相关论文: Quantum Eigenvalue Transformations for Arbitrary M…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Under suitable assumptions, the algorithms in [Lin, Tong, Quantum 2020] can estimate the ground state energy and prepare the ground state of a quantum Hamiltonian with near-optimal query complexities. However, this is based on a block…
In this work, we address the challenge of generalization in quantum reinforcement learning (QRL) for combinatorial optimization, focusing on the Traveling Salesman Problem (TSP). Training quantum policies on large TSP instances is often…
Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called…
We present an analytical solution to the angle-finding problem in quantum signal processing (QSP) for monomials of odd degree. Specifically, we show that to implement a monomial of degree \( n \), where \( n \) is odd, it suffices to choose…
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…
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 $f(\theta)$,…
Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…
Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the…
Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for 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…
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…
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
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…
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 present an efficient quantum circuit for block encoding pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and…