State-dependent Trotter Limits and their approximations

Abstract

The Trotter product formula is a key instrument in numerical simulations of quantum systems. However, computers cannot deal with continuous degrees of freedom, such as the position of particles in molecules, or the amplitude of electromagnetic fields. It is therefore necessary to discretize these variables to make them amenable to digital simulations. Here, we give sufficient conditions to conclude the validity of this approximate discretized physics. Essentially, it depends on the state-dependent Trotter error, for which we establish explicit bounds that are also of independent interest.

arXiv comment16 pages, 5 figures

References in corpus (24)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Charge insensitive qubit design derived from the Cooper pair box
• Efficient simulation of one-dimensional quantum many-body systems
• Encoding a qubit in an oscillator
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Open Quantum Systems. An Introduction
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Suppressing Charge Noise Decoherence in Superconducting Charge Qubits
• A Theory of Trotter Error
• Density matrix renormalization group study of the polaron problem in the Holstein model
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
• Hamiltonian simulation in the low-energy subspace
• Time-dependent unbounded Hamiltonian simulation with vector norm scaling
• One bound to rule them all: from Adiabatic to Zeno
• Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
• Dynamical Decoupling of Unbounded Hamiltonians
• Trotter errors from dynamical structural instabilities of Floquet maps in quantum simulation
• Universal Atom Interferometer Simulator -- Elastic Scattering Processes
• On the pointwise convergence of the integral kernels in the Feynman-Trotter formula
• Dynamical Decoupling and Homogenization of continuous variable systems
• Path integral in a magnetic field using the Trotter product formula

Cited by in corpus (9)

• Strong Error Bounds for Trotter & Strang-Splittings and Their Implications for Quantum Chemistry
• Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound
• Lower Bounds for the Trotter Error
• Trotterization is substantially efficient for low-energy states
• Convergence of Dynamics on Inductive Systems of Banach Spaces
• Energy-limited quantum dynamics
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Loss tolerant cross-Kerr enhancement via modulated squeezing