Quantum algorithms for matrix operations and linear systems of equations
arXiv:2202.04888 · doi:10.1088/1572-9494/ad2366
Abstract
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product, matrix-matrix product, the sum of two matrices, and calculation of determinant and inverse of a matrix. We encode the matrix entries into the probability amplitudes of pure initial states of senders. After applying a proper unitary transformation to the complete quantum system, the desired result can be found in certain blocks of the receiver's density matrix. These quantum protocols can be used as subroutines in other quantum schemes. Furthermore, we present an alternative quantum algorithm for solving linear systems of equations.
arXiv comment9 pages, 1 figure, 1 table, revised manuscript
References in corpus (21)
- Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
- Quantum Machine Learning
- Quantum algorithm for solving linear systems of equations
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Atomic quantum gases in periodically driven optical lattices
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- An approximate Fourier transform useful in quantum factoring
- Implementation of the Quantum Fourier Transform
- Preconditioned quantum linear system algorithm
- A quantum linear system algorithm for dense matrices
- Quantum algorithm for linear differential equations with exponentially improved dependence on precision
- Experimental Quantum Computing to Solve Systems of Linear Equations
- Experimental realization of quantum algorithm for solving linear systems of equations
- Quantum assisted Gaussian process regression
- Solving systems of linear equations on a quantum computer
- Solving Systems of Linear Equations with a Superconducting Quantum Processor
- Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
- Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices
- Complete structural restoring of transferred multi-qubit quantum state
- Quantum algorithm for matrix functions by Cauchy's integral formula
- Computing scalar products via a two-terminal quantum transmission line