Simulating Hamiltonian Dynamics with a Truncated Taylor Series

2014/12/15 by Dominic W. Berry, Andrew M. Childs, Richard Cleve +2 · 776 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Computer science #Hamiltonian (control theory) #Inverse #Mathematical analysis #Mathematical optimization #Mathematics #Neural Networks and Reservoir Computing #Operator (biology) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Series (stratigraphy) #Statistical physics #Taylor series #Unitary state #quant-ph

paper · pdf · doi:10.1103/physrevlett.114.090502

published in Physical Review Letters 114(9), 090502 (American Physical Society) · 5 pages

arxiv created 2014/12/15 · openalex publication_date 2015/03/03 · arxiv updated 2015/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.

Citations

• Simulating quantum dynamics on a quantum computer
• Efficient Quantum Algorithms for Simulating Sparse Hamiltonians
• Simulating physical phenomena by quantum networks
• On the Relationship Between Continuous- and Discrete-Time Quantum Walk
• Elementary gates for quantum computation
• Synthesis of Quantum Logic Circuits
• Simulating physics with computers

Cited by

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• Non-normality and dissipation in Markovian quantum dynamics: Implications for quantum simulation
• Time-Dependent Low-Energy Simulation Accelerates Adiabatic State Preparation
• Compressed variational quantum eigensolver for the Fermi-Hubbard model
• Time-Dependent Hamiltonian Simulation with Optimal Query Complexity
• Diagonal-Budgeted Trotterization for Efficient Quantum Hamiltonian Simulation
• Fermion-to-qubit mappings with varying resource requirements for quantum simulation

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