoration. Herein, we combined the InVEST Habitat Quality Model with the granularity inverse method to identify ecological sources in Jiashi county, China, based on the “source-corridor” ecological security pattern paradigm. The minimum cumulative resistance model and circuit theory were adopted to diagnose the ecological “pinch points”, barrier points, break points, and key restoration areas for land space. Our results show that: (1) the area of the ecological source and the total length of the ecological corridor were identified as 1331.13 km2 and 316.30 km, respectively; (2) there were 164 key ecological “pinch points” and 69 key ecological barrier points in Jiashi county, with areas of 15.13 km2 and 14.57 km2, respectively. Based on the above ecological security pattern, recovery strategies are put forward to improve regional ecosystem health. This study describes the best practices which can be used to guide the planning and implementation of ecosystem restoration at the local landscape scale.

Cryptographic hardness under projections for time-bounded Kolmogorov complexity

A version of time-bounded Kolmogorov complexity, denoted KT, has received attention in the past several years, due to its close connection to circuit complexity and to the Minimum Circuit Size Problem MCSP. Essentially all results about the complexity of MCSP hold also for MKTP (the problem of computing the KT complexity of a string). Both MKTP and MCSP are hard for SZK (Statistical Zero Knowledge) under BPP-Turing reductions; neither is known to be NP-complete.Recently, some hardness results for MKTP were proved that are not (yet) known to hold for MCSP. In particular, MKTP is hard for DET (a subclass of P) under nonuniform ≤mNC0 reductions. In this paper, we improve this, to show that MKTP‾ is hard for the (apparently larger) class NISZKL under not only ≤mNC0 reductions but even under projections. Also MKTP‾ is hard for NISZK under ≤mP/poly reductions. Here, NISZK is the class of problems with non-interactive zero-knowledge proofs, and NISZKL is the non-interactive version of the class SZKL that was studied by Dvir et al.As an application, we provide several improved worst-case to average-case reductions to problems in NP, and we obtain a new lower bound on MKTP (which is currently not known to hold for MCSP).

Reducing Short Circuit Current with a Novel Approach Model in Wind Power Plants

Wind energy from renewable energy sources, the share of electric power system is increasing faster than other sources. This requires the analysis of the effect of the wind power plants have on the power system in connection with the network. The wind produces energy-dashed and variable power, which can cause some disruptive effects. In this study, a short circuit analysis was performed using the DIgSILENT PowerFactory program. Minimum short circuit analysis calculations have been performed for 15 wind turbines and 19 bus-bar wind power plants. The error current has been reduced to a minimum by changing the transformer connection and ground resistance for the most commonly encountered phase-to-ground short circuit analysis. This application has been developed against more complex and costly methods. This prevents the generators from switching to island mode after a phase-to-ground short circuit current is affected by the fault.

The Detection of Open and Leakage Faults for Prebond TSV Test Based on Weak Current Source

During the manufacturing process of three-dimensional integrated circuits (3-D ICs), many defects may occur in through-silicon vias (TSVs). These defects affect the integrity of the signal passing through TSVs, therefore detecting these defects in the early production stage is crucial. This article proposed a built-in-self-test (BIST) method with a simple test structure and easily implemented fault detection process. Due to the fact that the defects in TSVs influence the charge/discharge speed of TSVs’ equivalent capacitance, a weak current source is designed as the central part of the proposed test structure, which can measure the TSVs’ charge/discharge speed and quantify it using digital values. The effectiveness and robustness of the proposed method is validated by HSPICE simulation. The minimum measurable fault, test time, and test circuit area are also assessed in this article. The simulation results show that the method this article proposed can detect weaker faults, compared with the traditional test methods.

Constant Depth Formula and Partial Function Versions of MCSP Are Hard

Attempts to prove the intractability of the Minimum Circuit Size Problem (MCSP) date as far back as the 1950s and are well-motivated by connections to cryptography, learning theory, and average-case complexity. In this work, we make progress, on two fronts, towards showing MCSP is intractable under worst-case assumptions. While Masek showed in the late 1970s that the version of MCSP for DNF formulas is NP-hard, extending this result to the case of depth-3 AND/OR formulas was open. We show that determining the minimum size of a depth- $d$ formula computing a given Boolean function is N P-hard under quasipolynomial-time randomized reductions for all constant $d\geq 2$ . Our approach is based on a method to “lift” depth- $d$ formula lower bounds to depth-( $d+1$ ). This method also implies the existence of a function with a $2^{\Omega_{d}(n^{1/5}}$ ) additive gap between its depth-d and depth-( $d+1$ ) formula complexity. We also make progress in the case of general, unrestricted circuits. We show that the version of MCSP where the input is a partial function (represented by a string in $\{0,1, ?\}^{\ast}$ ) is not in P under the Exponential Time Hypothesis (ETH). Intriguingly, we formulate a notion of lower bound statements being (P/poly)-recognizable that is closely related to Razborov and Rudich's definition of being (P/poly)-constructive. We show that unless there are subexponential-sized circuits computing SAT, the lower bound statements used to prove the correctness of our reductions cannot be (P/poly)-recognizable.

Measurement of the effect of parasitic capacitance in minimum ignition energy spark generation circuits

To accurately measure electrostatic discharge energy, a resistive-capacitive voltage discharge approach was used to measure the parasitic capacitance in a circuit. As a result, an output-stage parasitic capacitance in the circuit during the discharge process and a non-negligible storage-stage parasitic capacitance during the charging process were identified. By comparing the data obtained from the resistive-capacitive discharge voltage model and spark current RCL circuit model, the maximum relative deviation from the total circuit capacitance was 5.4% for both approaches. A model based on graded-stage parasitic capacitance was established to analyze the effect of this capacitance on discharge energy. The energy stored in the charging process increased because of the storage-stage parasitic capacitance, and the discharge energy decreased because of the output-stage parasitic capacitance. The energy calculated by the graded parasitic capacitance model was larger than that calculated by the single-stage parasitic capacitance model, with a maximum relative deviation of 36.7% under the test conditions. The smaller the charging capacitor, the more evident the effect of the parasitic capacitance on the discharge energy.

Numerical analysis of quantum circuits for state preparation and unitary operator synthesis

We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate configurations, we determine the maximum achievable fidelity as a function of quantum circuit size. This information allows us to identify the minimum circuit size needed for a specific target operation and enumerate the different gate configurations that allow a perfect implementation of the operation. We find that there are a large number of configurations that all produce the desired result, even at the minimum number of gates. We also show that the number of entangling gates can be reduced if we use multi-qubit entangling gates instead of two-qubit CNOT gates, as one might expect based on parameter counting calculations. In addition to treating the general case of arbitrary target states or unitary operators, we apply the numerical approach to the special case of synthesizing the multi-qubit Toffoli gate. This approach can be used to investigate any other specific few-qubit task and provides insight into the tightness of different bounds in the literature.

Intelligent Assessment of Mental Health Based on IoT Data

In order to solve the problem of the accuracy of mental health assessment of college students, the author proposes an intelligent assessment system for mental health based on IoT data. In order to improve the evaluation effect, the author based on the original student mental health crisis counseling risk evaluation system designs a new risk assessment system for student mental health crisis counseling. The system hardware section mainly optimizes the design of the main control chip and the minimum system circuit. At the same time, a psychological counseling risk calculation model is built to realize the process of quantifying the risk value. The membership degree of the risk value is calculated using the basic principle of fuzzy logic, and the evaluation result is introduced into this part of the calculation to obtain an accurate evaluation level. The evaluation accuracy of the design system can reach up to 99%, and the detection time is as low as 5 s, which greatly improves the evaluation performance. The use of the design system is better than the evaluation system currently in use.

RANCANG BANGUN SISTEM PENGAMANAN TRANSFUSI DARAH BERBASIS MIKROKONTROLER ATMega 8535

Blood warmer is a tool that is used to warm blood in the process of blood transfusion. Inside the blood warmer there are several main parts that must be considered, in the main part that must be considered is the blood fluid detector section. With the main purpose so that blood does not rise again fill the blood bag. The design of this tool aims to get the design of a security system for blood transfusion by using a photodiode detector as an indicator of blood flow that will be displayed in the form of sound. This research starts from the stages of collecting various sources, gathering information, designing tool products, designing and performing function tests. The hardware includes the design of the power supply circuit, the minimum system circuit of the ATMega8535 microcontroller, the liquid blood detector circuit, the buzzer circuit, and the servo motor circuit. While the design for software includes basic complier language programming. The working principle of the overall system is: The photodiode detector circuit will provide input to the microcontroller to be processed and produce output in the form of buzzer and servo motor closing the hose

Design of Switched-Capacitor DC-DC Voltage-Down Converters Driven by Highly Resistive Energy Transducer

Electrostatic vibration energy transducers have a relatively high output impedance (RET) and open-circuit voltage (VIN), so that voltage-down conversion is required for sensor/RF ICs. Switched-capacitor converters are the best candidate to create small-form-factor technology and are a low-cost solution because of their capability to fully integrate into sensor/RF ICs. To design switched-capacitor voltage-down converters (SC-VDCs) with a minimum circuit area for electrostatic vibration energy transducers, two steps are required. The first step requires an optimum design of DC-DC SC-VDCs driven by high RET with a minimum circuit area, and the second step requires an optimum design of AC-DC SC-VDCs based on the first step, to minimize the converter circuit area. This paper discusses circuit analysis and design optimization aimed at the first step. Switching frequency, the number of stages and the capacitance per stage were determined as a function of RET, VIN and the output voltage (Vo) and current (Io) to the load, to achieve a minimum circuit area. The relationship between Io and the power conversion efficiency was studied as well. The performance was validated by SPICE simulation in 250 nm BCD technology. An optimum design flow was proposed to design DC-DC SC-VDCs driven by high RET with a minimum circuit area under conditions where RET, VIN, Vo and Io were given. The second design step remains as future work.

Construction of GI Network Based on MSPA and PLUS Model in the Main Urban Area of Zhengzhou: A Case Study

With continuous urbanization and the fragmentation of green areas that affect human well-being, the establishment of a green infrastructure (GI) network is important in future urban planning. As a National Central City, Zhengzhou has a large population and is undergoing rapid economic development, resulting in an urgent demand for green space within the city in recent years. We selected the main urban area of Zhengzhou as the study area based on the two phases of Landsat 8 satellite remote sensing image data, for 2016 and 2021, and used the patch-generating land use simulation (PLUS) model to predict the spatial distribution of GI in the future; compared with traditional methods, this method identified green spaces from a future perspective. A GI network—consisting of an open space with vegetation as the main body—was designed for the main urban area of Zhengzhou using the traditional landscape ecological pattern theory, integrating morphological spatial pattern analysis (MSPA), the minimum cumulative resistance (MCR) model, circuit theory, and other methods. Evidently, the area of green space in Zhengzhou City in 2021 was 36 231.6 hm2. GI prediction results indicate that continuous expansion of the main urban area did not result in significant changes in the size of GI in the city. The GI within the urban area was relatively fragmented, forming 15 GI hubs, most of which were densely distributed along the edges of the main urban area. This study proposed the construction of a GI network with a target corridor and target points based on the existing corridor. This included the identification of seven target corridors and 15 target hubs; the total length of the corridor was 77.032 km, with a total of 31 target points. In summary, the GI network pattern of “one protection barrier, two lines, three loops and more points” was proposed. With new urban problems constantly emerging, this research could provide a theoretical reference basis for the planning of GI in the main urban area of the National Central City. The study provides concrete evidence on the optimum pattern for the construction of GI networks in cities with large populations.

Joint Device Pairing, Reflection Coefficients, and Power Control for NOMA Backscatter Systems

Non-orthogonal multiple access (NOMA) and backscatter communication are two emerging technologies for low-power communication. In this paper, we consider a NOMA backscatter system, where signals from two backscatter devices are multiplexed on a frequency resource block using NOMA in each time slot. Our objective is to maximize the average energy efficiency by optimizing backscatter device pairing, reflection coefficients of backscatter devices, and the transmit power of the reader. We formulate the average energy efficiency maximization problem subject to the minimum circuit power and the minimum data rate requirements of the backscatter devices, and the transmit power constraint of the reader. The formulated problem is nonconvex. To obtain a suboptimal solution for this problem, we use alternating optimization technique and decompose the problem into two subproblems. The subproblems are solved by using fractional programming, Dinkelbach’s algorithm, and successive convex approximation method. Simulation results show that our proposed algorithm converges quickly to a suboptimal solution. Our proposed algorithm outperforms several baseline algorithms, including the genetic algorithm, fixed device pairing scheme, conventional device pairing scheme, maximum transmit power allocation scheme, and random reflection coefficient selection scheme, in terms of the average energy efficiency. The optimality gap of our proposed algorithm is investigated by comparing with the optimal scheme, in which the optimal device pairing is obtained based on exhaustive search.

Integrating the ordered weighted averaging method to establish an ecological security pattern for the Jianghuai ecological economic zone in China: Synergistic intraregional development

• Considering ecosystem service trade-offs to identify ecological sources. • OWA was used to set up multiple ecological source scenarios. • Circuit theory was used to constructed an ecological security pattern. • Results can provide implications for ecosystem security in fast-growing cities. A well-constructed ecological security pattern (ESP) can promote linkages between ecological sources, mitigate the degradation of ecosystems, and facilitate sustainable urban development. However, when determining the ecological sources for ESPs, previous studies have less frequently or insufficiently considered the ecosystem service trade-offs. Our research aims to fill this research gap to improve the assessment of ESPs. Through a case study in a rapidly urbanizing region—the Jianghuai Ecological Economic Zone in China—we demonstrate the application possibilities of the proposed framework. Ecosystem services in the study area were evaluated using the Integrated Valuation of Ecosystem Services and Tradeoffs model, ecological sources were screened using the ordered weighted averaging method; then, an ESP was constructed using the minimum cumulative resistance model and circuit theory. The results indicated that crop production and water purification were higher in the east and lower in the west, while the water yield showed the opposite trend. Habitat quality and carbon storage were higher in the south and lower in the north. Eleven scenarios were set to determine ecological sources based on ecosystem service trade-offs. By comparing service efficiency, scenario 5 was selected as our optimal scenario, and the service efficiencies of ecological sources for crop production, water yield, habitat quality, carbon storage and water purification were 1.35, 1.15, 1.21, 1.06 and 0.92, respectively. There were no significant ecological sources in the developed eastern and central regions due to rapid urbanization and drastic land use changes in the area. There were 31 major ecological sources located in the western and northwestern parts of the study area, where water bodies and wetlands were well developed. There was a total of 70 ecological corridors in the study area, with 53 key ecological corridors. Based on these results, we proposed three measures to improve the sustainability of ecosystems to cope with the rapid urbanization while providing ecological quality. This study can provide implications for ecosystem security in other fast-growing cities.

Design of quaternary MIN and MAX circuits using graphene nanoribbon field effect transistors

This paper presents the design of digital logic schematics in quaternary logic. The quaternary logic is considered as best choice over the conventional two-valued logic due to its advantages such as faster computations, large memory storage, reduced interconnect length, ability to transmitting and receiving the large information, and simplification in testing. These advantages allow designing high performance circuit’s in the future integrated circuits. The new method is projected to develop the quaternary logic circuits utilizing graphene nanoribbon field effect transistors (GNRFETs). The quaternary logic circuits are developed based on GNRFETs wonderful properties, such as controlling the threshold voltage by changing the GNR width. This property makes them compatible to develop the multi-threshold digital circuits. To ensure the functionality of the digital circuits, the GNRFET based quaternary minimum (MIN) and maximum (MAX) circuits are developed. The proposed designs are simulated extensively in HSPICE tool for performance analysis. In comparison with the quaternary CNTFET based circuits, the proposed circuits optimized by 67.13%, 18.7%, 73.16% and 25.88%, in power consumption, delay, power delay product (PDP) and circuit area, respectively.

整合多重生态保护目标的广东省生态安全格局构建

PDF HTML阅读 XML下载 导出引用 引用提醒 整合多重生态保护目标的广东省生态安全格局构建 DOI: 10.5846/stxb202103220753 作者: 作者单位: 作者简介: 通讯作者: 中图分类号: 基金项目: 国家自然科学基金项目（41330747） Construction of ecological security pattern integrating multiple ecological protection objectives in Guangdong Province Author: Affiliation: Fund Project: The National Natural Science Foundation of China (41330747) 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:构建生态安全格局是缓解生态保护与经济发展之间的突出矛盾，保障可持续发展的有效空间途径。但目前生态安全格局的构建过于强调综合，简单叠加多种生态系统服务的方法忽视了不同服务间的权衡与协同关系，难以直接支撑不同目标下的生态保护决策。以广东省为例，重点关注生境维持、水源涵养、水质净化、粮食生产、土壤保持、洪水调节、沿海灾害缓解七种重要的生态系统服务，面向生物多样性保育、水资源利用、粮食生产、自然灾害防范等单一生态保护目标分别构建生态安全格局。研究结果表明，面向生物多样性保育目标的生态安全格局呈"双屏障带"式分布，生态源地主要分布在粤北生态发展区；面向水资源利用目标的水安全格局呈"五江一带"式分布，重点保护区主要位于河湖水库及周边绿地；面向粮食生产目标的生态源地主要分布在广东省东西两翼；面向自然灾害防范目标的生态源地在珠三角、湛江市、汕头市少有分布，集中在粤北生态发展区。基于多种生态系统服务综合重要性判定生态源地，并整合单一生态保护目标下的多重源地，识别综合生态源地共49536.10 km2，主要分布在珠三角外围和粤北生态发展区。基于最小累积阻力模型和电路模型，识别了总长度2268.07 km的生态廊道；夹点共32处，主要分布在中山市、珠海市、江门市、惠州市廊道中电流值较大的12处狭窄区；障碍点共44处，主要分布在广州市、中山市、珠海市、江门市、惠州市的19处，覆盖了廊道的大部分面积。整合多重生态保护目标，广东省生态保护修复策略的制定需要高度关注粤北生态发展区的生境质量提升，河湖水库及河岸带、库滨带的水生态安全，湛江市、汕头市的耕地保护和国土综合整治，沿海地区的自然灾害防范，同时积极开展珠三角的生态夹点保护和障碍点修复，重点提升生态廊道的连通性。 Abstract:Constructing ecological security pattern is an effectively spatial approach to alleviate the prominent contradiction between ecological protection and economic development to ensure sustainable development. However, the current construction of ecological security pattern emphasizes too much on synthesis. The simple method of superposition of multiple ecosystem services ignores the trade-offs and synergies among different ecosystem services, so it is difficult to directly support the ecological protection decision-making under different objectives. Taking Guangdong Province as an example, this study focused on seven important ecosystem services, including habitat maintenance, water conservation, water purification, grain production, soil conservation, flood risk mitigation, and coastal disaster mitigation. Ecological security patterns were constructed for single ecological conservation objectives, such as biodiversity conservation, water resource utilization, grain production, and natural disaster prevention. The results showed that the ecological security pattern for biodiversity conservation was distributed in a "double barrier zones" pattern, and the ecological sources were mainly distributed in the ecological development area of Northern Guangdong. The water security pattern for water resource utilization was distributed in the pattern of "five rivers-one belt", and the key protected areas were mainly located in rivers, lakes, reservoirs and the surrounding green space. Ecological sources for grain production were mainly distributed in the east and west wings of Guangdong Province. Ecological sources for natural disaster prevention were rarely distributed in Pearl River Delta, Zhanjiang and Shantou, but mainly concentrated in the ecological development area of Northern Guangdong. The comprehensively ecological sources with total area of 49536.10 km2 were identified by integrating the ecological sources determined based on the comprehensive importance of multiple ecosystem services, and the multiple sources under single ecological protection objectives, which were mainly distributed in the periphery of the Pearl River Delta and the ecological development area of Northern Guangdong. Based on the minimum cumulative resistance model and circuit model, ecological corridors with total length of 2268.07 km were identified, among which were long and narrow in the Pearl River Delta. There were 32 pinch points, mainly distributed in 12 narrows with high current value in the corridors of Zhongshan, Zhuhai, and Jiangmen. There were 44 barriers, mainly distributed in Zhongshan, Zhuhai, Jiangmen and Huizhou, with 19 barriers covering most of the corridors in these cities. For the integration of multiple ecological conservation objectives, several aspects should be focused in the formulation of ecological conservation and restoration strategies in Guangdong Province, including habitat quality improvement in ecological development area of Northern Guangdong, water security of rivers, lakes, reservoirs, riparian zones and reservoir shore zone, the cultivated land protection and comprehensive land control in Zhanjiang and Shantou, natural disaster prevention in coastal area. At the same time, the protection of pinch points and the restoration of barriers should be carried out to enhance the connectivity of the ecological corridors in the Pearl River Delta. 参考文献 相似文献 引证文献

基于生态安全格局的粤港澳地区陆域空间生态保护修复重点区域识别

区域和景观尺度的生态保护修复应以保障生态安全、促进生态过程实现为目标。将生态安全格局构建、生态连通性修复方法引入国土空间生态修复识别领域, 以粤港澳大湾区外延范围——粤港澳地区为研究区, 基于生态系统服务重要性和敏感性评价、最小阻力模型、电路理论模型, 识别了生态源地、生态廊道及障碍点、生态夹点、生态敏感区, 提供了一种中尺度的国土空间生态保护修复重点区域识别研究案例。结果表示：(1)研究区生态源地总面积5.27万km², 潜在生态廊道138条, 共同构成了环绕粤港澳大湾区的环形生态屏障, 但局部区域仍存在一定的保护空缺。(2)研究区生态障碍点、生态夹点面积分别为442.7、9.1 km², 对其进行针对性修复可显著改善生态连通性。(3)研究区生态敏感区共4302.48 km², 青云山、九连山、起微山等重要生态源地内存在部分生态退化区域, 对其进行修复可防范生态风险、提升生态功能。未来应通过空间规划途径对重要源地和生态廊道加强保护监管, 对生态节点、生态敏感区、生态退化区进行分区分类修复。研究结果可为未来粤港澳地区生态保护修复工作提供科学参考。;Ecological restoration in regional and landscape scale should aim to improve ecological connectivity and promote the realization of ecological processes. This paper introduces the ecological security pattern and the restoration of ecological connectivity into the field of ecological restoration identification. Taking the extended area of the Guangdong-Hong Kong-Macao Greater Bay Area, the Guangdong-Hong Kong-Macao region as the research area, based on the evaluation of the importance of ecological functions and ecological sensitivity, the minimum cumulative resistance model (MCR) and circuit theory model, the ecological source, ecological corridors, barriers, and ecological pinch points are identified, providing a meso-scale research case on the identification of key areas of land and space ecological restoration. The results indicate (1) The total area of ecological sources in the study area is 52700 km², which are mainly distributed in the main mountain ranges of northern, western and eastern Guangdong, and the central and eastern mountains of the Hong Kong Special Administrative Region, Lantau Island and Hong Kong Island. The ecological sources and ecological corridors together form a circular ecological barrier surrounding the Guangdong-Hong Kong-Macao Greater Bay Area, but there are still protection vacancies in some areas. (2) The areas of ecological barriers and ecological pinch points in the study area are 442.7 and 9.1 km² respectively. The targeted restoration of them can significantly improve ecological connectivity. (3) The ecological sensitive areas is 4302.48 km². There are some ecological degraded areas in important ecological sources such as Qingyun Mountain, Jiulian Mountain and Qiwei Mountain. Restoration of these areas can prevent ecological risks and improve ecological functions. In the future, ecological protection and restoration should strengthen the protection and supervision of important sources and ecological corridors through spatial planning, and carry out zoning and classification restoration of ecological nodes, ecological sensitive areas, and ecological degraded areas. The research results can provide a scientific reference for future ecological protection and restoration work in Guangdong, Hong Kong and Macao.

The Optimization and Application of 3-Bit Hermitian Gates and Multiple Control Toffoli Gates

The well-known 3-bit Hermitian gate (a Toffoli gate) has been implemented using Clifford + T circuits. Compared with the Peres gate, its implementation circuit requires more controlled-NOT (CNOT) gates. However, the Peres gate is not Hermitian. This paper reports four 3-bit Hermitian gates named LI gates. Whose realized circuits have the same T-count, T-depth, and CNOT-count as the Peres gate. Furthermore, two decomposition methods of a multiple control Toffoli (MCT) gate are proposed for different primary optimization goals. Then, we design the equality, less-than, and full comparators with the minimum circuit width using proposed Hermitian gates and optimized MCT gates. A fault-tolerant circuit is required for robust quantum computing. Clifford+T circuits are accepted solutions for fault-tolerant implementation. Considering T-count, T-depth, CNOT-count, and circuit width as the primary optimization goals, we design the optimized Clifford + T circuits of three comparators using LI gates and optimized MCT gates. Comparison and analysis show that the proposed comparators have better overall performances for T-count, T-depth, CNOT-count, and circuit width than the best-known comparators without quantum measurements.

Low-depth quantum state preparation

A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=\ensuremath{\lceil}{log}_{2}N\ensuremath{\rceil}$-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least $O(N)$ constant weight operations. However, the proof assumes that only $n$ qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with $O({n}^{2})$ circuit depth to encode any $N$ complex numbers using only single- and two-qubit gates, and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with $O({N}^{2})$ ancillary qubits, $O({n}^{2})$ circuit depth, and $O({n}^{2})$ average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits, and at most $O(n)$ qubits are entangled. We also prove a fundamental lower bound $\mathrm{\ensuremath{\Omega}}(n)$ for the minimum circuit depth and runtime with an arbitrary number of ancillary qubits, aligning with our scheme with $O({n}^{2})$. The algorithms are expected to have wide applications in both near-term and universal quantum computing.