Block encoding of sparse structured matrices coming from ocean acoustics in quantum computing

• URL: http://arxiv.org/abs/2405.18007v2
• Date: Tue, 9 Jul 2024 07:33:45 GMT
• Title: Block encoding of sparse structured matrices coming from ocean acoustics in quantum computing
• Authors: Chunlin Yang, Hongmei Yao, Zexian Li, Zhaobing Fan, Guofeng Zhang, Jianshe Liu,
• Abstract summary: Block encoding is a data input model commonly used in a quantum computer. New base scheme of block encoding is given which generalizes the one in citecamps2024 by removing the constraint that every data item should appear in all columns.
• Score: 2.4487770108795393
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Block encoding is a data input model commonly used in a quantum computer. It is an ingenious technique that embeds a matrix $A$ satisfying $\left\|A/ \alpha \right\| \leq 1$ into a larger unitary matrix $U_{A}$. Its complexity can affect the complexity of quantum algorithms in the framework of block encoding. In this paper, a new base scheme of block encoding is given which generalizes the one in \cite{camps2024explicit} by removing the constraint that every data item should appear in all columns. And applying preamplification and state preparation methods, the base scheme is further improved, which results in lower \textit{figures of merit} than that in special case \cite{sunderhauf2024block}. Then, the construction of oracles in block encoding schemes are discussed in detail. Considering special sparse structured matrices coming from ocean acoustics, two concrete examples are used to illustrate the feasibility of the proposed base scheme of block encoding and their explicit quantum circuits are implemented. Finally, the corresponding \verb|MATLAB| codes are presented to effectively simulate the quantum circuits.

Related papers

• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Linear Circuit Synthesis using Weighted Steiner Trees [45.11082946405984]
  CNOT circuits are a common building block of general quantum circuits. This article presents state-of-the-art algorithms for optimizing the number of CNOT gates. A simulated evaluation shows that the suggested is almost always beneficial and reduces the number of CNOT gates by up to 10%.
  arXiv  Detail & Related papers  (2024-08-07T19:51:22Z)
• Quantum sampling algorithms for quantum state preparation and matrix block-encoding [0.0]
  We first present an algorithm based on QRS that prepares a quantum state $|psi_frangle propto sumN_x=1 f(x)|xrangle$. We then adapt QRS techniques to the matrix block-encoding problem and introduce a QRS-based algorithm for block-encoding a given matrix $A = sum_ij A_ij |irangle langle j|$.
  arXiv  Detail & Related papers  (2024-05-19T03:46:11Z)
• Block encoding of matrix product operators [0.0]
  We present a procedure to block-encode a Hamiltonian based on its matrix product operator (MPO) representation. More specifically, we encode every MPO tensor in a larger unitary of dimension $D+2$, where $D = lceillog(chi)rceil$ is the number of subsequently contracted qubits that scales logarithmically with the virtual bond dimension.
  arXiv  Detail & Related papers  (2023-12-14T12:34:24Z)
• Circuit complexity of quantum access models for encoding classical data [4.727325187683489]
  We study the Clifford$+T$ complexity of constructing some typical quantum access models. We show that both sparse-access input models and block-encoding require nearly linear circuit complexities. Our protocols are built upon improved quantum state preparation and a selective oracle for Pauli strings.
  arXiv  Detail & Related papers  (2023-11-19T16:23:57Z)
• Block-encoding structured matrices for data input in quantum computing [0.0]
  We show how to construct block encoding circuits based on an arithmetic description of the sparsity and pattern of repeated values of a matrix. The resulting circuits reduce flag qubit number according to sparsity, and data loading cost according to repeated values.
  arXiv  Detail & Related papers  (2023-02-21T19:08:49Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Quantum Resources Required to Block-Encode a Matrix of Classical Data [56.508135743727934]
  We provide circuit-level implementations and resource estimates for several methods of block-encoding a dense $Ntimes N$ matrix of classical data to precision $epsilon$. We examine resource tradeoffs between the different approaches and explore implementations of two separate models of quantum random access memory (QRAM) Our results go beyond simple query complexity and provide a clear picture into the resource costs when large amounts of classical data are assumed to be accessible to quantum algorithms.
  arXiv  Detail & Related papers  (2022-06-07T18:00:01Z)
• FABLE: Fast Approximate Quantum Circuits for Block-Encodings [0.0]
  We propose FABLE, a method to generate approximate quantum circuits for block-encodings of matrices in a fast manner. FABLE circuits have a simple structure and are directly formulated in terms of one- and two-qubit gates. We show that FABLE circuits can be compressed and sparsified.
  arXiv  Detail & Related papers  (2022-04-29T21:06:07Z)
• Quantum algorithms for spectral sums [50.045011844765185]
  We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. We show how the algorithms and techniques used in this work can be applied to three problems in spectral graph theory.
  arXiv  Detail & Related papers  (2020-11-12T16:29:45Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.