Related papers: Quantum singular value transformation and beyond: …
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 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…
The quantum singular value transformation is a powerful quantum algorithm that allows one to apply a polynomial transformation to the singular values of a matrix that is embedded as a block of a unitary transformation. This paper shows how…
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…
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…
This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a…
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 computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
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 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…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
Quantum signal processing (QSP) and the quantum singular value transformation (QSVT) are pivotal tools for simplifying the development of quantum algorithms. These techniques leverage polynomial transformations on the eigenvalues or…
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…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the…
The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse…