Related papers: Measurement-based quantum phase estimation algorit…
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
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…
Quantum metrology employs quantum properties to enhance the precision of physical parameters, in order to characterize quantum states as well as channels. Frequency and temperature estimations are of fundamental importance for these tasks…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
State and measurement tomography make assumptions about the experimental states or measurements. These assumptions are often not justified because state preparation and measurement errors are unavoidable in practice. Here we describe how…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Quantum physics is generally concerned with real eigenvalues due to the unitarity of time evolution. With the introduction of $\mathcal{PT}$ symmetry, a widely accepted consensus is that, even if the Hamiltonian of the system is not…
We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant…
Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for fast extraction of information stored in the quantum state…
This paper proposes a power method for computing the dominant eigenvalues of a non-Hermitian dual quaternion matrix (DQM). Although the algorithmic framework parallels the Hermitian case, the theoretical analysis is substantially more…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
In quantum metrology schemes, one generally needs to prepare $m$ copies of $N$ entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here, we present a…