Parallelization techniques for quantum simulation of fermionic systems

Abstract

Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

27 pages, 12 figures; (v2) corrected a misplaced figure; (v3) updated for publication with minor changes

References in corpus (16)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Chiral effective field theory and nuclear forces
• Simulating Hamiltonian dynamics with a truncated Taylor series
• A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis
• Towards simulating 2D effects in lattice gauge theories on a quantum computer
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Lattice Quantum Chromodynamics and Electrodynamics on a Universal Quantum Computer
• Geometric Quantum Information Structure in Quantum Fields and their Lattice Simulation
• Suppressing Coherent Gauge Drift in Quantum Simulations
• Second-quantized fermionic operators with polylogarithmic qubit and gate complexity
• Non-Abelian gauge invariance from dynamical decoupling
• A Compact Fermion to Qubit Mapping Part 2: Alternative Lattice Geometries
• Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators