Related papers: A randomized quantum algorithm for statistical pha…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…
Quantum phase estimation is fundamental to advancing quantum science and technology. While much of the research has concentrated on estimating a single phase, the simultaneous estimation of multiple phases can yield significantly enhanced…
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 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.…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Quantum phase estimation provides a path to quantum computation of solutions to Hermitian eigenvalue problems $Hv = \lambda v$, such as those occurring in quantum chemistry. It is natural to ask whether the same technique can be applied to…
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…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard, eigenstate-centric form relies on carefully prepared coherent inputs that are costly or impractical for many strongly…
In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the…
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scaling. The proposed algorithms improve significantly from the…
We study the simultaneous estimation of multiple phases as a discretised model for the imaging of a phase object. We identify quantum probe states that provide an enhancement compared to the best quantum scheme for the estimation of each…
Quantum phase estimation is a central primitive in quantum algorithms and sensing, where performance is governed by the sensitivity of measurement signals to the target parameter. While existing methods have developed increasingly…
Quantum phase estimation (QPE) is the key subroutine of several quantum computing algorithms as well as a central ingredient in quantum computational chemistry and quantum simulation. While QPE strategies have focused on the estimation of a…
Quantum phase estimation is one of the most important tools in quantum algorithms. It can be made non-adaptive (meaning all applications of the unitary $U_\phi$ happen simultaneously) without using more applications of $U_\phi$, albeit at…
Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum…
Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
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 performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured. Most quantum…