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quantum Error Mitigation Relying on Permutation Filtering

IEEE TRANSACTIONS ON COMMUNICATIONS 2022年第3期70卷 1927-1942页

作者： Xiong, Yifeng Ng, Soon Xin Hanzo, Lajos Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed permutation-based methods are practically attractive, since they do not rely on any a priori information concerning the quantum channels. In this treatise, we propose a general framework termed as permutation filters, which includes the existing permutation-based methods as special cases. In particular, we show that the proposed filter design algorithm always converge to the global optimum, and that the optimal filters can provide substantial improvements over the existing permutation-based methods in the presence of narrowband quantum noise, corresponding to large-depth, high-error-rate quantum circuits.

关键词： quantum computing quantum algorithm Qubit Computers Optimization Task analysis Signal processing algorithms quantum error mitigation permutation filtering permutation symmetry variational quantum algorithms

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quantum computations for disambiguation and question answering

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quantum information processing 2022年第4期21卷 1-25页

作者： Correia, A. D. Moortgat, M. Stoof, H. T. C. Univ Utrecht Inst Theoret Phys Princetonpl 5 NL-3584 CC Utrecht Netherlands Univ Utrecht Utrecht Inst Linguist OTS Trans 10 NL-3512 JK Utrecht Netherlands Univ Utrecht Ctr Complex Syst Studies Leuvenlaan 4 NL-3584 CE Utrecht Netherlands

Automatic text processing is now a mature discipline in computer science, and so attempts at advancements using quantum computation have emerged as the new frontier, often under the term of quantum natural language processing. The main challenges consist in finding the most adequate ways of encoding words and their interactions on a quantum computer, considering hardware constraints, as well as building algorithms that take advantage of quantum architectures, so as to show improvement on the performance of natural language tasks. In this paper, we introduce a new framework that starts from a grammar that can be interpreted by means of tensor contraction, to build word representations as quantum states that serve as input to a quantum algorithm. We start by introducing an operator measurement to contract the representations of words, resulting in the representation of larger fragments of text. We then go on to develop pipelines for the tasks of sentence meaning disambiguation and question answering that take advantage of quantum features. For the first task, we show that our contraction scheme deals with syntactically ambiguous phrases storing the various different meanings in quantum superposition, a solution not available on a classical setting. For the second task, we obtain a question representation that contains all possible answers in equal quantum superposition, and we implement Grover's quantum search algorithm to find the correct answer, agnostic to the specific question, an implementation with the potential of delivering a result with quadratic speedup.

关键词： quantum natural language processing Grover's algorithm quantum search Question answering Syntactic ambiguities

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An adaptive threshold-based quantum image segmentation algorithm and its simulation

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quantum information processing 2022年第10期21卷 1-15页

作者： Yuan, Suzhen Zhao, Wenhao Gao, Shengwei Xia, Shuyin Hang, Bo Qu, Hong Chongqing Univ Posts & Telecommun Coll Opto Elect Engn Chongqing 400065 Peoples R China Hubei Univ Arts & Sci Comp Sch Xiangyang 441054 Peoples R China Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 611730 Peoples R China

Efficient and accurate image segmentation algorithm is critical to image processing. In this paper, we design a quantum image segmentation algorithm utilizing an adaptive threshold based on a moving average method, and we simulate it on the IBM quantum Experience (IBM Q) platform through the Qiskit extension. In the proposed method, an image is first divided into many 2 OE 2 regions, and each region's average value is considered the region's threshold value. In order to fully exploit quantum parallelism, we encode the core image (image to be segmented) and the three auxiliary images into one quantum superposition state sharing the same position qubits. The analysis results highlight that the proposed quantum image segmentation algorithm provides exponential speedup over the existing implementations, and the number of auxiliary qubits is reduced from exponential of q to polynomial. In addition, this paper presents an appealing example of simulating complex quantum image processing algorithms in quantum simulators.

关键词： quantum image segmentation quantum adder High parallelism Adaptive threshold quantum simulation

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A quantum genetic algorithm for optimization problems on the Bloch sphere

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quantum information processing 2022年第2期21卷 1-29页

作者： Amal, R. S. Ivan, J. Solomon Indian Inst Space Sci & Technol Dept Phys Trivandrum 695547 Kerala India

Optimization problems on the surface of a unit sphere are addressed using a quantum genetic algorithm. That a point on the surface of the Bloch sphere is representative of a pure state qubit is effectively used. Qubits are thought of as genes, and a sequence of qubits as a chromosome, and an ensemble of chromosomes as the population. The crossover and mutation of the genes are implemented using the superposition principle, and mutation is achieved through random phases in the superposition. As illustrations, examples pertaining to the Thomson optimization problem, the logarithmic Thomson optimization problem, and the evaluation of the geometric measure of entanglement are presented.

关键词： Genetic algorithm quantum crossover Optimization on Bloch sphere

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Concentration of Data Encoding in Parameterized quantum Circuits 36

Concentration of Data Encoding in Parameterized Quantum Circ...

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36th Conference on Neural information processing Systems (NeurIPS)

作者： Li, Guangxi Ye, Ruilin Zhao, Xuanqiang Wang, Xin Univ Technol Sydney Sydney NSW Australia Baidu Res Inst Quantum Comp Beijing Peoples R China Peking Univ Beijing Peoples R China

ISBN: (纸本)9781713871088

Variational quantum algorithms have been acknowledged as the leading strategy to realize near-term quantum advantages in meaningful tasks, including machine learning and optimization. When applied to tasks involving classical data, such algorithms generally begin with data encoding circuits and train quantum neural networks (QNNs) to minimize target functions. Although QNNs have been widely studied to improve these algorithms' performance on practical tasks, there is a gap in systematically understanding the influence of data encoding on the eventual performance. In this paper, we make progress in filling this gap by considering the common data encoding strategies based on parameterized quantum circuits. We prove that, under reasonable assumptions, the distance between the average encoded state and the maximally mixed state could be explicitly upper-bounded with respect to the width and depth of the encoding circuit. This result in particular implies that the average encoded state will concentrate on the maximally mixed state at an exponential speed on depth. Such concentration seriously limits the capabilities of quantum classifiers, and strictly restricts the distinguishability of encoded states from a quantum information perspective. To support our findings, we numerically verify these results on both synthetic and public data sets. Our results highlight the significance of quantum data encoding and may shed light on the future design of quantum encoding strategies.

关键词： Machine learning

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Machine learning in the quantum realm: The state-of-the-art, challenges, and future vision

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EXPERT SYSTEMS WITH APPLICATIONS 2022年第0期194卷 116512-116512页

作者： Houssein, Essam H. Abohashima, Zainab Elhoseny, Mohamed Mohamed, Waleed M. Minia Univ Fac Comp & Informat Al Minya Egypt Nahda Univ Fac Comp Sci Bani Suwayf Egypt Univ Sharjah Sharjah U Arab Emirates Mansoura Univ Fac Comp & Informat Mansoura Egypt

Machine learning has become a ubiquitous and effective technique for data processing and classification. Furthermore, due to the superiority and progress of quantum computing in many areas (e.g., cryptography, machine learning, healthcare), a combination of classical machine learning and quantum information processing has established a new field, called, quantum machine learning. One of the most frequently used applications of quantum computing is machine learning. This paper aims to present a comprehensive review of state-of-the-art advances in quantum machine learning. Besides, this paper outlines recent works on different architectures of quantum deep learning, and illustrates classification tasks in the quantum domain as well as encoding methods and quantum subroutines. Furthermore, this paper examines how the concept of quantum computing enhances classical machine learning. Two methods for improving the performance of classical machine learning are presented. Finally, this work provides a general review of challenges and the future vision of quantum machine learning.

关键词： quantum machine learning quantum computing quantum deep learning quantum inspired Hybrid quantum-classical quantum classification Variational quantum algorithms

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Wasserstein quantum Monte Carlo: A Novel Approach for Solving the quantum Many-Body Schrodinger Equation 37

Wasserstein Quantum Monte Carlo: A Novel Approach for Solvin...

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37th Conference on Neural information processing Systems (NeurIPS)

作者： Neklyudov, Kirill Nys, Jannes Thiede, Luca Carrasquilla, Juan Felipe Liu, Qiang Welling, Max Makhzani, Alireza Vector Inst Toronto ON Canada Ecole Polytech Fed Lausanne EPFL Inst Phys Lausanne Switzerland Ecole Polytech Fed Lausanne EPFL Ctr Quantum Sci & Engn Lausanne Switzerland Univ Toronto Toronto ON Canada Univ Waterloo Waterloo ON N2L 3G1 Canada UT Austin Austin TX USA Microsoft Redmond WA 98052 USA AI4Science Amsterdam Netherlands

ISBN: (纸本)9781713899921

Solving the quantum many-body Schrodinger equation is a fundamental and challenging problem in the fields of quantum physics, quantum chemistry, and material sciences. One of the common computational approaches to this problem is quantum Variational Monte Carlo (QVMC), in which ground-state solutions are obtained by minimizing the energy of the system within a restricted family of parameterized wave functions. Deep learning methods partially address the limitations of traditional QVMC by representing a rich family of wave functions in terms of neural networks. However, the optimization objective in QVMC remains notoriously hard to minimize and requires second-order optimization methods such as natural gradient. In this paper, we first reformulate energy functional minimization in the space of Born distributions corresponding to particle-permutation (anti-)symmetric wave functions, rather than the space of wave functions. We then interpret QVMC as the Fisher-Rao gradient flow in this distributional space, followed by a projection step onto the variational manifold. This perspective provides us with a principled framework to derive new QMC algorithms, by endowing the distributional space with better metrics, and following the projected gradient flow induced by those metrics. More specifically, we propose "Wasserstein quantum Monte Carlo" (WQMC), which uses the gradient flow induced by the Wasserstein metric, rather than the Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.

关键词： Wave functions

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Agile Time quantum Round Robin Algorithm

Agile Time Quantum Round Robin Algorithm

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2024 IEEE International Conference on Signal processing, Informatics, Communication and Energy Systems, SPICES 2024

作者： Qais Mirkar, Sulalah Bobal, Amiksha Gattani, Sanjana Mukesh Patel School of Technology Management and Engineering Dept. of Information Technology Mumbai India Mukesh Patel School of Technology Management and Engineering CSE-Cyber Security Mumbai India

ISBN: (纸本)9798350376135

In multitasking operating systems, CPU scheduling algorithms are accountable for the queuing of tasks for execution on the CPU. The effectiveness of a CPU scheduling algorithm is measured through CPU utilization, throughput, and process waiting times. One such scheduling algorithm is Round Robin (RR), a preemptive methodology that allocates time in quanta (parts) to execute the processes in a loop. The problems with a static quantum, such as too many context switches and process starvation are addressed by the proposed algorithm named Agile Time quantum Round Robin (ATQRR). The algorithm dynamically modifies the remaining time based on real-Time system factors. To ensure a thorough validation, a comprehensive analysis of the existing literature has been undertaken to compare ATQRR with other similar approaches. This review has focused on many criteria, like average turnaround time, waiting times, throughput, context switch overhead, and the fairness of process scheduling. © 2024 IEEE.

关键词： Scheduling algorithms

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Error-mitigated photonic variational quantum eigensolver using a single-photon ququart

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OPTICA 2022年第1期9卷 88-95页

作者： Lee, Donghwa Lee, Jinil Hong, Seongjin Lim, Hyang-Tag Cho, Young-Wook Han, Sang-Wook Shin, Hyundong Rehman, Junaid Ur Kim, Yong-Su Korea Inst Sci & Technol KIST Ctr Quantum Informat Seoul 02792 South Korea Korea Univ Sci & Technol KIST Sch Div Nano & Informat Technol Seoul 02792 South Korea Yonsei Univ Dept Phys Seoul 03722 South Korea Kyung Hee Univ Dept Elect & Informat Convergence Engn Yongin 17104 South Korea

Variational quantum algorithms, a representative class of modern quantum algorithms, provide practical uses of near-term quantum processors. The size of the problem that can be encoded and solved on a quantum processor is limited by the dimension of the Hilbert space associated with the processor. One common approach for increasing the system dimension is to utilize a larger number of quantum systems. Here, we adopt an alternative approach to utilize multiple degrees of freedom of individual quantum systems to experimentally resource-efficiently increase the Hilbert space. We report experimental implementation of the variational quantum eigensolver (VQE) using four-dimensional photonic quantum states of single photons. The four-dimensional quantum states are implemented by utilizing polarization and path degrees of freedom of a single photon. Our photonic VQE is equipped with a quantum error mitigation protocol that efficiently reduces the effects of Pauli noise in the quantum processing unit. We apply our photonic VQE to estimate the ground state energy of the He - H+ cation. Simulation and experimental results demonstrate that our experimental resource-efficient photonic VQE can accurately estimate the bond dissociation curve, even in the presence of large noise in the quantum processing unit. We also discuss further possible resource-efficient enhancement of the Hilbert space in photonic quantum processors. Our results propose that photonic systems utilizing multiple degrees of freedom can provide a resource-efficient avenue to implement practical near-term quantum processors. (C) 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

关键词： Optical elements Photons Polarization quantum information processing quantum noise Wave plates

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Solving Burgers' equation with quantum computing

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quantum information processing 2022年第1期21卷 1-13页

作者： Oz, Furkan Vuppala, Rohit K. S. S. Kara, Kursat Gaitan, Frank Oklahoma State Univ Sch Mech & Aerosp Engn Stillwater OK 74078 USA Lab Phys Sci 8050 Greenmead Dr College Pk MD 20740 USA

Computational fluid dynamics (CFD) simulations are a vital part of the design process in the aerospace industry. Although reliable CFD results can be obtained with turbulence models, direct numerical simulation of complex bodies in three spatial dimensions (3D) is impracticable due to the massive amount of computational elements. For instance, a 3D direct numerical simulation of a turbulent boundary-layer over the wing of a commercial jetliner that resolves all relevant length scales using a serial CFD solver on a modern digital computer would take approximately 750 million years or roughly 20% of the earth's age. Over the past 25 years, quantum computers have become the object of great interest worldwide as powerful quantum algorithms have been constructed for several important, computationally challenging problems that provide enormous speed-up over the best-known classical algorithms. In this paper, we adapt a recently introduced quantum algorithm for partial differential equations to Burgers' equation and develop a quantum CFD solver that determines its solutions. We used our quantum CFD solver to verify the quantum Burgers' equation algorithm to find the flow solution when a shockwave is and is not present. The quantum simulation results were compared to: (i) an exact analytical solution for a flow without a shockwave;and (ii) the results of a classical CFD solver for flows with and without a shockwave. Excellent agreement was found in both cases, and the error of the quantum CFD solver was comparable to that of the classical CFD solver.

关键词： quantum algorithms Computational fluid dynamics Fluid mechanics Burgers' equation

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