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We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
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…
Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulation. Among them, a simple and powerful technique, called…
Simulating the time dynamics of an observable under Hamiltonian evolution is one of the most promising candidates for quantum advantage as we do not expect efficient classical algorithms for this problem except in restricted settings. Here,…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational…
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…
We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…
We study a qDRIFT-type randomized method to simulate Lindblad dynamics by decomposing its generator into an ensemble of Lindbladians, $\mathcal{L} = \sum_{a \in \mathcal{A}} \mathcal{L}_a$, where each $\mathcal{L}_a$ comprises a simple…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…