Quantum Simulation of Second-Quantized Hamiltonians in Compact Encoding

Abstract

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. We show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the ${\varphi }^4$-theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

published version with some corrections; 27 pages, 4 figures

References in corpus (10)

• Simulated Quantum Computation of Molecular Energies
• Exponential algorithmic speedup by quantum walk
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Hartree-Fock on a superconducting qubit quantum computer
• Quantum Simulation of Quantum Field Theory in the Light-Front Formulation
• Simulating Hadronic Physics on NISQ devices using Basis Light-Front Quantization
• Light-Front Field Theory on Current Quantum Computers
• Variational quantum eigensolvers for sparse Hamiltonians
• Quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion
• Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

Cited by in corpus (3)

• Solving hadron structures using the basis light-front quantization approach on quantum computers
• Second-quantized fermionic operators with polylogarithmic qubit and gate complexity
• Quantum simulation of quantum mechanical system with spatial noncommutativity