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Related papers: Lower Bounds for the Trotter Error

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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…

Quantum Physics · Physics 2024-12-24 Kasra Hejazi , Jay Soni , Modjtaba Shokrian Zini , Juan Miguel Arrazola

Quantum simulation is a cornerstone application of quantum computing, yet how fundamental quantum resources--entanglement and non-stabilizerness (``magic")--shape simulation fidelity remains an open question. In this work, we establish a…

Quantum Physics · Physics 2026-04-16 Xiangran Zhang , Jue Xu , Qi Zhao , You Zhou

The Lie--Trotter product formula is a foundational approximation for the quantum partition function, yet obtaining rigorous error bounds for the unbounded Hamiltonians common in physics remains a significant challenge. This paper provides a…

Quantum Physics · Physics 2025-10-21 Xuda Ye , Zhennan Zhou

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the…

Quantum Physics · Physics 2023-07-26 W. Gong , Yaroslav Kharkov , Minh C. Tran , Przemyslaw Bienias , Alexey V. Gorshkov

Classical simulations of time-dependent quantum systems are widely used in quantum control research. In particular, these simulations are commonly used to host iterative optimal control algorithms. This is convenient for algorithms that are…

Quantum Physics · Physics 2021-11-23 Tyler Jones , Kaiah Steven , Xavier Poncini , Matthew Rose , Arkady Fedorov

Quantum simulation is one of the most promising scientific applications of quantum computers. Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable…

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…

The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation…

Quantum Physics · Physics 2022-02-09 Changhao Yi

Trotter decomposition is the basis of the digital quantum simulation. Asymmetric and symmetric decompositions are used in our GPU demonstration of the digital adiabatic quantum simulations of $2+1$ dimensional quantum $\mathbb{Z}_2$ lattice…

Quantum Physics · Physics 2020-09-02 Xiaopeng Cui , Yu Shi

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…

Quantum Physics · Physics 2017-07-05 Ying Li , Simon C. Benjamin

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…

Quantum Physics · Physics 2023-05-15 Guang Hao Low , Yuan Su , Yu Tong , Minh C. Tran

Simulating the dynamic evolutions of physical and molecular systems in a quantum computer is of fundamental interest in many applications. Its implementation requires efficient quantum simulation algorithms. The Lie-Trotter-Suzuki…

Quantum Physics · Physics 2022-11-15 Yue Yu , Yulin Chi , Chonghao Zhai , Jieshan Huang , Qihuang Gong , Jianwei Wang

We investigate the effect of stochastic control errors on the Hamiltonian that controls a closed quantum system. Quantum information technologies require careful control for preparing a desired state used as an information resource.…

Quantum Physics · Physics 2023-09-04 Kohei Kobayashi

Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols…

Quantum Physics · Physics 2024-06-11 Hongzheng Zhao , Ao Chen , Shu-Wei Liu , Marin Bukov , Markus Heyl , Roderich Moessner

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…

Quantum Physics · Physics 2025-01-30 Yonah Borns-Weil , Di Fang

Hamiltonian simulations are key subroutines in adiabatic quantum computation, quantum control, and quantum many-body physics, where quantum dynamics often happen in the low-energy sector. In contrast to time-independent Hamiltonian…

Quantum Physics · Physics 2026-01-06 Shuo Zhou , Zhaokai Pan , Weiyuan Gong , Tongyang Li

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Numerical Analysis · Mathematics 2024-06-11 Lei-Hong Zhang , Ren-Cang Li

We propose an iterative variational quantum algorithm to simulate the time evolution of arbitrary initial states within a given subspace. The algorithm compresses the Trotter circuit into a shorter-depth parameterized circuit, which is…

Quantum Physics · Physics 2026-02-24 Seung Park , Dongkeun Lee , Jeongho Bang , Hoon Ryu , Kyunghyun Baek

Quantum simulation of dynamics is an important goal in the NISQ era, within which quantum error mitigation may be a viable path towards modifying or eliminating the effects of noise. Most studies on quantum error mitigation have been…

Quantum Physics · Physics 2024-01-31 Yue Ma , M. S. Kim

Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing…