Creating and manipulating a Laughlin-type $\nu =1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits

Abstract

Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $\nu =1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.

arXiv comment7 pages, 7 figures

References in corpus (18)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Simulation
• The theory of variational hybrid quantum-classical algorithms
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Electrodynamics of Correlated Electron Materials
• Elucidating Reaction Mechanisms on Quantum Computers
• Universal digital quantum simulation with trapped ions
• Procedure for systematically tuning up crosstalk in the cross resonance gate
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Fractional Quantum Hall States and Jack Polynomials
• Solving strongly correlated electron models on a quantum computer
• Low Depth Quantum Simulation of Electronic Structure
• Nearly optimal lattice simulation by product formulas
• Quantum algorithms to simulate many-body physics of correlated fermions
• Incompressible Quantum Liquids and New Conservation Laws
• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
• Abelian and non-Abelian statistics in the coherent state representation
• Unified Fock space representation of fractional quantum Hall states

Cited by in corpus (13)

• Many-body physics in the NISQ era: quantum programming a discrete time crystal
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Preparing quantum many-body scar states on quantum computers
• Realizing topologically ordered states on a quantum processor
• Graph state representation of the toric code
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• Braiding fractional quantum Hall quasiholes on a superconducting quantum processor
• Isolated zero mode in a quantum computer from a duality twist
• Fermionic quantum computation with Cooper pair splitters
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Measurable fractional spin for quantum Hall quasiparticles on the disk