Tensor Quantum Programming

• URL: http://arxiv.org/abs/2403.13486v1
• Date: Wed, 20 Mar 2024 10:44:00 GMT
• Title: Tensor Quantum Programming
• Authors: A. Termanova, Ar. Melnikov, E. Mamenchikov, N. Belokonev, S. Dolgov, A. Berezutskii, R. Ellerbrock, C. Mansell, M. Perelshtein,
• Abstract summary: We develop an algorithm that encodes Matrix Product Operators into quantum circuits with a depth that depends linearly on the number of qubits. It demonstrates effectiveness on up to 50 qubits for several frequently encountered in differential equations, optimization problems, and quantum chemistry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully demonstrated a quantum advantage due to the ease with which the results can be adequately replicated on classical computers through the use of tensor network algorithms. Additionally, it remains unclear even in theory where exactly these advantages are rooted within quantum systems because the logarithmic complexity commonly associated with quantum algorithms is also present in algorithms based on tensor networks. In this article, we propose a novel approach called Tensor Quantum Programming, which leverages tensor networks for hybrid quantum computing. Our key insight is that the primary challenge of algorithms based on tensor networks lies in their high ranks (bond dimensions). Quantum computing offers a potential solution to this challenge, as an ideal quantum computer can represent tensors with arbitrarily high ranks in contrast to classical counterparts, which indicates the way towards quantum advantage. While tensor-based vector-encoding and state-readout are known procedures, the matrix-encoding required for performing matrix-vector multiplications directly on quantum devices remained unsolved. Here, we developed an algorithm that encodes Matrix Product Operators into quantum circuits with a depth that depends linearly on the number of qubits. It demonstrates effectiveness on up to 50 qubits for several matrices frequently encountered in differential equations, optimization problems, and quantum chemistry. We view this work as an initial stride towards the creation of genuinely practical quantum algorithms.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Quantum Subroutine for Variance Estimation: Algorithmic Design and Applications [80.04533958880862]
  Quantum computing sets the foundation for new ways of designing algorithms. New challenges arise concerning which field quantum speedup can be achieved. Looking for the design of quantum subroutines that are more efficient than their classical counterpart poses solid pillars to new powerful quantum algorithms.
  arXiv  Detail & Related papers  (2024-02-26T09:32:07Z)
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval [1.6421520075844793]
  A prime example is the weight optimization of laminated composite materials, which to this day remains a formidable problem. The rapidly developing field of quantum computation may offer novel approaches for addressing these intricate problems.
  arXiv  Detail & Related papers  (2024-02-09T15:01:56Z)
• Realization of quantum algorithms with qudits [0.7892577704654171]
  We review several ideas indicating how multilevel quantum systems, also known as qudits, can be used for efficient realization of quantum algorithms. We focus on techniques of leveraging qudits for simplifying decomposition of multiqubit gates, and for compressing quantum information by encoding multiple qubits in a single qudit. These theoretical schemes can be implemented with quantum computing platforms of various nature, such as trapped ions, neutral atoms, superconducting junctions, and quantum light.
  arXiv  Detail & Related papers  (2023-11-20T18:34:19Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Quantum Annealing for Single Image Super-Resolution [86.69338893753886]
  We propose a quantum computing-based algorithm to solve the single image super-resolution (SISR) problem. The proposed AQC-based algorithm is demonstrated to achieve improved speed-up over a classical analog while maintaining comparable SISR accuracy.
  arXiv  Detail & Related papers  (2023-04-18T11:57:15Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Parametric Synthesis of Computational Circuits for Complex Quantum Algorithms [0.0]
  The purpose of our quantum synthesizer is enabling users to implement quantum algorithms using higher-level commands. The proposed approach for implementing quantum algorithms has a potential application in the field of machine learning.
  arXiv  Detail & Related papers  (2022-09-20T06:25:47Z)
• Optimizing Tensor Network Contraction Using Reinforcement Learning [86.05566365115729]
  We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges.
  arXiv  Detail & Related papers  (2022-04-18T21:45:13Z)
• Parametrized Complexity of Quantum Inspired Algorithms [0.0]
  Two promising areas of quantum algorithms are quantum machine learning and quantum optimization. Motivated by recent progress in quantum technologies and in particular quantum software, research and industrial communities have been trying to discover new applications of quantum algorithms.
  arXiv  Detail & Related papers  (2021-12-22T06:19:36Z)
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks [2.28438857884398]
  We introduce quantum algorithms to solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning. We will also present new quantum algorithms for neural networks, or deep learning.
  arXiv  Detail & Related papers  (2021-11-05T16:36:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.