Related papers: Infinite quantum signal processing
Quantum signal processing (QSP) has emerged as a unifying subroutine in quantum algorithms. In QSP, we are given a function $f$ and a unitary black-box $U$, and the goal is to construct a quantum circuit for implementing $f(U)$ to a given…
Quantum Signal Processing (QSP), together with the quantum singular value transformation, is one of the central quantum algorithms due to its efficiency and generality in many fields including quantum simulation, quantum machine learning,…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
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…
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…
Here we investigate analogy between quantum signal processing (QSP) and the adiabatic-impulse model (AIM) in order to implement the QSP algorithm with fast quantum logic gates. QSP is an algorithm that uses single-qubit dynamics to perform…
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…
Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a…
Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…
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…
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…
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial…
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…
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…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
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 algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a 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…
This paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomials by using a key step of Prony's method and is numerically…