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Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources.…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
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…
These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices. The general strategy is presented following the recent book with H.T. Yau. We extend the scope of…
We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel…
Inspired by random walk on graphs, diffusion map (DM) is a class of unsupervised machine learning that offers automatic identification of low-dimensional data structure hidden in a high-dimensional dataset. In recent years, among its many…
Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…
We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…
Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require…
An intriguing interpretation of the time-evolution of dynamical systems is to view it as a computation that transforms an initial state to a final one. This paradigm has been explored in discrete systems such as cellular automata models,…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational…
We provide several quantum algorithms for continuous optimization that do not require gradient estimation. Instead, we encode the optimization problem into the dynamics of a physical system and coherently simulate the time evolution. We…
The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting…
We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for…