Related papers: Hamiltonian simulation with nearly optimal depende…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
This paper concerns a first-order algorithmic technique for a class of optimal control problems defined on switched-mode hybrid systems. The salient feature of the algorithm is that it avoids the computation of Fr\'echet or G\^ateaux…
A random walk-based method is proposed to efficiently compute the solution of a large class of fractional in time linear systems of differential equations (linear F-ODE systems), along with the derivatives with respect to the system…
Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…
Efficient simulation of quantum dynamics with time-dependent Hamiltonians is important not only for time-varying systems but also for time-independent Hamiltonians in the interaction picture. Such simulations are more challenging than their…
We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform nearest-neighbor hopping we show that…
Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…
Hamiltonian learning is a cornerstone for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing readily deployable quantum metrology techniques primarily focus on…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal changes of worldline configurations,…
Projective measurements of a single two-level quantum mechanical system (a qubit) evolving under a time-independent Hamiltonian produce a probability distribution that is periodic in the evolution time. The period of this distribution is an…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
We study the regimes in which Hamiltonian simulation benefits from randomization. We introduce a sparse-QSVT construction based on composite stochastic decompositions, where dominant terms are treated deterministically and smaller…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
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…