Circuit Complexity Research Articles

Algebraic Language for the Efficient Representation and Optimization of Quantum Circuits

Abstract The use of graphical language in quantum computing for the representation of algorithms, although intuitive, is not very useful for different tasks such as the description of quantum circuits in text environments, the calculation of quantum states or the optimization of quantum circuits. While classical circuits can be represented either by circuit graphs or by Boolean expressions, quantum circuits have until now predominantly been illustrated as circuit graphs because no formal language for quantum circuits that allows algebraic manipulations has so far been accepted. This work proposes a means to represent quantum circuits in a convenient and concise manner, similar to the way Boolean expressions are used in classical circuits. The proposed notation allows the consistent and parameterized description of quantum algorithms, as well as the easy handling of the elements that compose it to achieve powerful optimizations in the number of gates of the circuits. To visualize it, a software implementation of an algebraic quantum circuit framework has been made, which allows describing quantum circuits, as well as their respective state vectors, using the proposed algebraic language.

State preparation by shallow circuits using feed forward

Fault tolerant quantum computers repetitively apply a four-step procedure: First, perform a few one and two-qubit quantum gates. Second, perform a syndrome measurement on a subset of the qubits. Third, perform fast classical computations to establish if and where errors occurred. And, fourth, correct the errors with a correction step. The next iteration applies the same procedure with new one and two-qubit gates. Even though current error-rates prohibit this procedure to work and fault tolerant quantum computing remains a distant goal, the same procedure can already prove useful today. In this work we make use of this four-step scheme not to carry out fault-tolerant computations, but to enhance short, constant-depth, quantum circuits that perform 1 qubit gates and nearest−neighbor 2 qubit gates.We introduce a new computational model called Local Alternating Quantum Classical Computations(LAQCC). In this model, qubits are placed in a grid and they can only interact with their direct neighbors; the quantum circuits are of constant depth with intermediate measurements; a classical controller can perform log-depth computations on these intermediate measurement outcomes and control future quantum operations based on the outcome. This model fits naturally between quantum algorithms in the NISQ era and full-fledged fault-tolerant quantum computation. We first prove that any Clifford circuit has an equivalent LAQCC circuit, and that any LAQCC circuit can be simulated by a QNC1circuit. Next, we conjecture the non-simulatability of LAQCC by showing that LAQCC contains the class of Instantaneous Quantum Polynomial-time circuits. We also show that any LAQCC circuit with polynomial-sized quantum circuits and unbounded classical computations is contained in the class of quantum circuits equipped with post-selection gates with respect to the task of state preparation. We continue by presenting LAQCC implementations of different subroutines, including OR-gates, quantum Fourier transforms and Threshold gates. These subroutines prove vital in constructing three state preparation routines in the main part of this work. Preparing a uniform superposition uses constant-depth arithmetic gates, combined with an exact Grover implementation by Long. For the W-state, we employ a compress-uncompress method to switch between a binary and one-hot encoding. This method extends to the more generalized Dicke-states, the superposition of n-bit strings of Hamming weight k, for k=O(n), but fails for higher k due to the birthday paradox. We extend this protocol to a protocol that prepares many-body scar states, highly excited states with low entanglement and longer coherence times than states with the same energy density. We present a circuit for preparing Dicke-states for larger k requiring log-depth circuits that maps between the factoradic number system and the combinatorial number system.

Central mechanisms of muscle tone regulation: implications for pain and performance

Muscle tone represents a foundational property of the motor system with the potential to impact musculoskeletal pain and motor performance. Muscle tone is involuntary, dynamically adaptive, interconnected across the body, sensitive to postural demands, and distinct from voluntary control. Research has historically focused on pathological tone, peripheral regulation, and contributions from passive tissues, without consideration of the neural regulation of active tone and its consequences, particularly for neurologically healthy individuals. Indeed, simplistic models based on the stretch reflex, which neglect the central regulation of tone, are still perpetuated today. Recent advances regarding tone are dispersed across different literatures, including animal physiology, pain science, motor control, neurology, and child development. This paper brings together diverse areas of research to construct a conceptual model of the neuroscience underlying active muscle tone. It highlights how multiple tonic drive networks tune the excitability of complex spinal feedback circuits in concert with various sources of sensory feedback and in relation to postural demands, gravity, and arousal levels. The paper also reveals how tonic muscle activity and excitability are disrupted in people with musculoskeletal pain and how tone disorders can lead to marked pain and motor impairment. The paper presents evidence that integrative somatic methods address the central regulation of tone and discusses potential mechanisms and implications for tone rehabilitation to improve pain and performance.

Metaplasticity-Enabled Graphene Quantum Dot Devices for Mitigating Catastrophic Forgetting in Artificial Neural Networks.

The limitations of deep neural networks in continuous learning stem from oversimplifying the complexities of biological neural circuits, often neglecting the dynamic balance between memory stability and learning plasticity. In this study, artificial synaptic devices enhanced with graphene quantum dots (GQDs) that exhibit metaplasticity is introduced, a higher-order form of synaptic plasticity that facilitates the dynamic regulation of memory and learning processes similar to those observed in biological systems. The GQDs-assisted devices utilize interface-mediated modifications in asymmetric conductive pathways, replicating classical synaptic plasticity mechanisms. This allows for repeatable and linearly programmable adjustments to future weight changes linked to historical weights. Incorporating metaplasticity is essential for achieving generalization within deep neural networks, which enables them to adapt more fluidly to new information while retaining previously acquired knowledge. The GQDs-device-based system achieved a 97% accuracy on the fourth MNIST dataset task, while consistently achieving performance levels above 94% on prior tasks. This performance substantiates the feasibility of directly transferring metaplasticity principles to deep neural networks, thereby addressing the challenges associated with catastrophic forgetting. These findings present a promising hardware solution for developing neuromorphic systems with robust and sustained learning capabilities that can effectively bridge the gap between artificial and biological neural networks.

Quantum implementation of bilinear interpolation algorithm based on NEQR and center alignment

Abstract In the field of quantum image processing, scaling techniques have been extensively studied as a critical subfield. Predominantly, these techniques leverage bilinear interpolation method. However, the current quantum bilinear interpolation algorithm remains in its initial version, resulting in a significant flaw: the centers of the source image and the interpolated image are misaligned. This flaw not only leads to results identical to nearest neighbor interpolation during integer multiple image scaling-down but also causes excessive qubit usage. To tackle these issues, our study introduces an innovative bilinear interpolation method with the following key advancements. Firstly, by integrating the NEQR representation with an enhanced bilinear interpolation from OpenCV, the central misalignment is effectively rectified. Secondly, resolving the central misalignment enables our method to prevent the degradation to nearest neighbor interpolation during integer multiple image reduction. Finally, based on the characteristics of optimization algorithms and quantum computing, along with simpler quantum modules and quantum convolution algorithms, the steps of the quantum image scaling algorithm have been optimized to reduce circuit complexity. Through a series of simulation experiments and complexity analyses, it has been demonstrated that our method, compared to the initial bilinear interpolation method, exhibits lower circuit complexity and significantly reduces qubit usage.

An Efficient ZK Compiler from SIMD Circuits to General Circuits

We propose a generic compiler that can convert any zero-knowledge (ZK) proof for SIMD circuits to general circuits efficiently, and an extension that can preserve the space complexity of the proof systems. Our compiler can immediately produce new results improving upon state of the art.By plugging in our compiler to Antman, an interactive sublinear-communication protocol, we improve the overall communication complexity for general circuits from O(C3/4) to O(C1/2). Our implementation shows that for a circuit of size 227, it achieves up to 83.6× improvement on communication compared to the state-of-the-art implementation. Its end-to-end running time is at least 70% faster in a 10Mbps network.Using the recent results on compressed Σ-protocol theory, we obtain a discrete-log-based constant-round zero-knowledge argument with O(C1/2) communication and common random string length, improving over the state of the art that has linear-size common random string and requires heavier computation.We improve the communication of a designated n-verifier zero-knowledge proof from O(nC/B+n2B2) to O(nC/B+n2). To demonstrate the scalability of our compilers, we were able to extract a commit-and-prove SIMD ZK from Ligero and cast it in our framework. We also give one instantiation derived from LegoSNARK, demonstrating that the idea of CP-SNARK also fits in our methodology.

Anti-Interference All-Optical Logic Computing Based on a 2D Polarization-Sensitive Photodiode.

Optical logic operation is promising for ultrafast information processing and optical computing due to the high computation speed and low power consumption. However, conventional optical logic devices require either a complex structure and circuit design or a constant voltage supply, which impedes the development of high-density integrated circuits. Here, all-optical logic devices are designed using a self-powered polarization-sensitive photodiode of the GeSe homojunction, which is attributed to an anisotropic band structure and built-in electric field. The single photodiode can realize linear logic functions (AND, OR, NAND) and a nonlinear logic gate (XOR) by programming wavelength, power density, and polarization angle. Moreover, complex logic functions (XNOR, Y = IN1, Y = IN2, Y = IN1, and Y = IN2) can be achieved through integrating two photodiodes in parallel. In addition, the neural network algorithm is utilized to validate the feasibility of all-optical logic computing and anti-interference. This work proposes an avenue to design an all-optical reconfigurable logic operation in polarization-sensitive devices.

The Descriptive Complexity of Graph Neural Networks

We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those definable in the guarded fragment GFO+C of first-order logic with counting and with built-in relations. This puts GNNs in the circuit complexity class (non-uniform) $\text{TC}^0$. Remarkably, the GNN families may use arbitrary real weights and a wide class of activation functions that includes the standard ReLU, logistic "sigmoid", and hyperbolic tangent functions. If the GNNs are allowed to use random initialisation and global readout (both standard features of GNNs widely used in practice), they can compute exactly the same queries as bounded depth Boolean circuits with threshold gates, that is, exactly the queries in $\text{TC}^0$. Moreover, we show that queries computable by a single GNN with piecewise linear activations and rational weights are definable in GFO+C without built-in relations. Therefore, they are contained in uniform $\text{TC}^0$.Comment: Journal version for TheoretiCS

Complexity is not enough for randomness

We study the dynamical generation of randomness in Brownian systems as a function of the degree of locality of the Hamiltonian. We first express the trace distance to a unitary design for these systems in terms of an effective equilibrium thermal partition function, and provide a set of conditions that guarantee a linear time to design. We relate the trace distance to design to spectral properties of the time-evolution operator. We apply these considerations to the Brownian pp-SYK model as a function of the degree of locality pp. We show that the time to design is linear, with a slope proportional to 1/p1/p. We corroborate that when pp is of order the system size this reproduces the behavior of a completely non-local Brownian model of random matrices. For the random matrix model, we reinterpret these results from the point of view of classical Brownian motion in the unitary manifold. Therefore, we find that the generation of randomness typically persists for exponentially long times in the system size, even for systems governed by highly non-local time-dependent Hamiltonians. We conjecture this to be a general property: there is no efficient way to generate approximate Haar random unitaries dynamically, unless a large degree of fine-tuning is present in the ensemble of time-dependent Hamiltonians. We contrast the slow generation of randomness to the growth of quantum complexity of the time-evolution operator. Using known bounds on circuit complexity for unitary designs, we obtain a lower bound determining that complexity grows at least linearly in time for Brownian systems. We argue that these bounds on circuit complexity are far from tight and that complexity grows at a much faster rate, at least for non-local systems.

Single-qubit gate teleportation provides a quantum advantage

Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work \cite{TerhalDiVincenzo04}, Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation \cite{wang2021possibilistic}, a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.

A thin film lithium niobate near-infrared platform for multiplexing quantum nodes

Practical quantum networks will require multi-qubit quantum nodes. This in turn will increase the complexity of the photonic circuits needed to control each qubit and require strategies to multiplex memories. Integrated photonics operating at visible to near-infrared (VNIR) wavelength range can provide solutions to these needs. In this work, we realize a VNIR thin-film lithium niobate (TFLN) integrated photonics platform with the key components to meet these requirements, including low-loss couplers (<1 dB/facet), switches (>20 dB extinction), and high-bandwidth electro-optic modulators (>50 GHz). With these devices, we demonstrate high-efficiency and CW-compatible frequency shifting (>50% efficiency at 15 GHz), as well as simultaneous laser amplitude and frequency control. Finally, we highlight an architecture for multiplexing quantum memories and outline how this platform can enable a 2-order of magnitude improvement in entanglement rates over single memory nodes. Our results demonstrate that TFLN can meet the necessary performance and scalability benchmarks to enable large-scale quantum nodes.

A Biomolecular Circuit for Automatic Gene Regulation in Mammalian Cells with CRISPR Technology.

We introduce a biomolecular circuit for precise control of gene expression in mammalian cells. The circuit leverages the stochiometric interaction between the artificial transcription factor VPR-dCas9 and the anti-CRISPR protein AcrIIA4, enhanced with synthetic coiled-coil domains to boost their interaction, to maintain the expression of a reporter protein constant across diverse experimental conditions, including fluctuations in protein degradation rates and plasmid concentrations, by automatically adjusting its mRNA level. This capability, known as robust perfect adaptation (RPA), is crucial for the stable functioning of biological systems and has wide-ranging implications for biotechnological applications. This system belongs to a class of biomolecular circuits named antithetic integral controllers, and it can be easily adapted to regulate any endogenous transcription factor thanks to the versatility of the CRISPR-Cas system. Finally, we show that RPA also holds in cells genomically integrated with the circuit, thus paving the way for practical applications in biotechnology that require stable cell lines.

A modular entanglement-based quantum computer architecture

Abstract We propose a modular quantum computation architecture based on utilizing multipartite entanglement. Each module consists of a small-scale quantum computer comprising data, memory and entangling qubits. Entangling qubits are used to selectively couple different modules by harnessing some non-controllable, distance-dependent interaction, which is effectively controlled and enhanced via a proper adjusting of the internal state of the qubits. In this way, multipartite entangled states with different entanglement topologies can be shared between modules. These states are stored in memory qubits where they can be further processed so they can eventually be used to deterministically perform certain classes of gates or circuits between modules on demand, including parallel controlled-\textit{Z} gates with arbitrary interaction patterns, multi-qubit gates or whole Clifford circuits, depending on their entanglement structure. The usage of different kinds of multipartite entanglement rather than Bell pairs allows for more efficient and flexible coupling between modules, leading to a scalable quantum computation architecture.

The glutamatergic projections from the PVT to mPFC govern methamphetamine-induced conditional place preference behaviors in mice

BackgroundDrug addiction is closely related to the dysregulation of complex neural circuits. However, the neural connections underlying the symptoms of methamphetamine (METH)-induced addiction have yet to be elucidated. MethodsWe conducted ΔFosB (Delta FBJ murine osteosarcoma viral oncogene homolog B) associated immunofluorescence and electrophysiological recording experiments to measure the neural activity of paraventricular thalamus (PVT) neurons in METH treated mice. Then, the METH-mediated conditional place preference (CPP) behaviors were evaluated after chemogenetic manipulation of PVT neurons. Additionally, the neural projection from PVT to medial prefrontal cortex (mPFC) was verified through Adeno-associated virus (AAV) mediating neural tracing method, and its role on METH-mediated CPP behaviors was determined using chemogenetic and neural ablation strategies. ResultsWe found that glutamatergic neurons in PVT were activated by METH. Activating the glutamatergic neurons in PVT promoted the METH-mediated CPP behaviors, while inhibiting these neurons attenuated the CPP behaviors. Moreover, we observed PVT neurons showed robust neuronal projections to mPFC, activation of the mPFC→projecting neurons in PVT or the afferent terminals in mPFC derived from PVT enhanced METH-mediated CPP performance, and ablating the mPFC neurons receipting neural projection from PVT impeded these increased METH-mediated CPP phenotypes. LimitationsThe underlying molecular mechanism of the dysfunctional PVT neurons after METH treatment and the PVT neurons regulating the activity of mPFC target neurons remains unclear. ConclusionsThese results shed light on that PVT is a key METH addiction-controlling nucleus, and PVT → mPFC projection regulated METH-mediated CPP behaviors, which could serve as a vital pathway for morbidity and treatment for METH-mediated addiction.

Optogenetic control of dopamine receptor 2 reveals a novel aspect of dopaminergic neurotransmission in motor function.

Dopaminergic neurotransmission plays a crucial role in motor function through the coordination of dopamine receptor (DRD) subtypes, such as DRD1 and DRD2, thus the functional imbalance of these receptors can lead to Parkinson's disease. However, due to the complexity of dopaminergic circuits in the brain, it is limited to investigating the individual functions of each DRD subtype in specific brain regions. Here, we developed a light-responsive chimeric DRD2, OptoDRD2, which can selectively activate DRD2-like signaling pathways with spatiotemporal resolution. OptoDRD2 was designed to include the light-sensitive component of rhodopsin and the intracellular signaling domain of DRD2. Upon illumination with blue light, OptoDRD2 triggered DRD2-like signaling pathways, such as Gαi/o subtype recruitment, a decrease in cAMP levels, and ERK phosphorylation. To explore unknown roles of DRD2 in glutamatergic cell populations of basal ganglia circuitry, OptoDRD2 was genetically expressed in excitatory neurons in lateral globus pallidus (LGP) of the male mouse brain. The optogenetic stimulation of OptoDRD2 in the LGP region affected a wide range of locomotion-related parameters, such as increased frequency of movement and decreased immobility time, resulting in the facilitation of motor function of living male mice. Therefore, our findings indicate a potential novel role for DRD2 in the excitatory neurons of the LGP region, suggesting that OptoDRD2 can be a valuable tool enabling the investigation of unknown roles of DRD2 at specific cell types or brain regions.Significance Statement We developed a light-responsive chimeric dopamine receptor type 2, OptoDRD2, by combining the blue-light sensing part of rhodopsin and intracellular functional regions of DRD2. OptoDRD2 can selectively trigger DRD2-like downstream signaling pathways upon illumination of blue light. To explore unknown roles of DRD2 in glutamatergic cell populations of basal ganglia circuitry, OptoDRD2 was genetically expressed in excitatory neurons at lateral globus pallidus (LGP) in the mouse brain. Optogenetic stimulation of OptoDRD2 in living mice suggested a potential novel function of DRD2 in the LGP that enhances motor outputs. Therefore, OptoDRD2 enabled the precise control of DRD2-like signaling in specific cell types and brain regions, allowing the exploration of potential novel DRD2 functions in living mice.

Accurate modeling and parameters estimation of photovoltaic models: Analytical and artificial intelligence solutions

The single-diode model is a widely used framework for simulating solar cell behavior. It consists of a diode, a current source, and two resistors to replicate real-world performance. This work introduces three alternative single-diode equivalent circuits with five parameters each. The current-voltage relationships of these equivalent circuits are derived using the Lambert W function, and a closed-form analytical solution is presented using Special Trans Function Theory (STFT). Additionally, the paper introduces a chaotic variant of the Gorilla Troops Optimizer (GTO), referred to as CGTO, for parameter estimation. The effectiveness of the proposed alternative single-diode models and the CGTO algorithm was validated by comparing their accuracy, using root mean square error (RMSE) metrics, against traditional models across various solar cells and conditions (different values of irradiance and temperature). The analysis confirmed that the alternative configurations could achieve comparable precision in modeling solar cell characteristics under different conditions, challenging the exclusivity of the standard single-diode model's configuration. This indicates that various single-diode solar cell models can effectively represent the current-voltage behavior of solar cells. Furthermore, the configuration of elements in the classic SDM equivalent circuit is not definitive or the most precise. This opens the door for the creation of more sophisticated models of solar cells with diverse element configurations.

PW-FBPNN: A Hybrid Fault Diagnosis Method for Power Circuit Systems Combining Principal Component Analysis, Wavelet Packet Transform, and Fuzzy Neural Networks

Due to the complexity of fault states and the non-linear relationship between input and output responses, fault diagnosis in complex power circuit systems faces significant challenges. This study proposes a novel hybrid method, PW-FBPNN, which integrates principal component analysis (PCA), wavelet packet transform (WPT), and fuzzy back propagation neural network (FBPNN) to enhance fault diagnosis. The effectiveness of this method was demonstrated through experiments on the voltage divider basic operational amplifier and the second-order filter circuit of the four operational amplifiers. PW-FBPNN achieved 100% accuracy in diagnosing most types of faults, with a minimum accuracy of 91.67% for challenging faults. This method was significantly superior to existing methods such as FCM-HMM-SVM and KICA-DNN in terms of accuracy and computational efficiency and could complete the diagnosis in just 0.01 seconds. These results indicate that PW-FBPNN has the potential to improve fault diagnosis in power circuit systems, providing a promising solution for enhancing system reliability and maintenance efficiency.

An Enhanced Detection Method of Hardware Trojan Based on CNN- Attention-LSTM

The security issues caused by the insertion of hardware Trojans seriously threaten the security and reliability of the entire hardware device. This article constructs a detection model that combines convolutional neural networks (CNN) and long short-term memory networks (LSTM), and introduces attention mechanism to enhance the model's ability to recognize complex circuits. This method can automatically learn and optimize feature extraction and classification models, reduce reliance on manual experience through training on large amounts of data, and improve the intelligence level of detection. Especially, by combining attention mechanisms and LSTM models, it is possible to more effectively capture small anomalies in circuit design and improve the accuracy and efficiency of hardware Trojan detection. The experimental results show that the proposed CNN-Attention-LSTM model exhibits superior Trojan detection performance and good generalization ability on different datasets, with an precision of 96.3%, a recall rate of 94.7%, and an F1 score of 95.5%.

Unified linear response theory of quantum electronic circuits

Modeling the electrical response of multi-level quantum systems at finite frequency has been typically performed in the context of two incomplete paradigms: (i) input-output theory, which is valid at any frequency but neglects dynamic losses, and (ii) semiclassical theory, which captures dynamic dissipation effects well but is only accurate at low frequencies. Here, we develop a unifying theory, valid for arbitrary frequencies, that captures both the small-signal quantum behavior and the non-unitary effects introduced by relaxation and dephasing. The theory allows a multi-level system to be described by a universal small-signal equivalent-circuit model, a resonant RLC circuit, whose topology only depends on the number of energy levels. We apply our model to a double-quantum-dot charge qubit and a Majorana qubit, showing the capability to continuously describe the systems from adiabatic to resonant and from coherent to incoherent, suggesting new and realistic experiments for improved quantum state readout. Our model will facilitate the design of hybrid quantum–classical circuits and the simulation of qubit control and quantum state readout.

A Study of High Transient Response Low Dropout Linear Regulator Chips

Abstract. With the rapid development of the microelectronics industry in the world, electronic products are being updated more and more quickly. This has created a growing large market demand for power management chips. Low drop-out linear regulators have become one of the most widely used types of power management chips due to their advantages of high stability, low drop-out voltage, and fast response. This paper is a data collection study and comparison of improvement methods based on high transient response low drop-out linear regulators. It describes the basic principles of LDOs as well as the principles, advantages and disadvantages of different improvement methods. It was found that the method of shortening the overshoot and undershoot durations by constructing transient enhancement circuits was the best in terms of performance among the following research methods. The stability of capacitor-less LDO is harder to control. Using compensation circuits to improve stability will increase circuit complexity. The capacitor-coupled current mirror method has a longer startup time, because it takes some time for it to reach homeostasis. The high complexity and energy consumption of the dual feedback loop structure makes the circuit costly.