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The measurement of black hole spin is considered one of the key problems in relativistic astrophysics. Existing methods, such as continuum fitting, X-ray reflection spectroscopy and quasi-periodic oscillation analysis, have systematic…
The conventional spin dynamics simulations are performed in direct products of state spaces of individual spins. In a general system of n spins, the total number of elements in the state basis is >4^n. A system propagation step requires an…
Transport phenomena play a key role in a variety of application domains, and efficient simulation of these dynamics remains an outstanding challenge. While quantum computers offer potential for significant speedups, existing algorithms…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best…
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…
A family of double-quantum excitation schemes is described for the solution nuclear magnetic resonance (NMR) of near-equivalent spin-1/2 pairs. These new methods exploit the spinor behaviour of 2-level systems, whose signature is the change…
We introduce a powerful iterative algorithm to compute protein folding pathways, with realistic all-atom force fields. Using the path integral formalism, we explicitly derive a modified Langevin equation which samples directly the ensemble…
State-of-the-art algorithms for simulating fermions coupled to gauge fields often rely on integrating fermion degrees of freedom. While successful in simulating QCD at zero chemical potential, at finite density these approaches are hindered…
Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…
In this paper, we study the design of pulse sequences for NMR spectroscopy as a problem of time optimal control of the unitary propagator. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state.…
Efficient numerical methods are promising tools for delivering unique insights into the fascinating properties of physics, such as the highly frustrated quantum many-body systems. However, the computational complexity of obtaining the wave…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
This paper presents a numerical framework for the low-rank approximation of the solution to three-dimensional parabolic problems. The key contribution of this work is the tensorization process based on a tensor-train reformulation of the…
Optimal state transport across spin chains, which are proposed as quantum wires for information transfer in solid state quantum architectures, is an important topic for quantum technologies. In this work, we study {the remote restoring of a…
Physics-informed neural networks (PINNs) have been increasingly employed due to their capability of modeling complex physics systems. To achieve better expressiveness, increasingly larger network sizes are required in many problems. This…
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent noise case, the presence of correlation prevents the…
Simulating quantum many-body systems (QMBS) is one of the long-standing, highly non-trivial challenges in condensed matter physics and quantum information due to the exponentially growing size of the system's Hilbert space. To date, tensor…
Monte Carlo simulations are useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, leading to an exponential slow down in their convergence to a value. While solving the sign problem is generically…