Analysis of Superfast Encoding Performance for Electronic Structure Simulations

Abstract

In our recent work, we have examined various fermion to qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev Superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the $L_1$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as Hydrogen lattices. Our results showed that the resource efficiency of OSE is strongly affected by the spatial locality of the underlying single-particle basis. We find that OSE is outperformed by JW when the orbitals in the underlying single-particle basis are highly overlapping, which limits its applicability to near-term quantum chemistry simulations utilizing standard basis sets. In contrast, when orbitals are overlapping with only few others, as is the case of Hydrogen lattices with very tight orbitals, OSE fares comparatively better. Our results illustrate the importance of choosing the right combination of basis sets and fermion to qubit mapping to get the most out of a quantum device when simulating physical systems.

arXiv comment9 pages, 3 figures, corrected typos, updated to journal version

References in corpus (21)

• Quantum Simulation
• Fermionic quantum computation
• Hamiltonian Simulation by Qubitization
• Simulating Hamiltonian dynamics with a truncated Taylor series
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• A random compiler for fast Hamiltonian simulation
• Quantum Algorithms for Fermionic Simulations
• Gate count estimates for performing quantum chemistry on small quantum computers
• Solving strongly correlated electron models on a quantum computer
• Low Depth Quantum Simulation of Electronic Structure
• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• Mapping local Hamiltonians of fermions to local Hamiltonians of spins
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Lowering qubit requirements for quantum simulations of fermionic systems
• Operator Locality in Quantum Simulation of Fermionic Models
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Fermions without fermi fields
• Eliminating fermionic matter fields in lattice gauge theories
• Qubit Allocation for Noisy Intermediate-Scale Quantum Computers

Cited by in corpus (6)

• Quantum computational chemistry
• The Variational Quantum Eigensolver: a review of methods and best practices
• A unified framework of transformations based on the Jordan-Wigner transformation
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Fermihedral: On the Optimal Compilation for Fermion-to-Qubit Encoding
• Basis set convergence of Wilson basis functions for electronic structure