arXiv subjects

Shenggen Zheng

Publications and source records attributed to Shenggen Zheng.

At least 19 recordsLinked to original sources

arXiv2026

Causal-Class Hierarchies in Coherence-Constrained Channel Transformation

Higher-order quantum transformations allow multiple channel uses to be combined through different causal architectures, from parallel and fixed-order sequential networks to general higher-order processes. Whether this causal freedom improves channel transformation when the higher-order operation is also constrained by a resource theory remains largely unexplored. We study this question in the dynamical resource theory of coherence using a unified semidefinite-programming framework. For two qubit amplitude-damping channels and the identity target, we prove a strict causal hierarchy at every nontrivial damping strength under both maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC). In contrast, mixed-Pauli channels admit a common teleportation simulation that transfers the channel dependence to Bell-diagonal program states prepared in parallel. The remaining processing can then be absorbed into a single quantum operational, so parallel, fixed-order sequential, and general higher-order strategies achieve the same optimal error for any target. These results identify free program-state parallelisation as a structural obstruction to causal enhancement.

quant-ph↗

arXiv2026

Analytic Qubit Separation between POVMs and Projective Measurements

Generalized measurements can be implemented projectively after enlarging the Hilbert space, but this dilation changes the available local dimension. We construct a Bell functional with rational coefficients that separates the two measurement models at local dimension two. An explicit three-outcome qubit positive-operator-valued measure with rational matrix entries attains $2\sqrt2+1/100$. On the other hand, all qubit-projective strategies are bounded by $2\sqrt2+\sqrt5/250+\sqrt2/32400$, giving a fully analytic certified gap greater than $1/1000$. To our knowledge, this is the first fully analytic Bell-functional separation between qubit POVMs and qubit projective measurements over arbitrary shared two-qubit states. Lean certificate for the separation theorem is provided for completeness. Separately, an exact level-3 noncommutative sum-of-squares certificate proves that the explicit qubit strategy attains the unrestricted finite-dimensional tensor-product quantum optimum.

quant-ph↗

arXiv2026

Quantum Speedups for Testing Similar Means

Property testing of distributions is a central topic in information theory, learning theory, and statistics. While quantum algorithms are known to offer significant speedups for property testing of a single distribution or a pair of distributions, it is unclear whether quantum algorithms provide speedups for property testing of $m$ ($m\geq 3$) distributions. This work focuses on quantum algorithms for testing whether $m$ distributions have similar means or are $ε$-far from mean similarity under two models. In the query model, the algorithm can choose which distribution to sample from, whereas in the sampling model, the distributions are selected uniformly. We design quantum algorithms with complexities $\tilde{O}(1/ε)$ (the $\tilde{O}$ notation hides poly-logarithmic factors) and $\tilde{O}(\sqrt{m}/ε)$ in the query and sampling models, respectively, achieving quadratic speedups over the classical counterparts. We further establish quantum lower bounds of $Ω\left(1/ε\right)$ and $Ω\rbra{m^{1/3}+\frac{m^{1/4}}ε}$ for the query model and the sampling model, demonstrating the optimality of our quantum algorithms in terms of the dependence on $ε$ up to logarithmic factors.

quant-ph↗

arXiv2026

Distributed Exact Quantum Amplitude Amplification Algorithm for Arbitrary Quantum States

In the noisy intermediate-scale quantum (NISQ) era, distributed quantum computation has garnered considerable interest, as it overcomes the physical limitations of single-device architectures and enables scalable quantum information processing. In this study, we focus on the challenge of achieving exact amplitude amplification for quantum states with arbitrary amplitude distributions and subsequently propose a Distributed Exact Quantum Amplitude Amplification Algorithm (DEQAAA). Specifically, (1) it supports partitioning across any number of nodes $t$ within the range $2 \leq t \leq n$; (2) the maximum qubit count required for any single node is expressed as $\max \left(n_0,n_1,\dots,n_{t-1} \right) $, where $n_j$ represents the number of qubits at the $j$-th node, with $\sum_{j=0}^{t-1} n_j =n$; (3) it can realize exact amplitude amplification for multiple targets of a quantum state with arbitrary amplitude distributions; (4) we verify the effectiveness of DEQAAA by resolving a specific exact amplitude amplification task involving two targets (8 and 14 in decimal) via MindSpore Quantum, a quantum simulation software, with tests conducted on 4-qubit, 6-qubit, 8-qubit and 10-qubit systems. Notably, through the decomposition of $C^{n-1}PS$ gates, DEQAAA demonstrates remarkable advantages in both quantum gate count and circuit depth as the qubit number scales, thereby boosting its noise resilience. In the 10-qubit scenario, for instance, it achieves a reduction of over $97\%$ in both indicators compared to QAAA and EQAAA, underscoring its outstanding resource-saving performance.

quant-ph↗

arXiv2025

A Survey of Quantum Transformers: Architectures, Challenges and Outlooks

Quantum Transformers integrate the representational power of classical Transformers with the computational advantages of quantum computing. Since 2022, research in this area has rapidly expanded, giving rise to diverse technical paradigms and early applications. To address the growing need for consolidation, this paper presents the first comprehensive, systematic, and in-depth survey of quantum Transformer models. First, we delineate the research scope, focusing on improving Transformer parts with quantum methods, and introduce foundational concepts in classical Transformers and quantum machine learning. Then we organize existing studies into two main paradigms: PQC-based and QLA-based, with PQC-based paradigm further divided into QKV-only Quantum Mapping, Quantum Pairwise Attention, Quantum Holistic Attention. and Quantum-Assisted Optimization, analyzing their core mechanisms and architectural traits. We also summarize empirical results that demonstrate preliminary quantum advantages, especially on small-scale tasks or resource-constrained settings. Following this, we examine key technical challenges, such as complexity-resource trade-offs, scalability and generalization limitations, and trainability issues including barren plateaus, and provide potential solutions, including quantumizing classical transformer variants with lower complexity, hybrid designs, and improved optimization strategies. Finally, we propose several promising future directions, e.g., scaling quantum modules into large architectures, applying quantum Transformers to domains with inherently quantum data (e.g., physics, chemistry), and developing theory-driven designs grounded in quantum information science. This survey will help researchers and practitioners quickly grasp the overall landscape of current quantum Transformer research and promote future developments in this emerging field.

quant-ph↗

arXiv2025

BoolSkeleton: Boolean Network Skeletonization via Homogeneous Pattern Reduction

Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between Boolean networks. To tackle this challenge, we introduce BoolSkeleton, a novel Boolean network skeletonization method that improves the consistency and reliability of design-specific evaluations. BoolSkeleton comprises two key steps: preprocessing and reduction. In preprocessing, the Boolean network is transformed into a defined Boolean dependency graph, where nodes are assigned the functionality-related status. Next, the homogeneous and heterogeneous patterns are defined for the node-level pattern reduction step. Heterogeneous patterns are preserved to maintain critical functionality-related dependencies, while homogeneous patterns can be reduced. Parameter K of the pattern further constrains the fanin size of these patterns, enabling fine-tuned control over the granularity of graph reduction. To validate BoolSkeleton's effectiveness, we conducted four analysis/downstream tasks around the Boolean network: compression analysis, classification, critical path analysis, and timing prediction, demonstrating its robustness across diverse scenarios. Furthermore, it improves above 55% in the average accuracy compared to the original Boolean network for the timing prediction task. These experiments underscore the potential of BoolSkeleton to enhance design consistency in logic synthesis.

cs.AR↗

arXiv2025

CNOT Oriented Synthesis for Small-Scale Boolean Functions Using Spatial Structures of Parallelotopes

Quantum computing has garnered significant interest for its potential to achieve exponential speedups over classical approaches. However, in the Noisy Intermediate-Scale Quantum (NISQ) era, quantum circuit scalability remains limited by gate fidelity and qubit counts, restricting physical implementations to small-scale circuits. While prior work has explored logic network structures for quantum circuit synthesis, these methods often neglect the spatial structure intrinsic to Boolean functions. In this paper, we leverage this spatial structure, encoded by parallelotopes embedded in the hypercube defined by the Boolean function, to access a broader optimization space, enhancing synthesis efficiency and reducing circuit complexity. We propose the Spatial Structure-based Hypercube Reduction~(SSHR), a novel synthesis method tailored for small-scale Boolean functions ($\leq 8$). SSHR extracts global spatial features to minimize the use of Multi-Control Toffoli (MCT) gates. To further exploit spatial correlations, we introduce two variants: SSHR-H employs heuristic functions to accelerate synthesis runtime, while SSHR-I integrates an Integer Linear Programming (ILP) solver to maximize spatial structure utilization. Our approach outperforms existing techniques in small-scale circuit synthesis, achieving 56\% and 81\% reductions in CNOT gate counts compared to the Exclusive Sum-of-Products (ESOP) and Xor-And-Inverter Graph (XAG) methods, respectively.

quant-ph↗

arXiv2025

Quantum Compiler Design for Qubit Mapping and Routing: A Cross-Architectural Survey of Superconducting, Trapped-Ion, and Neutral Atom Systems

Quantum hardware development is progressing rapidly with substantial advancements achieved across leading platforms, including superconducting circuits, trapped-ion systems, and neutral atom arrays. As the pursuit of practical quantum advantage continues, efficient quantum program compilation becomes essential for transforming high-level representations of quantum algorithms into physically executable circuits. A fundamental challenge in this process is qubit mapping and gate scheduling, which play a critical role in adapting compiled circuits to the architectural constraints and physical limitations of specific quantum hardware. In this survey, we systematically review and categorize research on the qubit mapping and routing problems across the three mainstream quantum hardware platforms. We primarily explore the development of hardware-aware compilers for superconducting platforms, classifying existing methods into solver-based, heuristic-based, and machine learning-based approaches, and analyze their optimization targets, including gate count, circuit duration, fidelity, and scalability. Furthermore, we examine the evolution of trapped-ion and neutral atom devices, analyzing the distinct challenges posed by their hardware characteristics and highlighting specialized compilers tailored to these unique physical constraints. Finally, we summarize the key challenges and identify some promising opportunities for future research in quantum compiler design across these hardware platforms.

quant-ph↗

arXiv2024

Learning Parameterized Quantum Circuits with Quantum Gradient

Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization methods, which suffer from issues like gradient vanishing. In this work, we introduce a nested optimization model that leverages quantum gradient to enhance PQC learning for polynomial-type cost functions. Our approach utilizes quantum algorithms to identify and overcome a type of gradient vanishing-a persistent challenge in PQC learning-by effectively navigating the optimization landscape. We also mitigate potential barren plateaus of our model and manage the learning cost via restricting the optimization region. Numerically, we demonstrate the feasibility of the approach on two tasks: the Max-Cut problem and polynomial optimization. The method excels in generating circuits without gradient vanishing and effectively optimizes the cost function. From the perspective of quantum algorithms, our model improves quantum optimization for polynomial-type cost functions, addressing the challenge of exponential sample complexity growth.

quant-ph↗

arXiv2024

Distributed quantum architecture search

Variational quantum algorithms, inspired by neural networks, have become a novel approach in quantum computing. However, designing efficient parameterized quantum circuits remains a challenge. Quantum architecture search tackles this by adjusting circuit structures along with gate parameters to automatically discover high-performance circuit structures. In this study, we propose an end-to-end distributed quantum architecture search framework, where we aim to automatically design distributed quantum circuit structures for interconnected quantum processing units with specific qubit connectivity. We devise a circuit generation algorithm which incorporates TeleGate and TeleData methods to enable nonlocal gate implementation across quantum processing units. While taking into account qubit connectivity, we also incorporate qubit assignment from logical to physical qubits within our quantum architecture search framework. A two-stage progressive training-free strategy is employed to evaluate extensive circuit structures without circuit training costs. Through numerical experiments on three VQE tasks, the efficacy and efficiency of our scheme is demonstrated. Our research into discovering efficient structures for distributed quantum circuits is crucial for near-term quantum computing where a single quantum processing unit has a limited number of qubits. Distributed quantum circuits allow for breaking down complex computations into manageable parts that can be processed across multiple quantum processing units.

quant-ph↗

arXiv2024

Distributed Exact Generalized Grover's Algorithm

Distributed quantum computation has garnered immense attention in the noisy intermediate-scale quantum (NISQ) era, where each computational node necessitates fewer qubits and quantum gates. In this paper, we focus on a generalized search problem involving multiple targets within an unordered database and propose a Distributed Exact Generalized Grover's Algorithm (DEGGA) to address this challenge by decomposing it into arbitrary $t$ components, where $2 \leq t \leq n$. Specifically, (1) our algorithm ensures accuracy, with a theoretical probability of identifying the target states at $100\%$; (2) if the number of targets is fixed, the pivotal factor influencing the circuit depth of DEGGA is the partitioning strategy, rather than the magnitude of $n$; (3) our method requires a total of $n$ qubits, eliminating the need for auxiliary qubits; (4) we elucidate the resolutions (two-node and three-node) of a particular generalized search issue incorporating two goal strings (000000 and 111111) by applying DEGGA. The feasibility and effectiveness of our suggested approach is further demonstrated by executing the quantum circuits on MindSpore Quantum (a quantum simulation software). Eventually, through the decomposition of multi-qubit gates, DEGGA diminishes the utilization of quantum gates by $90.7\%$ and decreases the circuit depth by $91.3\%$ in comparison to the modified Grover's algorithm by Long. It is increasingly evident that distributed quantum algorithms offer augmented practicality.

quant-ph↗

arXiv2023

Lifting query complexity to time-space complexity for two-way finite automata

Time-space tradeoff has been studied in a variety of models, such as Turing machines, branching programs, and finite automata, etc. While communication complexity as a technique has been applied to study finite automata, it seems it has not been used to study time-space tradeoffs of finite automata. We design a new technique showing that separations of query complexity can be lifted, via communication complexity, to separations of time-space complexity of two-way finite automata. As an application, one of our main results exhibits the first example of a language $L$ such that the time-space complexity of two-way probabilistic finite automata with a bounded error (2PFA) is $\widetildeΩ(n^2)$, while of exact two-way quantum finite automata with classical states (2QCFA) is $\widetilde{O}(n^{5/3})$, that is, we demonstrate for the first time that exact quantum computing has an advantage in time-space complexity comparing to classical computing.

cs.CC↗

arXiv2023

Detection and evaluation of abnormal user behavior based on quantum generation adversarial network

Quantum computing holds tremendous potential for processing high-dimensional data, capitalizing on the unique capabilities of superposition and parallelism within quantum states. As we navigate the noisy intermediate-scale quantum (NISQ) era, the exploration of quantum computing applications has emerged as a compelling frontier. One area of particular interest within the realm of cyberspace security is Behavior Detection and Evaluation (BDE). Notably, the detection and evaluation of internal abnormal behaviors pose significant challenges, given their infrequent occurrence or even their concealed nature amidst vast volumes of normal data. In this paper, we introduce a novel quantum behavior detection and evaluation algorithm (QBDE) tailored for internal user analysis. The QBDE algorithm comprises a Quantum Generative Adversarial Network (QGAN) in conjunction with a classical neural network for detection and evaluation tasks. The QGAN is built upon a hybrid architecture, encompassing a Quantum Generator ($G_Q$) and a Classical Discriminator ($D_C$). $G_Q$, designed as a parameterized quantum circuit (PQC), collaborates with $D_C$, a classical neural network, to collectively enhance the analysis process. To address the challenge of imbalanced positive and negative samples, $G_Q$ is employed to generate negative samples. Both $G_Q$ and $D_C$ are optimized through gradient descent techniques. Through extensive simulation tests and quantitative analyses, we substantiate the effectiveness of the QBDE algorithm in detecting and evaluating internal user abnormal behaviors. Our work not only introduces a novel approach to abnormal behavior detection and evaluation but also pioneers a new application scenario for quantum algorithms. This paradigm shift underscores the promising prospects of quantum computing in tackling complex cybersecurity challenges.

quant-ph↗

arXiv2023

Fast Exact NPN Classification with Influence-aided Canonical Form

NPN classification has many applications in the synthesis and verification of digital circuits. The canonical-form-based method is the most common approach, designing a canonical form as representative for the NPN equivalence class first and then computing the transformation function according to the canonical form. Most works use variable symmetries and several signatures, mainly based on the cofactor, to simplify the canonical form construction and computation. This paper describes a novel canonical form and its computation algorithm by introducing Boolean influence to NPN classification, which is a basic concept in analysis of Boolean functions. We show that influence is input-negation-independent, input-permutation-dependent, and has other structural information than previous signatures for NPN classification. Therefore, it is a significant ingredient in speeding up NPN classification. Experimental results prove that influence plays an important role in reducing the transformation enumeration in computing the canonical form. Compared with the state-of-the-art algorithm implemented in ABC, our influence-aided canonical form for exact NPN classification gains up to 5.5x speedup.

cs.LG↗

arXiv2023

Semiquantum key distribution using initial states in only one basis without the classical user measuring

From the perspective of resource theory, it is interesting to achieve the same quantum task using as few quantum resources as possible. Semiquantum key distribution (SQKD), which allows a quantum user to share a confidential key with a classical user who prepares and operates qubits in only one basis, is an important example for studying this issue. To further limit the quantum resources used by users, in this paper, we constructed the first SQKD protocol which restricts the quantum user to prepare quantum states in only one basis and removes the classical user's measurement capability. Furthermore, we prove that the constructed protocol is unconditionally secure by deriving a key rate expression of the error rate in the asymptotic scenario. The work of this paper provides inspiration for achieving quantum superiority with minimal quantum resources.

quant-ph↗

arXiv2023

Performance of Grover's search algorithm with diagonalizable collective noises

Grover's search algorithm (GSA) is known to experience a loss of its quadratic speedup when exposed to quantum noise. In this study, we partially agree with this result and present our findings. First, we examine different typical diagonalizable noises acting on the oracles in GSA and find that the success probability decreases and oscillates around $1/2$ as the number of iterations increases. Secondly, our results show that the performance of GSA can be improved by certain types of noise, such as bit flip and bit-phase flip noise. Finally, we determine the noise threshold for bit-phase flip noise to achieve a desired success probability and demonstrate that GSA with bit-phase flip noise still outperforms its classical counterpart. These results suggest new avenues for research in noisy intermediate-scale quantum (NISQ) computing, such as evaluating the feasibility of quantum algorithms with noise and exploring their applications in machine learning.

quant-ph↗

arXiv2023

GSQAS: Graph Self-supervised Quantum Architecture Search

Quantum Architecture Search (QAS) is a promising approach to designing quantum circuits for variational quantum algorithms (VQAs). However, existing QAS algorithms require to evaluate a large number of quantum circuits during the search process, which makes them computationally demanding and limits their applications to large-scale quantum circuits. Recently, predictor-based QAS has been proposed to alleviate this problem by directly estimating the performances of circuits according to their structures with a predictor trained on a set of labeled quantum circuits. However, the predictor is trained by purely supervised learning, which suffers from poor generalization ability when labeled training circuits are scarce. It is very time-consuming to obtain a large number of labeled quantum circuits because the gate parameters of quantum circuits need to be optimized until convergence to obtain their ground-truth performances. To overcome these limitations, we propose GSQAS, a graph self-supervised QAS, which trains a predictor based on self-supervised learning. Specifically, we first pre-train a graph encoder on a large number of unlabeled quantum circuits using a well-designed pretext task in order to generate meaningful representations of circuits. Then the downstream predictor is trained on a small number of quantum circuits' representations and their labels. Once the encoder is trained, it can apply to different downstream tasks. In order to better encode the spatial topology information and avoid the huge dimension of feature vectors for large-scale quantum circuits, we design a scheme to encode quantum circuits as graphs. Simulation results on searching circuit structures for variational quantum eigensolver and quantum state classification show that GSQAS outperforms the state-of-the-art predictor-based QAS, achieving better performance with fewer labeled circuits.

quant-ph↗

arXiv2023

Rethinking NPN Classification from Face and Point Characteristics of Boolean Functions

NPN classification is an essential problem in the design and verification of digital circuits. Most existing works explored variable symmetries and cofactor signatures to develop their classification methods. However, cofactor signatures only consider the face characteristics of Boolean functions. In this paper, we propose a new NPN classifier using both face and point characteristics of Boolean functions, including cofactor, influence, and sensitivity. The new method brings a new perspective to the classification of Boolean functions. The classifier only needs to compute some signatures, and the equality of corresponding signatures is a prerequisite for NPN equivalence. Therefore, these signatures can be directly used for NPN classification, thus avoiding the exhaustive transformation enumeration. The experiments show that the proposed NPN classifier gains better NPN classification accuracy with comparable speed.

cs.CC↗