Efficient Product Formulas for Commutators and Applications to Quantum Simulation

Abstract

We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

arXiv comment18 pages, 11 figures

References in corpus (14)

• Elucidating Reaction Mechanisms on Quantum Computers
• Toward the first quantum simulation with quantum speedup
• A Theory of Trotter Error
• Floquet approach to ${\mathbb{Z}}_2$ lattice gauge theories with ultracold atoms in optical lattices
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Finding Exponential Product Formulas of Higher Orders
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Nearly optimal lattice simulation by product formulas
• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• Quantum Algorithms for Simulating the Lattice Schwinger Model
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Destructive Error Interference in Product-Formula Lattice Simulation
• Product Formulas for Exponentials of Commutators

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• Optimizing edge state transfer in a Su-Schrieffer-Heeger chain via hybrid analog-digital strategies
• Double-bracket quantum algorithms for diagonalization
• Trotter error with commutator scaling for the Fermi-Hubbard model
• Scaling of errors in digitized counterdiabatic driving
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• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Quantum Dynamic Programming
• Digital Quantum Simulation, Learning of the Floquet Hamiltonian, and Quantum Chaos of the Kicked Top
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• Approximating exponentials of commutators by optimized product formulas
• Double-bracket algorithm for quantum signal processing without post-selection
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Effective (Floquet) Lindblad generators from spectral unwinding
• Adaptive random compiler for Hamiltonian simulation
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Sub-Riemannian geometry of measurement based quantum computation
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics