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The cumulant representation is common in classical statistical physics for variables on the real line and the issue of closures of cumulant expansions is well elaborated. The case of phase variables significantly differs from the case of…
In this paper, we introduce a novel and general framework for the variational quantum simulation of Lindblad equations. Building on the close relationship between the unraveled Lindblad dynamics, stochastic Magnus integrators, and…
A major challenge for the realisation of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To…
The Dirac-Bergmann algorithm for the Hamiltonian analysis of constrained systems is a nice and powerful tool, widely used for quantization and non-perturbative counting of degrees of freedom. However, certain aspects of its application to…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…
This paper introduces GLINTS, a graphical tool for exploring variant narrowing computations in Maude. The most recent version of Maude, version 2.7.1, provides quite sophisticated unification features, including order-sorted equational…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple…
Let $R$ be an integral domain and $G$ be a subgroup of its group of units. We consider the category $\mathbf{\mathsf{Cob}}_G$ of 3-dimensional cobordisms between oriented surfaces with connected boundary, equipped with a representation of…
The gamma process is a natural model for monotonic degradation processes. In practice, it is desirable to extend the single gamma process to incorporate measurement error and to construct models for the degradation of several nominally…
We prove a conjectured asymptotic formula of Kuperberg from the representation theory of the Lie algebra $G_2$. Given a non-negative sequence $(a_n)_{n\geq 1}$, the identity $B(x)=A(xB(x))$ for generating functions $A(x)=1+\sum_{n\geq 1}…
We establish rigorous error bounds for prime counting using a truncated Gaussian (TG) kernel in the explicit formula framework. Our main theorem proves that the approximation error remains globally below 1/2 for all sufficiently large…
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
Amplitude Amplification offers a provable speedup for search problems, which is leveraged in combinatorial optimization by Grover Adaptive Search (GAS). The protocol demands deep circuits that are challenging with regards to NISQ…
The grammar representation of a narrowing tree for a syntactically deterministic conditional term rewriting system and a pair of terms is a regular tree grammar that generates expressions for substitutions obtained by all possible…
To contrast different generators for flow equations for Hamiltonians and to discuss the dependence of physical quantities on unitarily equivalent, but effectively different initial Hamiltonians, a numerically solvable model is considered…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…