Related papers: Generalized Quantum Signal Processing
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…
Implementing polynomial functions of Hermitian matrices on quantum hardware is a foundational task in quantum computing, critical for accurate Hamiltonian simulation, quantum linear system solving, high-fidelity state preparation, machine…
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…
Robust quantum control is crucial for achieving operations below the quantum error correction threshold. Quantum Signal Processing (QSP) transforms a unitary parameterized by $\theta$ into one governed by a polynomial function $f(\theta)$,…
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…
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…
We propose a unifying framework for the state preparation using quantum power method algorithms based on generalized quantum signal processing (GQSP). We apply GQSP to realize quantum analogs of classical power iteration, power Lanczos,…
Quantum signal processing (QSP) and quantum singular value transformation (QSVT), have emerged as unifying frameworks in the context of quantum algorithm design. These techniques allow to carry out efficient polynomial transformations of…
Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and…
The quantum singular value transformation has revolutionised quantum algorithms. By applying a polynomial to an arbitrary matrix, it provides a unifying picture of quantum algorithms. However, polynomials are restricted to definite parity…
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 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…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
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…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
We introduce the first randomized algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework for many quantum algorithms. Standard implementations of QSVT rely on block encodings of the Hamiltonian, which are costly…
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 (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…
We present a simplified exposition of some pieces of [Gily\'en, Su, Low, and Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value transformation (QSVT) framework for applying polynomial functions to block-encoded…
Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications…