Related papers: Product Formulas for Exponentials of Commutators
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…
This article discusses the convergence properties of the Max Product and Max Min variants of Durrmeyer type exponential sampling series. We first establish pointwise and uniform convergence of both operators in the space of log uniformly…
Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at…
We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.
The factorized form of the unitary coupled cluster ansatz is a popular state preparation ansatz for electronic structure calculations of molecules on quantum computers. It often is viewed as an approximation (based on the Trotter product…
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson $q$-exponential of the sum of two non-$q$-commuting operators as an (in general) infinite product of $q$-exponential operators involving repeated…
The large dimensionality of environments is the limiting factor in applying optimal control to open quantum systems beyond Markovian approximations. Multiple methods exist to simulate non-Markovian open systems which effectively reduce the…
As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product…
Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum…
In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological…
With quantum resources a precious commodity, their efficient use is highly desirable. Quantum autoencoders have been proposed as a way to reduce quantum memory requirements. Generally, an autoencoder is a device that uses machine learning…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
We present a numerical scheme for efficiently extracting the higher-order moments and cumulants of various operators on spin systems represented as tensor product states, for both finite and infinite systems, and present several…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…