Quantum Hermitian conjugate and encoding unnormalized matrices

• URL: http://arxiv.org/abs/2504.00015v2
• Date: Wed, 02 Apr 2025 07:47:26 GMT
• Title: Quantum Hermitian conjugate and encoding unnormalized matrices
• Authors: Alexander I. Zenchuk, Wentao Qi, Junde Wu,
• Abstract summary: We develop the family of matrix-manipulation algorithms based on the encoding the matrix elements into the probability amplitudes of the pure superposition state of a certain quantum system.<n>We introduce two extensions to these algorithms which allow (i) to perform Hermitian conjugation of matrices under consideration and (ii) to weaken the restriction to the absolute values of matrix elements unavoidably imposed by the normalization condition for a pure quantum state.
• Score: 49.494595696663524
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We further develop the family of matrix-manipulation algorithms based on the encoding the matrix elements into the probability amplitudes of the pure superposition state of a certain quantum system. We introduce two extensions to these algorithms which allow (i) to perform Hermitian conjugation of matrices under consideration and (ii) to weaken the restriction to the absolute values of matrix elements unavoidably imposed by the normalization condition for a pure quantum state. Both these extensions are applied to the matrix multiplication algorithm. Controlled measurement of ancilla state is implemented to avoid the problem of small success probability in the measurement process.

Related papers

• Matrix encoding method in variational quantum singular value decomposition [49.494595696663524]
  Conditional measurement is involved to avoid small success probability in ancilla measurement. The objective function for the algorithm can be obtained probabilistically via measurement of the state of a one-qubit subsystem.
  arXiv  Detail & Related papers  (2025-03-19T07:01:38Z)
• Remarks on controlled measurement and quantum algorithm for calculating Hermitian conjugate [46.13392585104221]
  We present two new aspects for the recently proposed algorithms for matrix manipulating.<n>First aspect is the controlled measurement which allows to avoid the problem of small access probability to the required ancilla state.<n>Second aspect is the algorithm for calculating the Hermitian conjugate of an arbitrary matrix.
  arXiv  Detail & Related papers  (2025-01-27T13:11:47Z)
• Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
  This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum. We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
  arXiv  Detail & Related papers  (2024-10-28T08:43:40Z)
• Entanglement-induced exponential advantage in amplitude estimation via state matrixization [11.282486674587236]
  Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing.<n>We introduce a novel algorithmic framework for quantum amplitude estimation by transforming pure states into their matrix forms.<n>We reconstruct amplitude estimation algorithms within the novel matrixization framework through a technique known as channel block encoding.
  arXiv  Detail & Related papers  (2024-08-25T04:35:53Z)
• Purely quantum algorithms for calculating determinant and inverse of matrix and solving linear algebraic systems [43.53835128052666]
  We propose quantum algorithms for the computation of the determinant and inverse of an $(N-1) times (N-1)$ matrix.<n>This approach is a straightforward modification of the existing algorithm for determining the determinant of an $N times N$ matrix.<n>We provide suitable circuit designs for all three algorithms, each estimated to require $O(N log N)$ in terms of space.
  arXiv  Detail & Related papers  (2024-01-29T23:23:27Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• 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 grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• 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)
• Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
  Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task. Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate. The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
  arXiv  Detail & Related papers  (2021-06-06T13:15:25Z)
• Quantum algorithms for powering stable Hermitian matrices [0.7734726150561088]
  Matrix powering is a fundamental computational primitive in linear algebra. We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms.
  arXiv  Detail & Related papers  (2021-03-15T12:20:04Z)

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.