Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition

Abstract

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

arXiv comment17 pages, 7 figures

References in corpus (31)

• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Fermionic quantum computation
• Hamiltonian Simulation by Qubitization
• Quantum algorithms for quantum chemistry and quantum materials science
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Efficient variational quantum simulator incorporating active error minimisation
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Theory of variational quantum simulation
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• A random compiler for fast Hamiltonian simulation
• Variational quantum simulation of general processes
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Real- and imaginary-time evolution with compressed quantum circuits
• Emerging quantum computing algorithms for quantum chemistry
• Hardware-efficient variational quantum algorithms for time evolution
• A Compact Fermion to Qubit Mapping
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Higher Order Methods for Simulations on Quantum Computers
• Fast-forwarding of Hamiltonians and Exponentially Precise Measurements
• Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Subspace Variational Quantum Simulator
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• The Bonsai algorithm: grow your own fermion-to-qubit mapping
• Local variational quantum compilation of a large-scale Hamiltonian dynamics
• A constructive algorithm for the Cartan decomposition of SU(2^N)
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Computation of Green's function by local variational quantum compilation
• Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation