Related papers: A Monte Carlo approach to bound Trotter error
Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause…
In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
Universal quantum simulation may provide insights into those many-body systems that cannot be described classically, and that cannot be efficiently simulated with current technology. The Trotter formula, which decomposes a desired unitary…
Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
We consider a Trotter-type-product formula for approximating the solution of a linear abstract Cauchy problem (given by a strongly continuous semigroup), where the underlying Banach space is a product of two spaces. In contrast to the…
Large particle systems are often described by high-dimensional (linear) kinetic equations that are simulated using Monte Carlo methods for which the asymptotic convergence rate is independent of the dimensionality. Even though the…
Although the simulation of quantum chemistry is one of the most anticipated applications of quantum computing, the scaling of known upper bounds on the complexity of these algorithms is daunting. Prior work has bounded errors due to…
The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies \cite{WBCH13a,HWBT14a} have cast a shadow on this hope by revealing that the complexity in gate count of such simulations…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
In a recent work, M. Troyer, F. Alet and S. Wessel \cite{brazilean} proposed a way to extend histogram methods to quantum systems in the World Line Quantum Monte Carlo (WLQMC) formulation. The strategy, also proposed in \cite{josedaniel},…
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and…
It is shown that for a certain class of the Kato functions the Trotter-Kato product formulae converge in Dixmier ideal C 1,$\infty$ in topology, which is defined by the $\times$ 1,$\infty$-norm. Moreover, the rate of convergence in this…
Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and…
Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational…
Quantum simulation offers a promising framework for quantum field theory calculations. Obtaining reliable results, however, requires careful characterization of systematic uncertainties. One important source is the boson truncation error,…
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…
Product-formula (PF) based quantum simulation is a promising approach for simulating quantum systems on near-term quantum computers. Achieving a desired simulation precision typically requires a polynomially increasing number of Trotter…
Efficient simulation of the semiclassical Schr\"odinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time…