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Transition of Anticoncentration in Gaussian Boson Sampling

Physical Review Letters 2025年第14期134卷 140601-140601页

作者： Adam Ehrenberg Joseph T. Iosue Abhinav Deshpande Dominik Hangleiter Alexey V. Gorshkov Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA IBM Quantum Almaden Research Center San Jose California 95120 USA Simons Institute for the Theory of Computing University of California at Berkeley Berkeley California 94720 USA

Gaussian boson sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian boson sampling are understood to the same degree as for these other schemes, we understand relatively little about the statistical properties of its output distribution. The most relevant statistical property, from the perspective of demonstrating quantum advantage, is the “anticoncentration” of the output distribution as measured by its second moment. The degree of anticoncentration features in arguments for the complexity-theoretic hardness of Gaussian boson sampling. In this Letter, we develop a graph-theoretic framework for analyzing the moments of the Gaussian boson sampling distribution. Using this framework, we show that Gaussian boson sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly.

关键词： Bosons

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Characterization, synthesis, and optimization of quantum circuits over multiple-control Z-rotation gates: A systematic study

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Physical Review A 2023年第2期108卷 022603-022603页

作者： Shihao Zhang Junda Wu Lvzhou Li Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-sen University Guangzhou 510006 China

We conduct a systematic study of quantum circuits composed of multiple-control Z-rotation (mczr) gates as primitives, since they are widely used components in quantum algorithms and also have attracted much experimental interest in recent years. We establish a circuit-polynomial correspondence to characterize the functionality of quantum circuits over the mczr gate set with continuous parameters. An analytic method for exactly synthesizing such quantum circuit to implement any given diagonal unitary matrix with an optimal gate count is proposed, which also enables the circuit depth optimal for specific cases with pairs of complementary gates. Furthermore, we present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any mczr circuit, which can also be applied to quantum circuits over any other commuting gate set. Besides the theoretical investigation, the practical performance of our circuit synthesis and optimization techniques is further evaluated numerically on two typical examples in quantum computing, including diagonal Hermitian operators and quantum approximate optimization algorithm circuits with tens of qubits, which can demonstrate a reduction in circuit depth by 33.40% and 15.55% on average over relevant prior works, respectively. Therefore, our methods and results provide a pathway for implementing quantum circuits and algorithms on recently developed devices.

关键词： Iterative methods

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Optimal Deterministic quantum Algorithm for the Promised Element Distinctness Problem

SSRN

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SSRN 2023年

作者： Li, Guanzhong Li, Lvzhou Institute of Quantum Computing and Computer Theory School of Computer and Engineering Sun Yat-sen University Guangzhou510006 China

The element distinctness problem is to determine whether a string of $N$ elements, i.e. $x=(x_1,\ldots,x_N)$ where $x_i\in \{1,\ldots,M\}$ and $M\geq N$, contains two elements of the same value (a.k.a colliding pair), for which Ambainis proposed an optimal quantum algorithm. The idea behind Ambainis' algorithm is to first reduce the problem to the promised version in which $x$ is promised to contain at most one colliding pair, and then design an algorithm $\mathcal{A}$ requiring $O(N^{2/3})$ queries based on quantum walk search for the promise problem. However, $\mathcal{A}$ is probabilistic and may fail to give the right answer. We thus, in this work, design a deterministic quantum algorithm for the promise problem which never errs and requires $O(N^{2/3})$ queries. This algorithm is proved optimal. Technically, we modify the quantum walk search operator on quasi-Johnson graph to have arbitrary phases, and then use Jordan's lemma as the analyzing tool to reduce the quantum walk search operator to the generalized Grover's operator. This allows us to utilize the recently proposed fixed-axis-rotation (FXR) method for deterministic quantum search, and hence achieve 100\% success. © 2023, The Authors. All rights reserved.

关键词： quantum computers

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Degenerate polarization entangled photon source based on a single Ti-diffusion lithium niobate waveguide in a polarization Sagnac interferometer

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Chinese Physics B 2023年第8期32卷 69-73页

作者：孙宇孙昌伟周唯杨然端家晨龚彦晓徐平祝世宁 National Laboratory of Solid State Microstructures and School of Physics Nanjing UniversityNanjing 210093China NanZhi Institude of Advanced Optoelectronic Integration Nanjing 210018China Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense TechnologyChangsha 410073China

Combining a Ti-diffusion periodically poled lithium niobate(PPLN)waveguide with a Sagnac interferometer,two opposite directions type-II spontaneous parametric down conversions(SPDC)occur coherently and yield a high brightness,high stability polarization entanglement *** source produces degenerate photon pairs at 1540.4 nm with a brightness of B=(1.36±0.03)×10^(6) pairs/(s·nm·m W).We perform quantum state tomography to reconstruct the density matrix of the output state and obtain a fidelity of F=0.983±*** high brightness and phase stability of our waveguide source enable a wide range of quantum information experiments operating at a low pump power as well as hold the advantage in mass production which can promote the practical applications of quantum technologies.

关键词： polarization entanglement source Sagnac interferometer quantum information lithium niobate waveguide

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Improved quantum linear system solver via quantum phase discrimination

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The European Physical Journal Special Topics 2025年 1-11页

作者： Liu, Zihao Li, Guanzhong Li, Lvzhou Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-sen University Guangzhou China Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong) Shenzhen China

The problem of solving linear systems is of great significance in both theory and practice, for which quantum solvers have been shown to provide an exponential speedup over the best-known classical solvers. Recently, a quantum linear system solver has been developed with the state-of-the-art complexity [1], which combines two techniques, namely, discrete adiabatic evolution and eigenstate filtering. However, the parameters of the quantum circuit for eigenstate filtering need to be precomputed classically via the discrete Fourier transform, which introduces additional computational overhead. In this paper, we improve the solver by presenting a new eigenstate filtering process termed quantum phase discrimination in which the circuit parameters are given directly in a concise and analytical form with negligible classical overhead, while maintaining the same quantum complexity.

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Polynomial-Time Classical Simulation of Noisy Circuits with Naturally Fault-Tolerant Gates

arXiv

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arXiv 2024年

作者： Nelson, Jon Rajakumar, Joel Hangleiter, Dominik Gullans, Michael J. Joint Center for Quantum Information & Computer Science University of Maryland and NIST United States Department of Computer Science University of Maryland United States Simons Institute for the Theory of Computing University of California at Berkeley United States

We construct a polynomial-time classical algorithm that samples from the output distribution of low-depth noisy Clifford circuits with any product-state inputs and final single-qubit measurements in any basis. This class of circuits includes Clifford-magic circuits and Conjugated-Clifford circuits, which are important candidates for demonstrating quantum advantage using non-universal gates. Additionally, our results generalize a simulation algorithm for IQP circuits [RWL24] to the case of IQP circuits augmented with CNOT gates, which is another class of non-universal circuits that are relevant to current experiments. Importantly, our results do not require randomness assumptions over the circuit families considered (such as anticoncentration properties) and instead hold for every circuit in each class. This allows us to place tight limitations on the robustness of these circuits to noise. In particular, we show that there is no quantum advantage at large depths with realistically noisy Clifford circuits, even with perfect magic state inputs, or IQP circuits with CNOT gates, even with arbitrary diagonal non-Clifford gates. The key insight behind the algorithm is that interspersed noise causes a decay of long-range entanglement, and at depths beyond a critical threshold, the noise builds up to an extent that most correlations can be classically simulated. To prove our results, we merge techniques from percolation theory with tools from Pauli path analysis. © 2024, CC BY.

关键词： Polynomial approximation

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Lightweight Authenticated Key Agreement Protocol for Smart Power Grid Systems Using PUF

IEEE Open Journal of the Communications Society

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IEEE Open Journal of the Communications Society 2024年 5卷 3568-3580页

作者： Zahoor, Amina Mahmood, Khalid Saleem, Muhammad Asad Badar, Hafiz Muhammad Sanaullah Le, Tuan-Vinh Das, Ashok Kumar Department of Computer Science Sahiwal57000 Pakistan National Yunlin University of Science and Technology Graduate School of Intelligent Data Science Douliu64002 Taiwan University of Electronic Science and Technology of China School of Computer Science and Engineering Chengdu611731 China Emerson University Multan Department of Emerging Computing Technologies Multan61000 Pakistan Fu Jen Catholic University Bachelor's Program of Artificial Intelligence and Information Security New Taipei City24206 Taiwan International Institute of Information Technology Hyderabad Center for Security Theory and Algorithmic Research Hyderabad500032 India

The Smart Power Grid (SPG) is pivotal in orchestrating and managing demand response in contemporary smart cities, leveraging the prowess of Information and Communication Technologies (ICTs). Within the immersive SPG environment, the ubiquitous deployment of smart meters stands as a testament to their paramount importance in the realm of vigilant monitoring and oversight. These smart meters are installed on high-tension electricity lines and transmit information about electricity outages and other issues to the utility center. To access services from utility centers, smart meters need to communicate securely over a public channel, even though the network itself is insecure. However, potential attacks from adversaries ( Ad) can exploit this communication. Therefore, protecting this communication is of utmost importance. Several privacy-preserving authentication protocols designed for SPG have been introduced in the literature. Nevertheless, a significant number of these protocols exhibit vulnerabilities to diverse security attacks. This article introduces a lightweight and anonymous authentication protocol specifically designed to address these concerns in the SPG environment. Our protocol ensures both security and efficiency, surpassing other comparable protocols in terms of its lightweight nature. By employing both formal and informal analysis, we showcase the robustness of our protocol against significant attacks while remaining lightweight. The proposed protocol provides added security features and incurs 23.8879% lower computation cost than related protocols. Consequently, our protocol is highly suitable for implementation in the SPG system. © 2020 IEEE.

关键词： Hash functions

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Experimental review on Majorana zero-modes in hybrid nanowires

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science China(Physics,Mechanics & Astronomy) 2021年第10期64卷 38-53页

作者： Ji-Bang Fu Bin Li Xin-Fang Zhang Guang-Zheng Yu Guang-Yao Huang Ming-Tang Deng Institute for Quantum Information&State Key Laboratory of High Performance Computing College of Computer Science and TechnologyNational University of Defense TechnologyChangsha 410073China

As the condensed matter analog of Majorana fermion, the Majorana zero-mode is well known as a building block of fault-tolerant topological quantum computing. This review focuses on the recent progress of Majorana experiments, especially experiments about semiconductor-superconductor hybrid devices. We first sketch Majorana zero-mode formation from a bottom-up view,which is more suitable for beginners and experimentalists. Then, we survey the status of zero-energy state signatures reported recently, from zero-energy conductance peaks, the oscillations, the quantization, and the interactions with extra degrees of freedom. We also give prospects of future experiments for advancing one-dimensional semiconductor nanowire-superconductor hybrid materials and devices.

关键词： electronic transport in nanoscale materials and structures quantum wires proximity efect superconducting low-dimensional structures

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Distributed quantum architecture search

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Physical Review A 2024年第2期110卷 022403-022403页

作者： Haozhen Situ Zhimin He Shenggen Zheng Lvzhou Li College of Mathematics and Informatics School of Electronic and Information Engineering Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong) Shenzhen 518045 China Institute of Quantum Computing and Software School of Computer Science and Engineering

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.

关键词： Machine learning quantum circuits

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Analysis of the gluon distribution with next-to-leading order splitting function at small-x^(*)

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Chinese Physics C 2024年第6期48卷 38-44页

作者：陈京萱王晓鹏蔡燕兵陈旭荣王倩 Key Laboratory of Atomic and Subatomic Structure and Quantum Control(MOE) Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of MatterInstitute of Quantum MatterSouth China Normal UniversityGuangzhou 510006China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Guangdong Provincial Key Laboratory of Nuclear ScienceSouthern Nuclear Science Computing CenterSouth China Normal UniversityGuangzhou 510006China Institute of Modern Physics Chinese Academy of SciencesLanzhou 730000China University of Chinese Academy of Sciences Beijing 100049China Lanzhou University Lanzhou 730000China School of Nuclear Science and Technology University of Chinese Academy of SciencesBeijing 100049China Guizhou Key Laboratory in Physics and Related Areas Guizhou University of Finance and EconomicsGuiyang 550025China Southern Center for Nuclear-Science Theory(SCNT) Institute of Modern PhysicsChinese Academy of SciencesHuizhou 516000China

An approximated solution for the gluon distribution from DGLAP evolution equations with the NLO splitting function in the small-x limit is *** first obtain simplified forms of the LO and NLO splitting functions in the small-x *** these approximated splitting functions,we obtain the analytical gluon distribution using the Mellin *** free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution *** find that the asymptotic behavior of the gluon distribution is consistent with the CJ15 data;however,the NLO results considering the"ladder"structure of gluon emission are slightly better than the LO *** results indicate that the corrections from NLO have a significant influence on the behavior of the gluon distribution in the small-x *** addition,we investigate the DGLAP evolution of the proton structure function using the analytical solution of the gluon *** differential structure function reveals that our results have a similar tendency to the CJ15 data at small-x.

关键词： DGLAP equation gluon distribution small-x structure function

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