Qubit encodings for lattices of dipolar planar rotors

Abstract

Near term quantum devices have recently garnered significant interest as promising candidates for investigating difficult-to-probe regimes in many-body physics. To this end, various qubit encoding schemes targeting second quantized Hamiltonians have been proposed and optimized. In this work, we investigate two qubit representations of the planar rotor lattice Hamiltonian. The first representation is realized by decomposing the rotor Hamiltonian projectors in binary and mapping them to spin-1/2 projectors. The second approach relies on embedding the planar rotor lattice Hilbert space in a larger space and recovering the relevant qubit encoded system as a quotient space projecting down to the physical degrees of freedom. This is typically called the unary mapping and is used for bosonic systems. We establish the veracity of the two encoding approaches using sparse diagonalization on small chains and discuss quantum phase estimation resource requirements to simulate small planar rotor lattices on near-term quantum devices.

References in corpus (29)

• The density-matrix renormalization group in the age of matrix product states
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Probing many-body dynamics on a 51-atom quantum simulator
• The Variational Quantum Eigensolver: a review of methods and best practices
• The ITensor Software Library for Tensor Network Calculations
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Quantum Monte Carlo with Directed Loops
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Qubit-excitation-based adaptive variational quantum eigensolver
• Convolutional and tail-biting quantum error-correcting codes
• Geometry Dependence of the Sign Problem
• Digital quantum simulation of molecular vibrations
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Quantum field theory for the chiral clock transition in one spatial dimension
• Improving Hamiltonian encodings with the Gray code
• Quantum algorithm for calculating molecular vibronic spectra
• Hamiltonian variational ansatz without barren plateaus
• A Comparison of Quantum Walk Implementations on NISQ Computers
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Quantum criticality in chains of planar rotors with dipolar interactions
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain
• Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo
• Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors