Related papers: A Monte Carlo approach to bound Trotter error
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…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
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…
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…
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…
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…
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…
In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows…
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…
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…
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…
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,…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
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…
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…
A multi-product formula (MPF) is a promising approach for Hamiltonian simulation efficiently both in the system size $N$ and the inverse allowable error $1/\varepsilon$ by combining Trotterization and the linear combination of unitaries…
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
Convergence of path integral simulations requires a substantial number of beads when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit through extrapolation, however they are restricted to…
Product formula approximations of the time-evolution operator on quantum computers are of great interest due to their simplicity, and good scaling with system size by exploiting commutativity between Hamiltonian terms. However, product…