Related papers: Non-unitary Time Evolution via the Chebyshev Expan…
We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev…
We present $TimeEvolver$, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix $i H$, where $H$…
We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
We provide a new perspective on non-Hermitian evolution in quantum mechanics by emphasizing the same method as in the Hermitian quantum evolution. We first give a precise description of the non unitary evolution, and collecting the basic…
We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the…
We carry Chebyshev-polynomial expansion of the inverse localization length of Hermitian and non-Hermitian random chains as function of energy. For Hermitian models, the expansion produces numerically this energy-dependent function in one…
Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We…
Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause…
We present a numerical framework to study the cosmological background evolution in $f(R)$ gravity by employing a \textit{spectral Chebyshev collocation approach}. Unlike standard integration methods such as Runge--Kutta that often encounter…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff's results in this direction provide us with…
Calculating the spectral function of two dimensional systems is arguably one of the most pressing challenges in modern computational condensed matter physics. While efficient techniques are available in lower dimensions, two dimensional…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
The Krylov subspace method is a standard approach to approximate quantum evolution, allowing to treat systems with large Hilbert spaces. Although its application is general, and suitable for many-body systems, estimation of the committed…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…