Related papers: Generalized Quantum Singular Value Transformation
Given the ability to apply an unknown quantum channel acting on a $d$-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its…
In this work, we discuss two modifications that can be made to a known variational quantum singular value decomposition algorithm popular in the literature. The first is a change to the objective function which hints at improved performance…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation's…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most…
Despite significant advances in quantum algorithms, quantum programs in practice are often expressed at the circuit level, forgoing helpful structural abstractions common to their classical counterparts. Consequently, as many quantum…
Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum…
Quantum matrix inversion with the quantum singular value transformation (QSVT) requires a polynomial approximation to $1/x$. Several methods from the literature construct polynomials that achieve the known degree complexity…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it…
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group $\mathbb{Z}_N$ from two different points to get more efficient unitary…
Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using…
Quantum Singular Value Transformation (QSVT) provides a unified framework for applying polynomial functions to the singular values of a block-encoded matrix. QSVT prepares a state proportional to $\bA^{-1}\bb$ with circuit depth…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) are powerful techniques for the development of quantum procedures. They allow to derive circuits preparing desired polynomial transformations. Recent research…