Related papers: Semantic embedding for quantum algorithms
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) 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) 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 computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
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…
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…
Quantum singular value transformation (QSVT) is a framework that has been shown to unify many primitives in quantum algorithms. In this work, we leverage the QSVT framework in two directions. We first show that the QSVT framework can…
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…
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 machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by 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 algorithms can enhance machine learning in different aspects. In 2014, Rebentrost $et~al.$ constructed a least squares quantum support vector machine (LS-QSVM), in which the Swap Test plays a crucial role in realizing the…
Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the…
Classification using variational quantum circuits is a promising frontier in quantum machine learning. Quantum supervised learning (QSL) applied to classical data using variational quantum circuits involves embedding the data into a quantum…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block…
Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy, intermediate-scale quantum…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…