相关论文: Generation of eigenstates using the phase-estimati…
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…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
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…
Phase estimation is used in many quantum algorithms, particularly in order to estimate energy eigenvalues for quantum systems. When using a single qubit as the probe (used to control the unitary we wish to estimate the eigenvalue of), it is…
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…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
We propose a quantum algorithm for finding eigenvalues of non-unitary matrices. We show how to construct, through interactions in a quantum system and projective measurements, a non-Hermitian or non-unitary matrix and obtain its eigenvalues…
A basic building block of many quantum algorithms is the Phase Estimation algorithm (PEA). It estimates an eigenphase $\phi$ of a unitary operator $U$ using a copy of the corresponding eigenstate $|\phi\rangle$. Suppose, in place of…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
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…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Quantum phase estimation algorithm has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
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 present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states or simple mixed states,…
Quantum simulation of complex quantum systems and their properties often requires the ability to prepare initial states in an eigenstate of the Hamiltonian to be simulated. In addition, to compute the eigenvalues of a Hamiltonian is in…
We introduce a new statistical and variational approach to the phase estimation algorithm (PEA). Unlike the traditional and iterative PEAs which return only an eigenphase estimate, the proposed method can determine any unknown…