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2024 International Conference on quantum Computing and Engineering

作者： Venkatesh, Supreeth Mysore Macaluso, Antonio Nuske, Marlon Klusch, Matthias Dengel, Andreas Univ Kaiserslautern Landau RPTU Kaiserslautern Germany German Res Ctr Artificial Intelligence DFKI Saarbrucken Germany German Res Ctr Artificial Intelligence DFKI Kaiserslautern Germany

ISBN: (纸本)9798331541378

quantum computing is expected to transform a range of computational tasks beyond the reach of classical algorithms. In this work, we examine the application of variational quantum algorithms (VQAs) for unsupervised image segmentation to partition images into separate semantic regions. Specifically, we formulate the task as a graph cut optimization problem and employ two established qubit-efficient VQAs, which we refer to as Parametric Gate Encoding (PGE) and Ancilla Basis Encoding (ABE), to find the optimal segmentation mask. In addition, we propose Adaptive Cost Encoding (ACE), a new approach that leverages the same circuit architecture as ABE but adopts a problem-dependent cost function. We benchmark PGE, ABE and ACE on synthetically generated images, focusing on quality and trainability. ACE shows consistently faster convergence in training the parameterized quantum circuits in comparison to PGE and ABE. Furthermore, we provide a theoretical analysis of the scalability of these approaches against the quantum Approximate Optimization Algorithm (QAOA), showing a significant cutback in the quantum resources, especially in the number of qubits that logarithmically depends on the number of pixels. The results validate the strengths of ACE, while concurrently highlighting its inherent limitations and challenges. This paves way for further research in quantum-enhanced computer vision.

关键词： quantum algorithms variational circuits image segmentation combinatorial optimization

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QuCode: A Novel Conceptual Description of quantum algorithms 54

QuCode: A Novel Conceptual Description of Quantum Algorithms

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54th IEEE International Symposium on Multiple-Valued Logic (ISMVL)

作者： Ketineni, Hrithik Perkowski, Marek Portland State Univ Dept Elect & Comp Engn Portland OR 97207 USA

ISBN: (纸本)9798350343090;9798350343083

Conventional presentations of quantum algorithms overwhelmingly rely on mathematical formalism, posing an unnecessary barrier to conceptual understanding. The growing influence of quantum computing across diverse domains necessitates more accessible education on the subject. To engage a broader audience in quantum computing, we introduce a new approach for teaching quantum algorithms: drawing parallels to classical pseudocode. This approach, which we call "QuCode," is demonstrated through its application to several black box quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani, and Simon's algorithm.

关键词： Bernstein-Vazirani algorithm Deutsch-Jozsa algorithm oracle pedagogy pseudocode Simon's algorithm quantum algorithms quantum computing

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Near-Optimal quantum algorithms for Multivariate Mean Estimation 2022

Near-Optimal Quantum Algorithms for Multivariate Mean Estima...

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54th Annual ACM SIGACT Symposium on Theory of Computing (STOC)

作者： Cornelissen, Arjan Hamoudi, Yassine Jerbi, Sofiene Univ Amsterdam QuSoft Amsterdam Netherlands Univ Calif Berkeley Simons Inst Theory Comp Berkeley CA 94720 USA Univ Innsbruck Inst Theoret Phys Innsbruck Austria

ISBN: (纸本)9781450392648

We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian estimators [Lugosi and Mendelson, 2019] to the quantum setting. Unlike classically, where any univariate estimator can be turned into a multivariate estimator with at most a logarithmic overhead in the dimension, no similar result can be proved in the quantum setting. Indeed, [Heinrich, 2004] ruled out the existence of a quantum advantage for the mean estimation problem when the sample complexity is smaller than the dimension. Our main result is to show that, outside this low-precision regime, there does exist a quantum estimator that outperforms any classical estimator. More precisely, we prove that the approximation error can be decreased by a factor of about the square root of the ratio between the dimension and the sample complexity. Our approach is substantially more involved than in the univariate setting, where most quantum estimators rely only on phase estimation. We exploit a variety of additional algorithmic techniques such as linear amplitude amplification, the BernsteinVazirani algorithm, and quantum singular value transformation. Our analysis is also deeply rooted in proving concentration inequalities for multivariate truncated statistics. Finally, we describe several applications of our algorithms, notably in measuring the expectation values of commuting observables and in the field of machine learning.

关键词： Mean Estimation Multivariate Statistics quantum algorithms Lower Bounds

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Towards a Pattern Language for quantum algorithms 1st

Towards a Pattern Language for Quantum Algorithms

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1st International Workshop on quantum Technology and Optimization Problems (QTOP)

作者： Leymann, Frank Univ Stuttgart IAAS Univ Str 38 D-70569 Stuttgart Germany

ISBN: (纸本)9783030140823;9783030140816

Creating quantum algorithms is a difficult task, especially for computer scientist not used to quantum computing. But quantum algorithms often use similar elements. Thus, these elements provide proven solutions to recurring problems, i.e. a pattern language. Sketching such a language is a step towards establishing a software engineering discipline of quantum algorithms.

关键词： quantum algorithms Pattern languages Software engineering

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Contextuality and Sparsity in quantum algorithms

Contextuality and Sparsity in Quantum Algorithms

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作者： Kirby, William M. Tufts University

学位级别：Ph.D., Doctor of Philosophy

In this thesis we study quantum algorithms motivated by two unifying concepts: contextuality and sparsity. Contextuality is a characteristic feature of quantum mechanics, and identifying contextuality in quantum algorithms provides a means for distinguishing them from their classical counterparts. We first describe how contextuality may be identified in variational quantum eigensolvers (VQEs), which are a leading algorithm for noisy intermediate-scale quantum computers. We then show how to construct a classical phase-space model for any noncontextual Hamiltonian, which provides a classical simulation algorithm for noncontextual VQE and allows us to prove that the \textsc{noncontextual Hamiltonian problem} is only NP-complete, rather than QMA-complete. Finally, we describe an approximation method called contextual subspace VQE that permits us to partition a general Hamiltonian into a noncontextual part and a contextual part, and estimate its ground state energy using a technique that combines classical simulation of the noncontextual part with quantum simulation of the contextual part. By using more quantum resources (in qubits and simulated terms of the Hamiltonian), we can increase the accuracy of the approximation. We present results of simulating contextual subspace VQE on electronic structure Hamiltonians, and find that to reach chemical accuracy in most cases it requires fewer qubits and simulated terms than standard VQE. A Hamiltonian is sparse in some particular basis when it contains only polynomially-many nonzero entries in each row and column, meaning that each basis state only propagates into polynomially-many others at first order. Time evolution under sparse Hamiltonians is generally efficiently simulable by quantum algorithms provided efficient unitaries (oracles) exist that identify the locations and values of the nonzero matrix elements. We present two new results on sparse Hamiltonian simulation. The first is an extension of VQE to the sparse Hamilt

关键词： quantum algorithms quantum computing quantum contextuality quantum simulation Sparse matrices

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Fast quantum algorithms of Solving an Instance of Quadratic Congruence on a quantum Computer

Fast Quantum Algorithms of Solving an Instance of Quadratic ...

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5th International Symposium on Parallel Architectures, algorithms and Programming (PAAP)

作者： Chang, Weng-Long Feng, Mang Natl Kaohsiung Univ Appl Sci Dept Comp Sci & Informat Engn 415 Chien Kung Rd Kaohsiung 807 Taiwan Chinese Acad Sci Wuhan Inst Phys & Math State Key Lab Magnet Resonance & Atom & Mol Phys Wuhan 430071 Peoples R China

ISBN: (纸本)9780769548982;9781467345668

It is assumed that P is the product of two prime numbers q(1) and q(2). If there is an integer 0 < M < P such that M-2 equivalent to C (mod P), i. e., the congruence has a solution, then C is said to be a quadratic congruence (mod P). Quadratic congruence (mod P) is a NP-complete problem. If the value of C is equal to one, then four integer solutions for M-2 equivalent to 1 (mod P) are, respectively, b, P - b, 1 and P - 1, where 1 < P - b < (P / 2) and (P / 2) < b < P - 1. This is a special case of quadratic congruence (mod P). In this paper, it is shown that four integer solutions for M-2 equivalent to 1 (mod P) can be found by means of the proposed quantum algorithms with polynomial quantum gates, polynomial quantum bits and the successful probability that is the same as that of Shor's order-finding algorithm.

关键词： component Data Structures and algorithms quantum algorithms

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quantum algorithms to Simulate Many-Body Physics of Correlated Fermions

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Physical Review Applied 2018年第4期9卷 044036-044036页

作者： Zhang Jiang Kevin J. Sung Kostyantyn Kechedzhi Vadim N. Smelyanskiy Sergio Boixo NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL) Moffett Field California 94035 USA Stinger Ghaffarian Technologies Inc. 7701 Greenbelt Road Suite 400 Greenbelt Maryland 20770 USA Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor Michigan 48109 USA USRA NASA Ames Research Center Moffett Field California 94035 USA Google Venice California 90291 USA

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. We discuss simulating strongly correlated fermionic systems using near-term quantum devices. We focus specifically on two-dimensional (2D) or linear geometry with nearest-neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with O(N2) gates and O(N) circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those describing the quantum states. Furthermore, we propose an algorithm to implement the 2D fermionic Fourier transformation on a 2D qubit array with only O(N1.5) gates and O(N) circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model—again on a 2D qubit array—with O(N) gates and O(N) circuit depth. Finally, we discuss how these algorithms can be used to determine the ground-state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.

关键词： quantum algorithms quantum correlations in quantum information quantum information with solid state qubits quantum simulation Heavy-fermion systems Strongly correlated systems Hubbard model Superconducting qubits

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Variable time amplitude amplification and quantum algorithms for linear algebra problems

Variable time amplitude amplification and quantum algorithms...

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29th International Symposium on Theoretical Aspects of Computer Science (STACS)

作者： Ambainis, Andris Univ Latvia Fac Comp Raina Bulv 19 LV-1586 Riga Latvia

ISBN: (纸本)9783939897354

quantum amplitude amplification is a method of increasing a success probability of an algorithm from a small epsilon > 0 to Theta(1) with less repetitions than classically. In this paper, we generalize quantum amplitude amplification to the case when parts of the algorithm that is being amplified stop at different times. We then apply the new variable time amplitude amplification to give two new quantum algorithms for linear algebra problems. Our first algorithm is an improvement of Harrow et al. algorithm for solving systems of linear equations. We improve the running time of the algorithm from O(k(2) log N) to O(k log(3) k logN) where k is the condition number of the system of equations. Our second algorithm tests whether a matrix A is singular or far-from-singular, faster then the previously known algorithms.

关键词： quantum computing quantum algorithms amplitude amplification linear equations

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Topological Structure of quantum algorithms 13

Topological Structure of Quantum Algorithms

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28th Annual IEEE/ACM Symposium on Logic in Computer Science (LICS)

作者： Vicary, Jamie Natl Univ Singapore Ctr Quantum Technol Singapore 117548 Singapore

ISBN: (纸本)9781479904136

We use a categorical topological semantics to examine the Deutsch-Jozsa, hidden subgroup and single-shot Grover algorithms. This reveals important structures hidden by conventional algebraic presentations, and allows novel proofs of correctness via local topological operations, giving for the first time a satisfying high-level explanation for why these procedures work. We also investigate generalizations of these algorithms, providing improved analyses of those already in the literature, and a new generalization of the single-shot Grover algorithm.

关键词： quantum computing quantum algorithms topology category theory

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quantum algorithms for approximate function loading

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Physical Review Research 2023年第3期5卷 033114-033114页

作者： Gabriel Marin-Sanchez Javier Gonzalez-Conde Mikel Sanz Department of Physical Chemistry University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain EHU Quantum Center University of the Basque Country UPV/EHU Apartado 644 48080 Bilbao Spain IKERBASQUE Basque Foundation for Science Plaza Euskadi 5 48009 Bilbao Spain Basque Center for Applied Mathematics (BCAM) Alameda de Mazarredo 14 48009 Bilbao Spain

Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods for the noisy intermediate-scale quantum era inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity ε and under certain smoothness conditions, we prove that the complexity of the implementation of the Grover-Rudolph algorithm without ancillary qubits, first introduced by Möttönen et al., results into O(2k0(ε)), with n the number of qubits and k0(ε) asymptotically independent of n. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational Ansatz is explicitly tailored to the landscape of the function, leading to a quasioptimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples.

关键词： quantum algorithms quantum computation

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