Related papers: Quantum phase estimation of multiple eigenvalues f…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
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…
Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary…
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 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…
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…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
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…
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…
We introduce a classical estimator for the post-processing of quantum phase estimation data generated either by quantum-Fourier-transform-based or quantum-signal-processing-based methods. We focus on the estimation of a single target phase…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
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 phase estimation is an important routine in many quantum algorithms, particularly for estimating the ground state energy in quantum chemistry simulations. This estimation involves applying powers of a unitary to the ground state,…
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…
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…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
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…
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault…
The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the…
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…