Related papers: A generalized framework for quantum subspace diago…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large\rev{-}scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized…
We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
We show how to visualize the process of diagonalizing the Hamiltonian matrix to find the energy eigenvalues and eigenvectors of a generic one-dimensional quantum system. Starting in the familiar sine-wave basis of an embedding infinite…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Infinite quasiperiodic arrangements in space, such as quasicrystals, are typically described as projections of higher-dimensional periodic lattices onto the physical dimension. The concept of a reference higher-dimensional space, called a…
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…
First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…
Optimizing over separable quantum objects is challenging for two key reasons: determining separability is NP-hard, and the dimensionality of the problem grows exponentially with the number of qubits. We address both challenges by…
We propose quantum-selected configuration interaction (QSCI), a class of hybrid quantum-classical algorithms for calculating the ground- and excited-state energies of many-electron Hamiltonians on noisy quantum devices. Suppose that an…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the…
The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of…
We describe a semidefinite relaxation method which finds lower bounds to the ground state energy of a quantum Hamiltonian subject to Hermitian linear constraints along with approximations of ground state expectation values. We show that…
We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum…