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Recent work shows that quantum signal processing (QSP) and its multi-qubit lifted version, quantum singular value transformation (QSVT), unify and improve the presentation of most quantum algorithms. QSP/QSVT characterize the ability, by…
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…
Multivariable Quantum Signal Processing (M-QSP) [1] is expected to provide an efficient means to handle polynomial transformations of multiple variables simultaneously. However, we noticed several inconsistencies in the main Theorem 2.3 and…
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) provides a representation of scalar polynomials of degree $d$ as products of matrices in $\mathrm{SU}(2)$, parameterized by $(d+1)$ real numbers known as phase factors. QSP is the mathematical foundation of…
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 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 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) 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) 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 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 state preparation is a task to prepare a state with a specific function encoded in the amplitude, which is an essential subroutine in many quantum algorithms. In this paper, we focus on multivariate state preparation, as it is an…
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…
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) 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…
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…
We provide in this work a form of Modular Quantum Signal Processing that we call iterated quantum signal processing. This method recursively applies quantum signal processing to the outputs of other quantum signal processing steps, allowing…
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) and its extensions are increasingly popular frameworks for developing quantum algorithms. Yet QSP implementations still struggle to complete a classical pre-processing step ('QSP-processing') that determines…
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…