Related papers: First-Order Trotter Error from a Second-Order Pers…
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…
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…
Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science, and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good…
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…
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 foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
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 computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We…
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 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…
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…
Understanding algorithmic error accumulation in quantum simulation is crucial due to its fundamental significance and practical applications in simulating quantum many-body system dynamics. Conventional theories typically apply the triangle…
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…
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…
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…
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,…
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where…
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…
We present a general framework for promoting first-order pulse sequences in quantum simulation to higher-order sequences that maintain robustness in the presence of finite pulse-width effects. Our approach maps a given first-order pulse…