Strong empiricalHamiltonian simulation
Ising Trotter-step benchmark · 3 qubits
A first-order nearest-neighbor ZZ evolution scaffold expressed as CNOT–RZ–CNOT blocks.
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A first-order nearest-neighbor ZZ evolution scaffold expressed as CNOT–RZ–CNOT blocks.
A problem-inspired layer combining ZZ interactions and transverse X rotations for a ring Ising model.
Simulate strongly correlated fermionic systems — notoriously hard for classical computers — on a quantum computer with 2D or linear (1D) nearest-neighbor qubit-qubit couplings, of the kind typical of superconducting transmon qubit arrays, including preparing the relevant quantum states and evolving the system in time, with the Fermi-Hubbard model as a worked example.
The two-site Fermi-Hubbard dimer Hamiltonian, mapped to qubits via the Jordan-Wigner transformation: nearest-neighbor hopping competing with on-site Coulomb repulsion.
A compact Hamiltonian-simulation pattern for spin chains: alternate local field rotations with entangling ZZ evolution.
The anisotropic Heisenberg (XXZ) spin-chain Hamiltonian: exchange-coupled spins with tunable easy-axis/easy-plane anisotropy Δ, U(1)-symmetric under total-Sz rotation.
Given a hard combinatorial problem, rewrite it as an Ising spin model whose lowest-energy spin configurations are exactly that problem's solutions, so that a machine which minimizes energy can be pointed at the problem at all.
The classical (longitudinal-field) Ising Hamiltonian expressed as a diagonal SparsePauliOp: a foundational Z-only spin model with no quantum superposition dynamics of its own.
Given a braid on n strands with m crossings and an integer k, compute a certain additive approximation to the Jones polynomial of the link obtained by closing the braid, evaluated at the primitive root of unity e^(2πi/k).
Simulate the quantum kicked rotator model — used to study quantum chaos, localization and the Anderson transition — with a quantum algorithm that scales better than classical simulation of the same model.
The transverse-field Ising model (TFIM): the standard minimal Hamiltonian exhibiting a quantum (zero-temperature) phase transition driven by competing Z-Z order and X-field disorder.
Given a compact, orientable three-manifold presented by a Heegaard splitting, compute a certain additive approximation to its Turaev-Viro invariant, the scalar topological invariant that takes the same value on homeomorphic manifolds.
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