Large Circuits Research Articles

Boost efficiency with buffer and bottom stack optimization in Cu2BaSn(S,Se)4 solar cells by simulation

Cu2BaSn(S,Se)4 is gaining tremendous attention as a potential absorber due to its non-toxicity, earth abundance, and low antisite defects opposing Cu2ZnSn(S,Se)4. However, the highest experimental efficiency of 6.17 % is achieved with the device structure Al:ZnO/Mg:ZnO/Zn1-xCdxS/Cu2BaSn(S,Se)4/Mo where the drawback is large open circuit voltage (VOC) loss stemming from the large cliff at the absorber/buffer interface and back contact recombination. Therefore, finding a suitable non-toxic buffer with modification of the bottom stack is crucial. In this regard, Cu2BaSn(S,Se)4 solar cells based on diverse buffers are numerically simulated using SCAPS-1D with Ni as back contact and introducing back surface field (BSF) at the absorber/Ni interface. At first, a baseline model validating the experimental efficiency is designed. The application of Ni enhanced efficiency to 7.92 % due to the formation of ohmic contact. Further, it is improved to 9.91 % with anti-reflection coating. Afterward, a total of 780 solar cells were designed with six buffer and eight BSF combinations by optimizing the absorber, buffer, and interface properties where the highest efficiency of 28.11 % with incredible fill factor (90 %) and less VOC loss (0.24 V) is accomplished for the Al:ZnO/Mg:ZnO/TiO2/Cu2BaSn(S,Se)4/CuI/Ni solar cell. Further, the importance of BSF is analyzed via energy band diagrams, Mott-Schottky and Nyquist plots. The outcomes disclosed that the BSF greatly influences the energy band alignment, built-in potential, depletion width, and recombination resistance of solar cells, underscoring its significance in improving performance. Overall, the present work proposes an efficient strategy to modify the device configuration of Cu2BaSn(S,Se)4 solar cells to enhance their efficiency.

Energy Band Alignment and Defect Synergistic Regulation Enable Air-Solution-Processed Kesterite Solar Cells With the Lowest VOC Deficit.

The major challenge in preparing high-performance Cu2ZnSn(S,Se)4 solar cells is the large open circuit voltage deficit (VOC-def). A new strategy utilizing the synergistic substitution of Ag and In dual cations has been proposed to simultaneously address the problems of undesirable interface band alignment and high-density detrimental bulk defects, obtaining decreased carrier recombination rate and increased minority carrier lifetime. The shorter In-S/Se bonds move the CBM higher by generating stronger repulsive force than the Sn-S/Se bonds, thus adjusting the interface band alignment. Ag substitution can effectively suppress Cu─Zn disorder, while Ag, In dual substitution can further passivate Sn-related defects and solve the issue of low carrier concentration in Ag single-substituted samples. Besides, the superior carrier property of In-Se materials significantly enhanced the device carrier lifetime and minority carrier diffusion length. The state-of-the-art air-solution-processed CZTSSe device without any addition treatment with 14.33% efficiency and 580mV VOC is obtained, possessing the lowest VOC-def value currently available in the CZTSSe field (VOC/VOC SQ = 64.7%). This work emphasizes the synergistic modulation of band alignment, defect level, grain growth, and carrier transportation by dual cation substitution, which paves a convenient and effective way to realize high-performance solar cells and photovoltaic devices.

An efficient leakage power optimization framework based on reinforcement learning with graph neural network

Threshold voltage (Vth\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{th}$$\\end{document}) assignment is convenient for leakage optimization due to the exponential relation between leakage power and Vth\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{th}$$\\end{document} by swapping logic cells without routing effort. However, it poses great challenge in large scale circuit design as an NP-hard problem. Machine learning-based approaches have been proposed to solve this problem, aiming to achieve well tradeoff between leakage power reduction and runtime speed up without new induced timing violation. In this paper, a leakage power optimization framework based on reinforcement learning (RL) with graph neural network (GNN) is first-ever proposed to formulate Vth\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{th}$$\\end{document} assignment as a RL process by learning timing and physical characteristics of each circuit instance with GNN. Multiple instances are selected in a non-overlapped manner for each RL action iteration to speed up convergence and decouple timing interdependence along circuit path, where the corresponding reward is carefully defined to tradeoff between leakage reduction and potential timing violation. The proposed framework was validated by the Opencores and IWLS 2005 benchmark circuits with TSMC 28 nm technology. Experimental results demonstrate that our work outperforms prior non-analytical and GNN-based methods with better leakage power optimization by additional 5% to 17% reduction, which is highly consistent with the commercial tool. When transferring the trained RL-based framework to unseen circuits, it achieves the roughly identical leakage optimization results as seen circuit and speed up the runtime by 5.7×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} to 8.5×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ imes$$\\end{document} compared with commercial tool.

Probabilistic safety analysis of the large primary circuit leakages accident scenarios in the VVER-reactor

Probabilistic safety analysis of the loss of coolant accidents in the VVER-type reactor plant has been performed taking into account the internal initiating events of the reactor primary circuit large leakages. Swedish program code RiskSpectrum PSA was used for probabilistic safety analysis. Logical probabilistic models of the accident scenarios of the large primary circuit leakages in the VVER-type reactor were developed taking into account different operation modes of the power plant unit. Critical paths and probabilities of the accident scenarios occurrence of the large leakages were identified. The critical path of development of the reactor primary circuit large leakages accident with large leakages of 140–346 mm diameters is the accident sequence with a leak in the pipeline to the reactor pressurizer vessel. It has been established that the greatest contribution to the failure of safety functions during this initiating event is made by the failures due to common causes of the supporting systems (cooling and ventilation systems), critical consumers cooling circuit, emergency injection system. The critical path of the accident with large leakages of 346–850 mm diameters is the accident sequence with the rupture of any of the four primary circuit loops. The greatest contribution to the failure of safety functions during this initiating event is made by the failures due to common causes of the emergency injection system elements. Based on the accident analysis, recommendations for increase of performance reliability of safety functions during the large leakages accidents under all operation states of the nuclear power plant unit were given. In order to increase reliability of safety systems, it is necessary to eliminate failures due to common causes of equipment, increase the reliability of operation of supporting systems, change the maintenance and checking equipment procedures.

The Brain's Best Kept Secret Is Its Degenerate Structure.

Degeneracy is defined as multiple sets of solutions that can produce very similar system performance. Degeneracy is seen across phylogenetic scales, in all kinds of organisms. In neuroscience, degeneracy can be seen in the constellation of biophysical properties that produce a neuron's characteristic intrinsic properties and/or the constellation of mechanisms that determine circuit outputs or behavior. Here, we present examples of degeneracy at multiple levels of organization, from single-cell behavior, small circuits, large circuits, and, in cognition, drawing conclusions from work ranging from bacteria to human cognition. Degeneracy allows the individual-to-individual variability within a population that creates potential for evolution.

Circuits for the spectroscopic readout of bits from molecular quantum-dot cellular automata

Molecular quantum-dot cellular automata (QCA) may provide high speed, low-power, classical information processing in the post-CMOS era. The readout of molecular QCA bits is challenging because the molecules may be much smaller than transistors and even single-electron transistors. This paper builds on a recent proposal for the spectroscopic readout of bits from asymmetric QCA molecules. Here, we propose circuits for fanning out a bit onto a large QCA circuit to increase the spectroscopic signal-to-noise ratio. As the number of molecules in a fanout circuit grows, the internal bias of each asymmetric cell accumulates, and the circuit may become stuck, tolerating only a very small internal bias. We also propose the use of an applied electric field to compensate for a candidate molecule’s internal bias, thereby restoring switchability, even when the internal bias is significant.

Solving the Hele–Shaw flow using the Harrow–Hassidim–Lloyd algorithm on superconducting devices: A study of efficiency and challenges

The development of quantum processors for practical fluid flow problems is a promising yet distant goal. Recent advances in quantum linear solvers have highlighted their potential for classical fluid dynamics. In this study, we evaluate the Harrow–Hassidim–Lloyd (HHL) quantum linear systems algorithm (QLSA) for solving the idealized Hele–Shaw flow. Our focus is on the accuracy and computational cost of the HHL solver, which we find to be sensitive to the condition number, scaling exponentially with problem size. This emphasizes the need for preconditioning to enhance the practical use of QLSAs in fluid flow applications. Moreover, we perform shots-based simulations on quantum simulators and test the HHL solver on superconducting quantum devices, where noise, large circuit depths, and gate errors limit performance. Error suppression and mitigation techniques improve accuracy, suggesting that such fluid flow problems can benchmark noise mitigation efforts. Our findings provide a foundation for future, more complex application of QLSAs in fluid flow simulations.

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.

Partitioning of a 2-bit hash function across 66 communicating cells.

Powerful distributed computing can be achieved by communicating cells that individually perform simple operations. Here, we report design software to divide a large genetic circuit across cells as well as the genetic parts to implement the subcircuits in their genomes. These tools were demonstrated using a 2-bit version of the MD5 hashing algorithm, which is an early predecessor to the cryptographic functions underlying cryptocurrency. One iteration requires 110 logic gates, which were partitioned across 66 Escherichia coli strains, requiring the introduction of a total of 1.1 Mb of recombinant DNA into their genomes. The strains were individually experimentally verified to integrate their assigned input signals, process this information correctly and propagate the result to the cell in the next layer. This work demonstrates the potential to obtain programable control of multicellular biological processes.

Robust Qubit Mapping Algorithm via Double-Source Optimal Routing on Large Quantum Circuits

Qubit mapping is a critical aspect of implementing quantum circuits on real hardware devices. Currently, the existing algorithms for qubit mapping encounter difficulties when dealing with larger circuit sizes involving hundreds of qubits. In this article, we introduce an innovative qubit mapping algorithm, Duostra, tailored to address the challenge of implementing large-scale quantum circuits on real hardware devices with limited connectivity. Duostra operates by efficiently determining optimal paths for double-qubit gates and inserting SWAP gates accordingly to implement the double-qubit operations on real devices. Together with two heuristic scheduling algorithms, Limitedly Exhaustive Search and Shortest-Path Estimation, it yields results of good quality within a reasonable runtime, thereby striving toward achieving quantum advantage. Experimental results showcase our algorithm’s superiority, especially for large circuits beyond the NISQ era. For example, on large circuits with more than 50 qubits, we can reduce the mapping cost on an average 21.75% over the virtual best results among QMAP, t \(|ket\rangle\) , Qiskit, and SABRE. Besides, for mid-size circuits such as the SABRE-large benchmark, we improve the mapping costs by 4.5%, 5.2%, 16.3%, 20.7%, and 25.7%, when compared to QMAP, TOQM, t \(|ket\rangle\) , Qiskit, and SABRE, respectively.

Recent Progresses on Hybrid Lithium Niobate External Cavity Semiconductor Lasers.

Thin film lithium niobate (TFLN) has become a promising material platform for large scale photonic integrated circuits (PICs). As an indispensable component in PICs, on-chip electrically tunable narrow-linewidth lasers have attracted widespread attention in recent years due to their significant applications in high-speed optical communication, coherent detection, precision metrology, laser cooling, coherent transmission systems, light detection and ranging (LiDAR). However, research on electrically driven, high-power, and narrow-linewidth laser sources on TFLN platforms is still in its infancy. This review summarizes the recent progress on the narrow-linewidth compact laser sources boosted by hybrid TFLN/III-V semiconductor integration techniques, which will offer an alternative solution for on-chip high performance lasers for the future TFLN PIC industry and cutting-edge sciences. The review begins with a brief introduction of the current status of compact external cavity semiconductor lasers (ECSLs) and recently developed TFLN photonics. The following section presents various ECSLs based on TFLN photonic chips with different photonic structures to construct external cavity for on-chip optical feedback. Some conclusions and future perspectives are provided.

A molecular proximity sensor based on an engineered, dual-component guide RNA.

One of the goals of synthetic biology is to enable the design of arbitrary molecular circuits with programmable inputs and outputs. Such circuits bridge the properties of electronic and natural circuits, processing information in a predictable manner within living cells. Genome editing is a potentially powerful component of synthetic molecular circuits, whether for modulating the expression of a target gene or for stably recording information to genomic DNA. However, programming molecular events such as protein-protein interactions or induced proximity as triggers for genome editing remains challenging. Here we demonstrate a strategy termed "P3 editing", which links protein-protein proximity to the formation of a functional CRISPR-Cas9 dual-component guide RNA. By engineering the crRNA:tracrRNA interaction, we demonstrate that various known protein-protein interactions, as well as the chemically-induced dimerization of protein domains, can be used to activate prime editing or base editing in human cells. Additionally, we explore how P3 editing can incorporate outputs from ADAR-based RNA sensors, potentially allowing specific RNAs to induce specific genome edits within a larger circuit. Our strategy enhances the controllability of CRISPR-based genome editing, facilitating its use in synthetic molecular circuits deployed in living cells.

Heterointerface engineering of yolk-shell-structured Mn2O3/RuO2 for boosting oxygen electrocatalysis in rechargeable liquid and flexible zinc-air batteries

Rational construction of high-efficient bifunctional oxygen electrocatalysts is of crucial significance for rechargeable Zn-air batteries (ZABs). Here, the yolk-shell-structured Mn2O3/RuO2 heterojunction is purposely constructed via the Kirkendall effect as a robust bifunctional oxygen electrocatalyst for simultaneously driving oxygen evolution and reduction reactions (OER and ORR). The strong interactions between Mn2O3 and RuO2 induces the surface reconstruction that brings the electronic transfer from Mn to Ru, and the changes of coordination environments of metal atoms. Meanwhile, the yolk-shell structure enables maximum contact of the active sites with the electrolyte and prevents the dissolution and peroxidation of active species. As a result, the yolk-shell-structured Mn2O3/RuO2 shows an outstanding bifunctional activity with a very low potential gap of ΔE = 0.60 V. Moreover, the ZABs assembled with Mn2O3/RuO2 render a large open circuit voltage of 1.53 V, a high specific capacity of 742.1 mA h g−1 and an exceptional cycling stability over 850 h that significantly outperforms those of Pt/C+RuO2-based ZABs. Moreover, the self-made flexible solid-state ZAB with Mn2O3/RuO2 cathode also shows good charge–discharge reversibility and flexibility at different bending angles. This work provides a feasible method for the design of efficient oxygen electrocatalysts to promote the practical application of ZABs.

Automatic Correction of Arithmetic Circuits in the Presence of Multiple Bugs by Groebner Basis Modification

One promising approach to verify large arithmetic circuits is making use of Symbolic Computer Algebra (SCA), where the circuit and the specification are translated to a set of polynomials, and the verification is performed by the ideal membership testing. Here, the main problem is the monomial explosion for buggy arithmetic circuits, which makes obtaining the word-level remainder become unfeasible. So, automatic correction of such circuits remains a significant challenge. Our proposed correction method partitions the circuit based on primary output bits and modifies the related Groebner basis based on the given suspicious gates, which makes it independent of the word-level remainder. We have applied our method to various signed and unsigned multipliers, with various sizes and numbers of suspicious and buggy gates. The results show that the proposed method corrects the bugs without area overhead. Moreover, it is able to correct the buggy circuit on average 51.9× and 45.72× faster in comparison with the state-of-the-art correction techniques, having single and multiple bugs, respectively.

Advancing Global Pose Refinement: A Linear, Parameter-Free Model for Closed Circuits via Quaternion Interpolation.

Global pose refinement is a significant challenge within Simultaneous Localization and Mapping (SLAM) frameworks. For LIDAR-based SLAM systems, pose refinement is integral to correcting drift caused by the successive registration of 3D point clouds collected by the sensor. A divergence between the actual and calculated platform paths characterizes this error. In response to this challenge, we propose a linear, parameter-free model that uses a closed circuit for global trajectory corrections. Our model maps rotations to quaternions and uses Spherical Linear Interpolation (SLERP) for transitions between them. The intervals are established by the constraint set by the Least Squares (LS) method on rotation closure and are proportional to the circuit's size. Translations are globally adjusted in a distinct linear phase. Additionally, we suggest a coarse-to-fine pairwise registration method, integrating Fast Global Registration and Generalized ICP with multiscale sampling and filtering. The proposed approach is tested on three varied datasets of point clouds, including Mobile Laser Scanners and Terrestrial Laser Scanners. These diverse datasets affirm the model's effectiveness in 3D pose estimation, with substantial pose differences and efficient pose optimization in larger circuits.

A novel design of multiplexer based on the cellular interaction in quantum dot technology with energy dissipation analysis

This paper addresses the challenge of efficiently designing multiplexer structures in quantum-dot technology circuits. Specifically, it introduces a novel approach to constructing a 2-to-1 multiplexer through a unique gate design that relies on the interaction between cells. The key focus of this design is to minimize the utilization of cells, thereby conserving space and facilitating the creation of more complex combinational and sequential circuits. The methodology involves developing a gate structure that requires the least number of cells compared to existing designs. This reduction in cell usage not only optimizes space utilization but also enhances the scalability of the multiplexer for integration into larger circuits. The proposed gate structure demonstrates a significant improvement, achieving a 15% reduction in the number of cells compared to the previously best-known design. To further evaluate the effectiveness of this novel gate design, the study extends its analysis to include the implementation of various complex circuits such as a 4-to-1 multiplexer, D latch, and T latch. These structures are synthesized using the newly proposed gate design as a fundamental building block. To validate the functionality and performance of these circuits, simulations are conducted using the QCADesigner simulation tool. This comprehensive simulation enables a thorough assessment of the proposed structures across different circuit configurations, providing insights into their operational efficiency and suitability for practical applications in quantum-dot technology.

Investigating Dynamic Behavior in SAG Mill Pebble Recycling Circuits: A Simulation Approach

The dynamics of milling circuits, particularly those involving Semi-Autogenous Grinding (SAG) mills, are not adequately studied, despite their critical importance in mineral processing. This paper aims to investigate the dynamic behavior of an SAG mill pebble recycling circuit under varying feed ore conditions, focusing on both uncontrollable parameters (such as ore hardness) and controllable parameters (including circuit layout and pebble crusher configurations). The study is carried out with Simulink dynamic simulations. Our findings reveal several key insights. Firstly, plant designs based solely on static simulations may not be adequate for large or complex circuits, as they fail to account for the dynamic nature of milling processes. Second, incorporating stockpiles after pebble crushing can effectively mitigate the impact of dynamic fluctuations, leading to more stable circuit performance. Third, different circuit layouts can facilitate easier maintenance and operational flexibility. Notably, finer pebble crushing can enhance circuit throughput by 5% to 10%.

Inhomogeneous Halide Anions Distribution along Out-of-Plane Direction in Wide-Bandgap Perovskite Solar Cells and Its Effect on Open Circuit Voltage Loss and Phase Segregation.

The large open circuit voltage (VOC) loss and phase segregation are two main obstacles hindering the development of wide-bandgap perovskite solar cells (PSCs). Even though substantial progress has been made through crystallization regulation and surface modification on perovskite, the mechanism of VOC loss and phase segregation has rarely been studied. In this paper, we first investigate the halide ions distribution along the out-of-plane direction and find the initial inhomogeneous distribution of halide ions during the crystallization process is an important reason. It leads to the formation of an unfavorable potential well in PSCs, resulting in VOC loss as well as generation of strong strain exacerbating phase segregation. Through introducing melatonin (MT) into perovskite precursors, a homogeneous distribution of halide anions is realized due to the well-regulated crystallization. Consequently, the treated PSCs exhibit an optimized power conversion efficiency (PCE) of 22.88% with a VOC loss as low as 0.38 V, which are the best values for wide-bandgap PSCs up to now.

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits and discuss the mechanisms for this advantage.

АНАЛІЗ МЕТОДІВ ОПТИМІЗАЦІЇ ГЛИБИНИ КВАНТОВОЇ СХЕМИ

This work reviews methods for optimizing quantum circuit depth, encompassing theoretical techniques, algorithmic innovations, and practical applications. Recent advancements demonstrate substantial improvements in circuit depth optimization, yet the issue of scalability remains unresolved. Key research contributions, such as the advanced exact synthesis of Clifford+T circuits, have shown promising results in reducing the number of T-gates, thus enhancing computational efficiency. However, the practical implementation of these methods in real-world noisy environments has yet to be fully evaluated. Further studies have developed automated optimization techniques for large quantum circuits with continuous parameters, significantly minimizing gate counts while maintaining structural integrity. Despite these advancements, challenges persist in assessing the performance of these optimized circuits on actual quantum hardware and integrating them into various quantum algorithms. The qubit routing problem also presents significant hurdles, particularly in systems with limited communication, necessitating effective methodologies to optimize qubit placement and movement. A comprehensive full-stack approach, incorporating hardware, software, and compiler optimizations, has provided valuable insights into architectural comparisons and design strategies. This approach highlights the importance of noise-aware compilation and the need for microarchitecture-specific optimizations to improve program success rates on current quantum devices. This paper underscores the need for scalable, hardware-agnostic optimization methods and extensive experimental validation. Integrating graph neural networks for quantum circuit optimization presents a promising future research direction. The analysis concludes that while significant progress has been made, unresolved issues such as computational complexity, limited experimental validation, and the diversity of quantum algorithms necessitate ongoing research to fully realize the potential of quantum computing. In conclusion, optimizing the depth of quantum circuits is a multifaceted problem requiring continuous research and development. The integration of theoretical advancements with practical implementations is crucial for overcoming current limitations and unlocking the full potential of quantum computing. Continued efforts in this area will be vital for achieving scalable and efficient quantum computations