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The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be $O(\|H\| t)$ in the worst case, which essentially states that one can not go across the multiple scales as the…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…
We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution…
Trotter product formulas are a natural and powerful approach to perform quantum simulation. However, the error analysis of product formulas is challenging, and their cost is often overestimated. It is established that Trotter error can be…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Trotterization is the most common and convenient approximation method for Hamiltonian simulations on digital quantum computers, but estimating its error accurately is computationally difficult for large quantum systems. Here, we develop a…
Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested…
Suppressing the Trotter error in dynamical quantum simulation typically requires running deeper circuits, posing a great challenge for noisy near-term quantum devices. Studies have shown that the empirical error is usually much smaller than…
Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation,…
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded…
The product formula, commonly known as Trotter decomposition, is a central tool for digital quantum simulation, whose performance depends critically on how the Hamiltonian is partitioned into tractable blocks. Standard decompositions…
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…
Multi-product formulas (MPF) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
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…
Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. The interest often lies in estimating observables rather than explicitly obtaining…