Mapping local Hamiltonians of fermions to local Hamiltonians of spins

Abstract

We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan-Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.

Added explicit mapping

References in corpus (2)

• Ground state entanglement and geometric entropy in the Kitaev's model
• An Introduction to Quantum Order, String-net Condensation, and Emergence of Light and Fermions

Cited by in corpus (157)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum algorithms for quantum chemistry and quantum materials science
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum optimization using variational algorithms on near-term quantum devices
• Criticality, the area law, and the computational power of PEPS
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Quantum Simulation for High Energy Physics
• Solving strongly correlated electron models on a quantum computer
• Fermionic Projected Entangled Pair States
• N-representability is QMA-complete
• Adiabatic Quantum Simulation of Quantum Chemistry
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Nearly optimal lattice simulation by product formulas
• Emerging quantum computing algorithms for quantum chemistry
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum algorithms to simulate many-body physics of correlated fermions
• General Methods for Digital Quantum Simulation of Gauge Theories
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Tensor Network Algorithms: a Route Map
• Gluon Field Digitization for Quantum Computers
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Fault-Tolerant Quantum Simulations of Chemistry in First Quantization
• Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
• An area law for the entropy of low-energy states
• The Bond-Algebraic Approach to Dualities
• A Compact Fermion to Qubit Mapping
• Lowering qubit requirements for quantum simulations of fermionic systems
• Superfast encodings for fermionic quantum simulation
• Observables can be tailored to change the entanglement of any pure state
• Unitary circuits for strongly correlated fermions
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Majorana Fermion Codes
• Operator Locality in Quantum Simulation of Fermionic Models
• Quantum Simulation of Quantum Field Theories in Trapped Ions
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• A randomized quantum algorithm for statistical phase estimation
• Fermionic quantum processing with programmable neutral atom arrays
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Simulating Quantum Materials with Digital Quantum Computers
• Local spin operators for fermion simulations
• Eliminating fermionic matter fields in lattice gauge theories
• Provably accurate simulation of gauge theories and bosonic systems
• Bosonization in three spatial dimensions and a 2-form gauge theory
• Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur Batteries
• Computational Complexity in Electronic Structure
• Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware
• Digital Quantum Simulation with Rydberg Atoms
• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Towards near-term quantum simulation of materials
• Quantum codes for quantum simulation of Fermions on a square lattice of qubits
• Connecting global and local energy distributions in quantum spin models on a lattice
• Resource Estimation for Quantum Variational Simulations of the Hubbard Model
• Majorana loop stabilizer codes for error correction of fermionic quantum simulations
• Quantum spins on star graphs and the Kondo model
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• The Feynman problem and Fermionic entanglement: Fermionic theory versus qubit theory
• Exact bosonization in arbitrary dimensions
• Non-unitary operations for ground-state calculations in near term quantum computers
• Free fermions behind the disguise
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Characterization of solvable spin models via graph invariants
• Fermionic computation is non-local tomographic and violates monogamy of entanglement
• Quantum simulation of interacting high-dimensional systems: the influence of noise
• Equivalence between fermion-to-qubit mappings in two spatial dimensions
• An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase
• Probing the Kitaev honeycomb model on a neutral-atom quantum computer
• On the complexity of implementing Trotter steps
• Causal Fermions in Discrete Spacetime
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Quantum Simulation of Z2 Lattice Gauge theory with minimal resources
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Duality as a Feasible Physical Transformation
• Jordan-Wigner transformations for tree structures
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion
• Complexity phase diagram for interacting and long-range bosonic Hamiltonians
• Optimal local unitary encoding circuits for the surface code
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
• HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware
• Four-qubit pure states as fermionic states
• Hardware-efficient fermionic simulation with a cavity-QED system
• Variational solutions to fermion-to-qubit mappings in two spatial dimensions
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Simulating high-temperature superconductivity model Hamiltonians with atoms in optical lattices
• Variational Quantum Eigensolver for SU($N$) Fermions
• Bosonization based on Clifford algebras and its gauge theoretic interpretation
• Can neural quantum states learn volume-law ground states?
• A unified framework of transformations based on the Jordan-Wigner transformation
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Fermionic approach to variational quantum simulation of Kitaev spin models
• Error-correcting codes for fermionic quantum simulation
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• Fermionic state discrimination by local operations and classical communication
• Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits
• Quantum annealing with twisted fields
• Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates
• Adaptive projected variational quantum dynamics
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model
• Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates
• Hubbard physics with Rydberg atoms: using a quantum spin simulator to simulate strong fermionic correlations
• Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture
• Analysis of Superfast Encoding Performance for Electronic Structure Simulations
• Bosonization of Majorana modes and edge states
• Ultrafast Hybrid Fermion-to-Qubit mapping
• A tensor network approach to 2D bosonization
• The qudit Pauli group: non-commuting pairs, non-commuting sets, and structure theorems
• Free-Fermion Subsystem Codes
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Unambiguous discrimination of Fermionic states through local operations and classical communication
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Digital quantum simulation of lattice fermion theories with local encoding
• Quantum techniques for eigenvalue problems
• Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
• Neutron-nucleus dynamics simulations for quantum computers
• Local Jordan-Wigner transformations on the torus
• Local quantum overlapping tomography
• Gauged cooling of topological excitations and emergent fermions on quantum simulators
• On the locality of qubit encodings of local fermionic modes
• Clifford circuit based heuristic optimization of fermion-to-qubit mappings
• Hardware-efficient quantum phase estimation via local control
• Parallelization techniques for quantum simulation of fermionic systems
• The Hilbert-space structure of free fermions in disguise
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Basis set convergence of Wilson basis functions for electronic structure
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Local fermion-to-qudit mappings: a practical recipe for four-level systems
• Simulating Topological Order on Quantum Processors
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Investigating Stark many-body localization with continuous unitary transformation flows
• Expanding the Class of Free Fermions via Twin-Collapse Methods
• (2+1)D quantum electrodynamics at finite density on a quantum computer
• On sampling determinantal and Pfaffian point processes on a quantum computer
• A minimal tensor network beyond free fermions
• A simple quantum simulation algorithm with near-optimal precision scaling
• Quantum memory assisted observable estimation
• Co-Designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
• Quantum Routing and Entanglement Dynamics Through Bottlenecks
• Engineering quasi-steady-state correlations in uncorrelated thermal states using stochastic driving
• Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers
• Quantum Simulation of Nuclear Dynamics in First Quantization
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms