Quantum algorithms for Schrieffer-Wolff transformation
arXiv:2201.13304 · doi:10.1103/PhysRevResearch.4.043023
Abstract
The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of unperturbed Hamiltonian. This unitary transformation decoupling the low-energy and high-energy subspaces for the transformed Hamiltonian can be realized by quantum circuits. We give a fully quantum algorithm for realizing the SW transformation. We also propose a hybrid quantum-classical algorithm for finding the effective Hamiltonian on NISQ hardware, where a general cost function is used to indicate the decoupling degree. Numerical simulations without or with noise and experiments on quantum computer ibmq_manila are implemented for a Heisenberg chain model. Our results verify the algorithm and show its validity on near-term quantum computers.
arXiv comment11 pages, 5 figures
References in corpus (40)
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Circuit Quantum Electrodynamics
- Efficient simulation of one-dimensional quantum many-body systems
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Measuring entanglement entropy through the interference of quantum many-body twins
- A Theory of Fault-Tolerant Quantum Computation
- Efficient variational quantum simulator incorporating active error minimisation
- Schrieffer-Wolff transformation for quantum many-body systems
- Direct estimations of linear and non-linear functionals of a quantum state
- Universal Quantum Estimator
- A tunable coupling scheme for implementing high-fidelity two-qubit gates
- In-Medium Similarity Renormalization Group for Nuclei
- Critical Quantum metrology with a finite-component quantum phase transition
- Learning-based quantum error mitigation
- Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators
- Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
- Variational algorithms for linear algebra
- Kondo Quantum Criticality of Magnetic Adatoms in Graphene
- Quantum state transmission via a spin ladder as a robust data bus
- Enhancing optomechanical coupling via the Josephson effect
- Methodology for replacing indirect measurements with direct measurements
- A numerical canonical transformation approach to quantum many body problems
- Cavity quantum electrodynamics with semiconductor quantum dots: The role of phonon-assisted cavity feeding
- Vibrational Sidebands and Kondo-effect in Molecular Transistors
- Generalized Schrieffer-Wolff Formalism for Dissipative Systems
- High-harmonic generation in one-dimensional Mott insulator
- Nuclear spin cooling using Overhauser field selective coherent population trapping
- Energy spectra for quantum wires and 2DEGs in magnetic fields with Rashba and Dresselhaus spin-orbit interactions
- QuESTlink -- Mathematica embiggened by a hardware-optimised quantum emulator
- Low-energy effective Hamiltonians for correlated electron systems beyond density functional theory
- Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics
- Effective Hamiltonians for interacting superconducting qubits -- local basis reduction and the Schrieffer-Wolff transformation
- Quantum algorithm for universal implementation of projective measurement of energy
- Rescuing a Quantum Phase Transition with Quantum Noise
- Effective Hamiltonians in the Quantum Rabi Problem
Cited by in corpus (5)
- Pymablock: an algorithm and a package for quasi-degenerate perturbation theory
- Schrieffer-Wolff transformation for non-Hermitian systems: application for -symmetric circuit QED
- Recursive relations and quantum eigensolver algorithms within modified Schrieffer--Wolff transformations for the Hubbard dimer
- Systematic Schrieffer-Wolff-transformation approach to Josephson junctions: quasiparticle effects and Josephson harmonics
- The toric code under antiferromagnetic isotropic Heisenberg interactions