Related papers: Tight Bounds for Quantum Phase Estimation and Rela…
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 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…
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…
An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the systematic errors in gates and…
Quantum phase estimation algorithm (PEA) is one of the most important algorithms in early studies of quantum computation. It is also a key for many other quantum algorithms, such as the quantum counting algorithm and the Shor's integer…
Phase estimation is known to be a robust method for single-qubit gate calibration in quantum computers, while Bayesian estimation is widely used in devising optimal methods for learning in quantum systems. We present Bayesian phase…
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)…
In this thesis, attention is paid to small experimental testbed applications with respect to the quantum phase estimation algorithm, the core approach for finding energy eigenvalues. An iterative scheme for quantum phase estimation (IPEA)…
We study the phase discrimination problem, in which we want to decide whether the eigenphase $\theta\in(-\pi,\pi]$ of a given eigenstate $|\psi\rangle$ with eigenvalue $e^{i\theta}$ is zero or not, using applications of the unitary $U$…
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…
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
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 investigate the response to noise, in the form of glassy disorder present in circuit elements, in the success probability of the quantum phase estimation algorithm, a subroutine used to determine the eigenvalue - a phase - corresponding…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
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…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
Quantum parameter estimation plays a key role in many fields like quantum computation, communication and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model.…
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…
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…