Related papers: Improved Accuracy for Trotter Simulations Using Ch…
Quantum dynamics simulation via Hamilton simulation algorithms is one of the most crucial applications in the quantum computing field. While this task has been relatively considered the target in the fault-tolerance era, the experiment for…
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…
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…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
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…
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…
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…
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…
Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps $N$ and approximates the evolution of each step by a…
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 simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
We explore the applicability of a stochastic time-evolution algorithm based on probabilistic angle interpolation. To simplify the pre-processing of the algorithm, we take the continuous-time limit, thereby explicitly eliminating Trotter…
Quantum computers open the possibility of performing real-time calculations for quantum field theory scattering processes. We propose to use an index averaging the absolute value of the difference between the accurately calculated Trotter…
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…
Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for…
Simulation of continuous time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision, but it inevitably leads to increased computational efforts. This is particularly…
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…
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 demonstrate a post-quench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware that extends beyond the coherence time of the device. This is achieved using a hybrid quantum-classical algorithm that propagates a…
In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is…