Related papers: Mathematical and numerical analysis of quantum sig…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Quantum signal processing (QSP) is a methodology for constructing polynomial transformations of a linear operator encoded in a unitary. Applied to an encoding of a state $\rho$, QSP enables the evaluation of nonlinear functions of the form…
Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some…
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) 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…
Quantum signal processing (QSP) is a highly successful algorithmic primitive in quantum computing which leads to conceptually simple and efficient quantum algorithms using the block-encoding framework of quantum linear algebra. Multivariate…
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…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
Quantum signal processing (QSP) is a framework for implementing certain polynomial functions via quantum circuits. To construct a QSP circuit, one needs (i) a target polynomial $P(z)$, which must satisfy $\lvert P(z)\rvert\leq 1$ on the…
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…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
Quantum signal processing (QSP) and generalized quantum signal processing (GQSP) are essential tools for implementing the block encoding of matrix functions. The achievable polynomials of QSP have restrictions on parity, while GQSP…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) provide an efficient framework for implementing polynomials of block-encoded matrices, and thus offer a systematic approach to quantum algorithm design.…
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…
As in classical reversible computing, Quantum Arithmetic is typically seen as a set of tools that process binary data encoded into a quantum register to set the value of another quantum register. This article presents another approach to…