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The Fermi-Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
Clinical machine learning applications are often plagued with confounders that are clinically irrelevant, but can still artificially boost the predictive performance of the algorithms. Confounding is especially problematic in mobile health…
We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
The real-time correlators of quantum field theories can be directly probed through new approaches to simulation, such as quantum computing and tensor networks. This provides a new framework for computing scattering observables in lattice…
We introduce an algorithm to improve the error scaling of product formulas by randomly sampling the generator of their exact error unitary. Our approach takes an arbitrary product formula of time $t$, $S_k(t)$ with error $O(t^{k+1})$ and…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…
We derive a universal nonperturbative bound on the distance between unitary evolutions generated by time-dependent Hamiltonians in terms of the difference of their integral actions. We apply our result to provide explicit error bounds for…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schr\"odinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum…
We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the…
Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
We introduce a novel protocol, which enables Heisenberg-limited quantum-enhanced sensing using the dynamics of any interacting many-body Hamiltonian. Our approach - dubbed butterfly metrology - utilizes a single application of forward and…
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…