Related papers: Multivariable QSP and Bosonic Quantum Simulation u…
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…
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…
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 powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a…
Quantum signal processing (QSP), which enables systematic polynomial transformations on quantum data through sequences of qubit rotations, has emerged as a fundamental building block for quantum algorithms and data re-uploading quantum…
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to…
Quantum phase estimation is at the heart of most quantum algorithms with exponential speedup. In this letter we demonstrate how to utilize it to compute the dynamical response functions of many-body quantum systems. Specifically, we design…
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…
We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
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…
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…
Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic…
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) has emerged as a promising framework to manipulate and determine properties of quantum systems. QSP not only unifies most existing quantum algorithms but also provides tools to discover new ones. Quantum…
Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly…
A novel family of Cosine series Quantum Sampling (QCoSamp) operators appropriate for quantum computing is described. The development of quantum algorithms, analogous to classical algorithms, we apply to the harmonic analysis of signals. We…