Polynomial-depth quantum algorithm for computing matrix determinant

• URL: http://arxiv.org/abs/2401.16619v2
• Date: Thu, 16 May 2024 10:41:36 GMT
• Title: Polynomial-depth quantum algorithm for computing matrix determinant
• Authors: Alexander I. Zenchuk, Wentao Qi, Asutosh Kumar, Junde Wu,
• Abstract summary: We propose an algorithm for calculating the determinant of a square matrix, and construct a quantum circuit realizing it. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems.
• Score: 46.13392585104221
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We propose an algorithm for calculating the determinant of a square matrix, and construct the quantum circuit realizing it, using multiqubit control gates (representable in terms of Toffoli gates, CNOTs and SWAPs), Hadamard transformations and $Z$-operators. Each row of the matrix is encoded as a pure state of some quantum system. The admitted matrix is therefore arbitrary up to the normalization of quantum states of those systems. The depth of the proposed algorithm is $O(N^3\log \, N)$ for the $N\times N$ matrix.

Related papers

• Quantum multi-row iteration algorithm for linear systems with non-square coefficient matrices [7.174256268278207]
  We propose a quantum algorithm inspired by the classical multi-row iteration method. Our algorithm places less demand on the coefficient matrix, making it suitable for solving inconsistent systems.
  arXiv  Detail & Related papers  (2024-09-06T03:32:02Z)
• Generalized quantum Arimoto-Blahut algorithm and its application to quantum information bottleneck [55.22418739014892]
  We generalize the quantum Arimoto-Blahut algorithm by Ramakrishnan et al. We apply our algorithm to the quantum information bottleneck with three quantum systems. Our numerical analysis shows that our algorithm is better than their algorithm.
  arXiv  Detail & Related papers  (2023-11-19T00:06:11Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra [3.4137115855910767]
  We propose a class of randomized quantum algorithms for the task of sampling from matrix functions. Our use of qubits is purely algorithmic, and no additional qubits are required for quantum data structures.
  arXiv  Detail & Related papers  (2023-02-03T17:22:49Z)
• A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected weighted graph [4.045204834863644]
  We propose an efficient quantum algorithm to solve the eigenproblem of the Laplacian matrix of a fully connected weighted graph. Specifically, we adopt the optimal Hamiltonian simulation technique based on the block-encoding framework. We also show that our algorithm can be extended to solve the eigenproblem of symmetric (non-symmetric) normalized Laplacian matrix.
  arXiv  Detail & Related papers  (2022-03-28T02:24:08Z)
• Quantum algorithms for matrix operations and linear systems of equations [65.62256987706128]
  We propose quantum algorithms for matrix operations using the "Sender-Receiver" model. These quantum protocols can be used as subroutines in other quantum schemes.
  arXiv  Detail & Related papers  (2022-02-10T08:12:20Z)
• Quantum Algorithms based on the Block-Encoding Framework for Matrix Functions by Contour Integrals [1.5293427903448018]
  We show a framework to implement the linear combination of the inverses on quantum computers. We propose a quantum algorithm for matrix functions based on the framework.
  arXiv  Detail & Related papers  (2021-06-15T12:10:35Z)
• 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.