Related papers: Optimizing quantum phase estimation for the simula…
Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time…
Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product…
A typical goal of a quantum simulation is to find the energy levels and eigenstates of a given Hamiltonian. This can be realized by adiabatically varying the system control parameters to steer an initial eigenstate into the eigenstate of…
We numerically investigate quantum circuit elementary-gate level instantiations of the standard Quantum Phase Estimation (QPE) algorithm for the task of computing the ground-state energy of a quantum magnet; the disordered fully-connected…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
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 rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as…
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…
Quantum computers are a highly promising tool for efficiently simulating quantum many-body systems. The preparation of their eigenstates is of particular interest and can be addressed, e.g., by quantum phase estimation algorithms. The…
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This…
We adapt the robust phase estimation algorithm to the evaluation of energy differences between two eigenstates using a quantum computer. This approach does not require controlled unitaries between auxiliary and system registers or even a…
Estimating the ground-state energy of Hamiltonians is a fundamental task for which it is believed that quantum computers can be helpful. Several approaches have been proposed toward this goal, including algorithms based on quantum phase…