Related papers: Fourier transform-based linear combination of Hami…
Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
When applying Hamiltonian operator splitting methods for the time integration of multi-species Vlasov-Maxwell-Landau systems, the reliable and efficient numerical approximation of the Landau equation represents a fundamental component of…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
We present a unified algorithmic framework for quantum simulation of non-unitary dynamics and matrix functions, governed by the principle of spectral aliasing derived from the Poisson Summation Formula (PSF). By reinterpreting…
Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…
Virtually all verification and synthesis techniques assume that the formal specifications are readily available, functionally correct, and fully match the engineer's understanding of the given system. However, this assumption is often…
Quantum neural networks combine quantum computing with advanced data-driven methods, offering promising applications in quantum machine learning. However, the optimal paradigm for balancing trainability and expressivity in QNNs remains an…
We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard…
Analog quantum simulators emulate complex many-body dynamics through native continuous-time evolution under hardware-defined interactions. Yet once a platform is specified, its interaction structure is largely fixed by the underlying…
Quantum computers can efficiently simulate highly entangled quantum systems, offering a solution to challenges facing classical simulation of Quantum Field Theories (QFTs). This paper presents an alternative to traditional methods for…
Large language model (LLM) based services are primarily structured as client-server interactions, with clients sending queries directly to cloud providers that host LLMs. This approach currently compromises data privacy as all queries must…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay…
This study explores the utility of a kernel in complex Langevin simulations of quantum real-time dynamics on the Schwinger-Keldysh contour. We give several examples where we use a systematic scheme to find kernels that restore correct…