Hamiltonian Simulation for Fusion Materials

Simulating quantum time evolution e^{-iHt} is the core primitive behind every materials and chemistry use case in the Kronos quantum program.

The primitive: unitary time evolution

The reason quantum computers are interesting for materials at all is that simulating the time evolution of a quantum system is native to them. For a Hamiltonian H, the state evolves by the unitary U(t) = exp(-i H t / hbar). Classically, representing the state of n interacting fermions costs memory that grows exponentially; a quantum register stores it in n qubits and evolves it with a circuit.

i hbar d|psi>/dt = H |psi>
=> |psi(t)> = U(t)|psi(0)>,   U(t) = exp(-i H t / hbar)

# H for an electronic-structure problem (second quantization):
H = sum_pq  h_pq a_p^dag a_q
  + (1/2) sum_pqrs  g_pqrs a_p^dag a_q^dag a_r a_s
#   h_pq   one-electron integrals (kinetic + nuclear)
#   g_pqrs two-electron Coulomb integrals

Why Kronos cares

• First-wall tungsten and its response to 14 MeV neutron damage is a strongly correlated d-electron problem.
• Lithium-bearing breeder blanket chemistry governs tritium retention and release.
• REBCO high-temperature superconductors, the basis of the 16.84 T breeder magnets, are correlated-electron materials no classical method solves cleanly.

From fermions to qubits

To run on qubits the fermionic operators must be mapped to Pauli operators via the Jordan-Wigner or Bravyi-Kitaev transformation, turning H into a weighted sum of Pauli strings H = sum_k c_k P_k. Two implementation routes then exist: product-formula methods (Trotterization) and modern qubitization / LCU methods with better asymptotic scaling.

The eigenvalues of H are the energy levels we ultimately want; time evolution is the engine that quantum phase estimation uses to extract them, and the variational VQE approach uses shorter evolutions as ansatz building blocks. All of this is offline L0 work with a classical reference solve run alongside; none of it touches the real-time machines.