Gaussian Sampling Research Articles

Linear Cross-Entropy Certification of Quantum Computational Advantage in Gaussian Boson Sampling

Validation of quantum advantage claims in the context of Gaussian boson sampling (GBS) currently relies on providing evidence that the experimental samples genuinely follow their corresponding ground truth, i.e., the theoretical model of the experiment that includes all the possible losses that the experimenters can account for. This approach to verification has an important drawback: it is necessary to assume that the ground truth distributions are computationally hard to sample, that is, that they are sufficiently close to the distribution of the ideal, lossless experiment, for which there is evidence that sampling, either exactly or approximately, is a computationally hard task. This assumption, which cannot be easily confirmed, opens the door to classical algorithms that exploit the noise in the ground truth to efficiently simulate the experiments, thus undermining any quantum advantage claim. In this work, we argue that one can avoid this issue by validating GBS implementations using their corresponding ideal distributions directly. We explain how to use a modified version of the linear cross-entropy, a quantity that we call the LXE score, to find reference values that help us assess how close a given GBS implementation is to its corresponding ideal model. Finally, we analytically compute the score that would be obtained by a lossless GBS implementation. Published by the American Physical Society 2024

Realistic photon-number resolution in Gaussian boson sampling

Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024

CLLS: Efficient certificateless lattice-based signature in VANETs

The rapid development of Vehicular Ad-hoc Network (VANETs) has improved road safety and traffic management, and brought great convenience to intelligent transportation system (ITS). However, the transmission of data over open channels caused many security issues. Certificateless cryptography solves the certificate management and key escrow problems, which makes it the primary method for message authentication in VANETs. However, with the emergence of quantum computing, traditional cryptography faces a significant challenge. Lattice-based cryptography are regarded as effective post-quantum ciphers. Nevertheless, nearly all existing lattice-based certificateless signature schemes rely on Gaussian sampling or trapdoor techniques, resulting in computational inefficiencies and large key and signature sizes that are impractical for VANETs. To address these issues, we proposed the first efficient algebraic lattice-based certificateless signature scheme in VANETs based on the Dilithium signature algorithm. The security of our certificateless lattice-based signature(CLLS) scheme is based on the MSIS and MLWE hardness assumption, which makes the scheme resistant to quantum attacks and easy to implement. Our scheme did not use Gaussian sampling or trapdoor techniques, which improve the computational and storage efficiency. As a result, the public key of our scheme is 1X smaller than the previous scheme and the size of signature is 2X smaller than the previous efficient algebraic lattice scheme. In addition, compared to the most efficient existing CLLS scheme, the signing and verification computation cost of our scheme are reduced by 20% and 55% respectively and our proposed CLLS scheme has low power consumption. Furthermore, the security of our scheme achieves strong unforgeability against chosen-message attacks(SUF-CMA) in the random oracle model(ROM), which surpasses that of existing lattice-based certificateless signature schemes.

A dual-sampling based evolutionary algorithm for large-scale multi-objective optimization

The vast search space in large-scale multi-objective optimization represents a significant challenge for evolutionary algorithms to converge towards the Pareto Front. As an effective search strategy, direction-guided sampling technique could improve the search efficiency by exploring along the approximated directions to approach the Pareto set. However, the approximated directions may fail to interact with the true Pareto set and result in inefficient search. To address this issue, a dual-sampling method is proposed in this paper. In addition to the samples along the directions approximated by direction-guided sampling, fuzzy Gaussian sampling is applied to adjust the search direction and generate more accurate and evenly distributed solutions. Moreover, a convergence-and-diversity-based mating selection is introduced to balance the exploration and exploitation. The experiments on 72 test benchmarks with bi- and tri-objectives and 500 to 5000 decision variables show the superiority of the proposed algorithm compare with the state-of-the-art algorithms.

A Not So Discrete Sampler: Power Analysis Attacks on HAWK signature scheme

HAWK is a lattice-based signature scheme candidate to the fourth call of the NIST’s Post-Quantum standardization campaign. Considered as a cousin of Falcon (one of the future NIST post-quantum standards) one can wonder whether HAWK shares the same drawbacks as Falcon in terms of side-channel attacks. Indeed, Falcon signature algorithm and particularly its Gaussian sampler, has shown to be highly vulnerable to power-analysis attacks. Besides, efficiently protecting Falcon’s signature algorithm against these attacks seems a very challenging task. This work presents the first power analysis leakage review on HAWK signature scheme: it extensively assesses the vulnerabilities of a central and sensitive brick of the scheme, the discrete Gaussian sampler. Knowing the output x of the sampler for a given signature leads to linear information about the private key of the scheme. This paper includes several demonstrations of simple power analysis attacks targeting this sample x with various attacker strengths, all of them performed on the reference implementation on a ChipWhisperer Lite with STM32F3 target (ARM Cortex M4). We report being able to perform key recoveries with very low (to no) offline resources. As this reference implementation of HAWK is not claimed to be protected against side-channel attacks, the existence of such attacks is not surprising, but they still concretely warn about the use of this unprotected signature on physical devices. To go further, our study proposes a generic way of assessing the performance of a sidechannel attack on x even when less information is recovered, in a setting where some protections are implemented or when the attacker has less measurement possibilities. While it is easy to see that x is a sensitive value, quantifying the residual complexity of the key recovery with some knowledge about x (like the parity or the sign of some coefficients) is not straightforward as the underlying hardness assumption is the newly introduced Module-LIP problem. We propose to adapt the existing methodology of leaky LWE estimation tools (Dachman-Soled et al. at Crypto 2020) to exploit the retrieved information and lower down the residual key recovery complexity. To finish, we propose an ad-hoc technique to lower down the leakage on the identified vulnerability points. These modifications prevent our attacks on our platform and come with essentially no cost in terms of performance. It could be seen as a temporary solution and encourages more analysis on proven side-channel protection of HAWK like masking.

LB-CLAS: Lattice-based conditional privacy-preserving certificateless aggregate signature scheme for VANET

The rapid development of vehicular ad-hoc networks (VANETs) has brought great convenience to intelligent transportation, and the secure transmission of information in VANETs has become a serious problem. In addition, the protection of private information of vehicles is also a key issue. Aiming at the problem of how to guarantee the secure transmission of information in VANETs under the condition of satisfying security and privacy, we propose a lattice-based conditional privacy-preserving certificateless aggregate signature scheme (LB-CLAS) for VANETs. Instead of using Number Theory Research Unit (NTRU) lattices and discrete Gaussian sampling, the proposed LB-CLAS scheme is based on algebraic lattice. In addition, based on the module version of Small Integer Solution (MSIS) and module version of Learning With Error (MLWE) hard problems, we prove that the LB-CLAS scheme is existential unforgeability under adaptively chosen message attacks (EUF-CMA). Our LB-CLAS scheme employs individual signature verification in vehicle-to-vehicle (V2V) mode, while utilizing aggregate signatures and batch verification in vehicle-to-infrastructure (V2I) mode, with slightly differing transmission parameters between the two modes. Based on Dilithium, our LB-CLAS scheme solves the problem of high storage overhead and computational cost of existing schemes. The performance analysis shows that our LB-CLAS scheme is more efficient in terms of computation cost, storage overhead, and power consumption compared to existing schemes. Compared with existing schemes, our LB-CLAS scheme reduces the signature and verification overheads by more than 17.6% and 43.4%, respectively. Our LB-CLAS program also has significant advantages in batch verification. As the number of vehicles increases, our batch certification time cost is reduced by more than 90%. In addition, our LB-CLAS scheme has the smallest signature length, with a signature size that is 1X smaller than the most efficient existing scheme for the same level of security.

Frozen Gaussian sampling for scalar wave equations

In this article, we introduce the frozen Gaussian sampling (FGS) algorithm to solve the scalar wave equation in the high-frequency regime. The FGS algorithm is a Monte Carlo sampling strategy based on the frozen Gaussian approximation, which greatly reduces the computation workload in wave propagation and reconstruction. In this work, we propose feasible and detailed procedures to implement the FGS algorithm to approximate scalar wave equations with Gaussian and WKB initial conditions respectively. For both initial data cases, we rigorously analyze the error of applying this algorithm to wave equations of dimensionality d ≥ 3. In Gaussian initial data cases, we prove that the sampling error due to the Monte Carlo method is independent of the typical wave number. We also derive a quantitative bound of the sampling error in WKB initial data cases. Finally, we validate the performance of the FGS and the theoretical estimates about the sampling error through various numerical examples, which include using the FGS to solve wave equations with both Gaussian and WKB initial data of dimensionality d = 1, 2, and 3.

Smooth joint motion planning for redundant fiber placement manipulator based on improved RRT*

In automated fiber placement (AFP), addressing the continuous motion planning challenge of redundant layup manipulators in complex environments, this paper proposes an offline redundancy optimization algorithm based on improved RRT* (Rapidly-exploring Random Trees). This algorithm maximizes the utilization of kinematic redundancy to derive smooth joint trajectories devoid of collisions and singularities. Firstly, the algorithm entails constructing a search map by eliminating joint configurations that violate constraints, and subsequently planning and optimizing the joint path by minimizing a multi-objective cost under the map constraint. Furthermore, several strategies are introduced to enhance RRT* for redundancy optimization. These strategies include a piecewise Gaussian sampling strategy (PGSS) to guide efficient tree growth within complex channels and enable joint sampling constrained by task coordinates. Additionally, the improved Steering and Local Optimization method are proposed to plan joint motion while considering intermediate task sequences. The effectiveness of the proposed algorithm is demonstrated in handling complex motion planning scenarios, such as layup involving complex path curves or dense obstacles. Experimental results validate the algorithm's capability to find feasible collision-free and singularity-free paths in relevant scenarios, provided such paths exist. Moreover, trajectory smoothness is optimized with increasing iterations.

Distributed Identity Authentication with Lenstra-Lenstra-Lovász Algorithm-Ciphertext Policy Attribute-Based Encryption from Lattices: An Efficient Approach Based on Ring Learning with Errors Problem.

In recent years, research on attribute-based encryption (ABE) has expanded into the quantum domain. Because a traditional single authority can cause the potential single point of failure, an improved lattice-based quantum-resistant identity authentication and policy attribute encryption scheme is proposed, in which the generation of random values is optimized by adjusting parameters in the Gaussian sampling algorithm to improve overall performance. Additionally, in the key generation phase, attributes are processed according to their shared nature, which reduces the computational overhead of the authorization authority. In the decryption phase, the basis transformation of the Lenstra-Lenstra-Lovász (LLL) lattice reduction algorithm is utilized to rapidly convert shared matrices into the shortest vector form, which can reduce the computational cost of linear space checks. The experimental results demonstrate that the proposed method not only improves efficiency but also enhances security compared with related schemes.

Photon losses create tension for Gaussian boson sampling

Photon losses create tension for Gaussian boson sampling

A new visual sensing system for motion state estimation of lateral localization of intelligent vehicles

Accurate lateral localization is the basis of intelligent vehicle decision making and control and one of the core problems of autonomous driving. In the process of vehicle driving, the vehicle body vibration, road bumps, and slope change will affect the motion parameters of the camera, which influences the localization accuracy. Therefore, we investigate a vehicle visual localization method based on the motion state estimation of vehicle camera by Gaussian Bayes sphere. This method uses Gaussian spherical crown sampling and maximum likelihood search to estimate the motion state of the vehicle camera in real time. Then, the real-time homography matrix between the sampling ground plane and the pixel plane is calculated according to the results to convert the coordinate points of the lane lines to the sampling ground plane for lateral localization of vehicles. Last, the localization results are restored to the real scale by the lane line width. The road experimental results show that the average error of the proposed method for lateral localization of vehicles is 5.7 cm under different road conditions on campus roads, and that under different road conditions on urban roads is 5.9 cm. At the same time, the localization accuracy of the proposed method is tested on the slope and under different weather conditions, and good results are obtained.

Quantum-Inspired Classical Algorithm for Graph Problems by Gaussian Boson Sampling

We present a quantum-inspired classical algorithm that can be used for graph-theoretical problems, such as finding the densest k subgraph and finding the maximum weight clique, which are proposed as applications of a Gaussian boson sampler. The main observation from Gaussian boson samplers is that a given graph’s adjacency matrix to be encoded in a Gaussian boson sampler is non-negative and that computing the output probability of Gaussian boson sampling restricted to a non-negative adjacency matrix is thought to be strictly easier than general cases. We first provide how to program a given graph problem into our efficient classical algorithm. We then numerically compare the performance of ideal and lossy Gaussian boson samplers, our quantum-inspired classical sampler, and the uniform sampler for finding the densest k subgraph and finding the maximum weight clique and show that the advantage from Gaussian boson samplers is not significant in general. We finally discuss the potential advantage of a Gaussian boson sampler over the proposed quantum-inspired classical sampler. Published by the American Physical Society 2024

Realization of high-fidelity unitary operations on up to 64 frequency bins

The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling. Published by the American Physical Society 2024

Enhanced PSO feature selection with Runge-Kutta and Gaussian sampling for precise gastric cancer recurrence prediction

Gastric cancer (GC), characterized by its inconspicuous initial symptoms and rapid invasiveness, presents a formidable challenge. Overlooking postoperative intervention opportunities may result in the dissemination of tumors to adjacent areas and distant organs, thereby substantially diminishing prospects for patient survival. Consequently, the prompt recognition and management of GC postoperative recurrence emerge as a matter of paramount urgency to mitigate the deleterious implications of the ailment. This study proposes an enhanced feature selection model, bRSPSO-FKNN, integrating boosted particle swarm optimization (RSPSO) with fuzzy k-nearest neighbor (FKNN), for predicting GC. It incorporates the Runge-Kutta search, for improved model accuracy, and Gaussian sampling, enhancing the search performance and helping to avoid locally optimal solutions. It outperforms the sophisticated variants of particle swarm optimization when evaluated in the CEC 2014 test suite. Furthermore, the bRSPSO-FKNN feature selection model was introduced for GC recurrence prediction analysis, achieving up to 82.082 % and 86.185 % accuracy and specificity, respectively. In summation, this model attains a notable level of precision, poised to ameliorate the early warning system for GC recurrence and, in turn, advance therapeutic options for afflicted patients.

Speeding up the classical simulation of Gaussian boson sampling with limited connectivity

Gaussian boson sampling (GBS) plays a crucially important role in demonstrating quantum advantage. As a major imperfection, the limited connectivity of the linear optical network weakens the quantum advantage result in recent experiments. In this work, we introduce an enhanced classical algorithm for simulating GBS processes with limited connectivity. It computes the loop Hafnian of an n×n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \ imes n$$\\end{document} symmetric matrix with bandwidth w in O(nw2w)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(nw2^w)$$\\end{document} time. It is better than the previous fastest algorithm which runs in O(nw22w)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(nw^2 2^w)$$\\end{document} time. This classical algorithm is helpful on clarifying how limited connectivity affects the computational complexity of GBS and tightening the boundary for achieving quantum advantage in the GBS problem.

A Versatile Deposition Model for Natural and Processed Surfaces

This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create diverse natural and engineered surface textures, governed by probabilistic principles. The model’s formulation addresses key questions related to deposition initiation, nucleation point behaviour, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. A versatile algorithm, relying on six parameters and employing nested loops and Gaussian sampling, is developed. The algorithm’s efficacy is examined through extensive simulations, involving variations in nucleation scaling densities, aggregate scaling scenarios, spread factors, and diffusion rates. Surface statistics are computed for simulated deposits and analyzed using Fast Fourier Transform (FFT). The resulting database enables quantitative comparisons of surfaces generated with different parameters, where the database-derived parallel coordinates offer guidance for selecting optimal model parameters to achieve desired surface morphologies. The proposed approach is validated against urea-derived deposits, exhibiting statistical consistency and agreement with experimental observations. Overall, the model’s adaptable framework holds promise for understanding and predicting deposit growth on surfaces in diverse practical scenarios.

A versatile single-photon-based quantum computing platform

Quantum computing aims at exploiting quantum phenomena to efficiently perform computations that are unfeasible even for the most powerful classical supercomputers. Among the promising technological approaches, photonic quantum computing offers the advantages of low decoherence, information processing with modest cryogenic requirements, and native integration with classical and quantum networks. So far, quantum computing demonstrations with light have implemented specific tasks with specialized hardware, notably Gaussian boson sampling, which permits the quantum computational advantage to be realized. Here we report a cloud-accessible versatile quantum computing prototype based on single photons. The device comprises a high-efficiency quantum-dot single-photon source feeding a universal linear optical network on a reconfigurable chip for which hardware errors are compensated by a machine-learned transpilation process. Our full software stack allows remote control of the device to perform computations via logic gates or direct photonic operations. For gate-based computation, we benchmark one-, two- and three-qubit gates with state-of-the art fidelities of 99.6 ± 0.1%, 93.8 ± 0.6% and 86 ± 1.2%, respectively. We also implement a variational quantum eigensolver, which we use to calculate the energy levels of the hydrogen molecule with chemical accuracy. For photon native computation, we implement a classifier algorithm using a three-photon-based quantum neural network and report a six-photon boson sampling demonstration on a universal reconfigurable integrated circuit. Finally, we report on a heralded three-photon entanglement generation, a key milestone toward measurement-based quantum computing.

Generalizable Fourier Augmentation for Unsupervised Video Object Segmentation

The performance of existing unsupervised video object segmentation methods typically suffers from severe performance degradation on test videos when tested in out-of-distribution scenarios. The primary reason is that the test data in real- world may not follow the independent and identically distribution (i.i.d.) assumption, leading to domain shift. In this paper, we propose a generalizable fourier augmentation method during training to improve the generalization ability of the model. To achieve this, we perform Fast Fourier Transform (FFT) over the intermediate spatial domain features in each layer to yield corresponding frequency representations, including amplitude components (encoding scene-aware styles such as texture, color, contrast of the scene) and phase components (encoding rich semantics). We produce a variety of style features via Gaussian sampling to augment the training data, thereby improving the generalization capability of the model. To further improve the cross-domain generalization performance of the model, we design a phase feature update strategy via exponential moving average using phase features from past frames in an online update manner, which could help the model to learn cross-domain-invariant features. Extensive experiments show that our proposed method achieves the state-of-the-art performance on popular benchmarks.

Multi-distribution bi-deniable inner product encryption based on Decision-LWE

Bi-deniable Encryption scheme means that when the sender and the receiver are coerced, the coercer can obtain fake plaintext, random numbers, and secret keys. It’s a solution strategy in the case of information leakage. Compared with traditional encryption, deniable encryption can provide secret communications in situations of coercion in the Post-Quantum era. Compared with sender-deniable encryption and receiver-deniable encryption, bi-deniable encryption can achieve secret communications in the situation that both sender and receiver are coerced by the coercer. So, we propose to design a bi-deniable encryption scheme under the multi-distribution model. In our bi-deniable encryption scheme, we construct a bi-deniable encryption scheme based on the assumption of Decision-Learning With Errors (DLWE) under the multi-distribution model. Firstly, the principle of Inner Product Predicate Encryption (IPPE) is applied in our scheme. Secondly, we apply the framework of Bi-Translucent Set (BTS), combined with inner product predicate encryption. Thirdly, we construct a series of probabilistic polynomial time algorithms, which apply linear transformation between different lattice structures, and Regev dual encryption. Fourthly, the statistical indistinguishability between the sampling algorithm with discrete Gaussian sampling algorithm, and the computational indistinguishability between LWE’s ciphertext samples with uniform samples, the property of indistinguishability is applied in theorem proving, which obtain Indistinguishability under Chosen Plaintext Attacks (IND-CPA) security and the property of bi-deniability. Given the value range of the Gaussian parameter and security parameter in our scheme, the correctness of the bi-deniable encryption scheme is guaranteed. We also give the security proof of IND-CPA and bi-deniability’s property by a series of games. The ‘Inner-Product Bi-Translucent Set’ Bi-Deniable Encryption scheme under the multi-distribution model is based on Decision-LWE assumption, and can avoid quantum-resistant attacks. The bi-deniable encryption scheme is firstly constructed by the inner product with the Decision-LWE assumption, which can provide better properties of security and deniability.

Determining the effect of a floating point on the Falcon digital signature algorithm security

The object of research is digital signatures. The Falcon digital signature scheme is one of the finalists in the NIST post-quantum cryptography competition. Its distinctive feature is the use of floating-point arithmetic. However, floating-point arithmetic has so-called rounding noise, which accumulates during computations and in some cases may lead to significant changes in the processed values. The work considers the problem of using rounding noise to build attacks on implementation. The main result of the study is a novel attack on implementation, which enables the secret key recovery. This attack differs from existing attacks in using two separately secure implementations with different computation orders. As a result of the analysis, the conditions under which secret key recovery is possible were revealed. The attack requires 300,000 signatures and two implementations to recover key. The probability of successful attack ranges from 70 % to 76 %. This probability is explained by the structure of the Gaussian sampling algorithm used in the Falcon digital signature. At the same time, a necessary condition for conducting an attack is identical seed during signature generation. This condition makes the attack more theoretical than practical since the correct implementation of the Falcon makes probability of two identical seeds negligible. However, the possible usage of floating-point noise shows potential existence of additional attack vectors for the Falcon that should be covered in security models. The results could be used in the construction of digital signature security models and their implementation in existing information and communication systems