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We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
We study quantum speedups in quantum machine learning (QML) by analyzing the quantum singular value transformation (QSVT) framework. QSVT, introduced by [GSLW, STOC'19, arXiv:1806.01838], unifies all major types of quantum speedup; in…
We introduce a hybrid quantum-classical algorithm to compute the Green function for strongly correlated electrons on noisy intermediate-scale quantum (NISQ) devices. The technique consists in the construction of a non-orthogonal excitation…
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…
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…
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…
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…
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…
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…
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the…
Entanglement is a defining property of quantum systems. For a subsystem of a larger quantum system, one can formally define an operator known as the modular Hamiltonian, which is closely linked to the entanglement properties of that…
A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing…
We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the…
We propose a quantum inverse iteration algorithm which can be used to estimate the ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the…
The Green's function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of Green's function impedes the research of…
In this work, we discuss two modifications that can be made to a known variational quantum singular value decomposition algorithm popular in the literature. The first is a change to the objective function which hints at improved performance…
Quantum state tomography aims to estimate the state of a quantum mechanical system which is described by a trace one, Hermitian positive semidefinite complex matrix, given a set of measurements of the state. Existing works focus on…
We introduce a quantum algorithm to perform the Laplace transform on quantum computers. Already, the quantum Fourier transform (QFT) is the cornerstone of many quantum algorithms, but the Laplace transform or its discrete version has not…
Covariant relativistic quantum theory is used to study the covariant Green's function, which can be used to determine the proper time evolved wave functions that are solutions to the covariant Schr\"odinger type equation for a massive spin…
We evaluate the accuracy of the quantum inverse (Q-Inv) algorithm in which the multiplication of $\hat{H}^{-k}$ to the reference wavefunction is replaced by the Fourier Transformed multiplication of $e^{-i\lambda \hat{H}}$, as a function of…