Quick start¶

These examples use the modern solver path in jarvis.io.qiskit.inputs with qiskit>=2.0. They download Wannier tight-binding Hamiltonians from JARVIS-DFT on first use.

Single-\(k\)-point VQE¶

Run a single-\(k\)-point VQE on FCC aluminum (JVASP-816) and compare against classical diagonalization:

from jarvis.db.figshare import get_wann_electron, get_hk_tb
from jarvis.io.qiskit.inputs import HermitianSolver

# 1. Fetch the Wannier tight-binding Hamiltonian for Al from JARVIS-DFT
w, ef, atoms = get_wann_electron(jid="JVASP-816")

# 2. Build H(k) at a chosen k-point
hk = get_hk_tb(w=w, k=[0.5, 0.5, 0.0])

# 3. Solve for eigenvalues with VQE and with exact NumPy diagonalization
HS = HermitianSolver(hk)
vqe_energy, vqe_result, vqe = HS.run_vqe()      # min eigenvalue via VQE
classical_vals, classical_vecs = HS.run_numpy() # exact reference

print("VQE ground state:", vqe_energy)
print("Classical minimum:", min(classical_vals.real))

Choosing an ansatz¶

QuantumCircuitLibrary provides a set of hardware-efficient ansätze. Pass one to run_vqe via var_form:

from jarvis.core.circuits import QuantumCircuitLibrary

n_qubits = HS.n_qubits()
circ = QuantumCircuitLibrary(n_qubits=n_qubits, reps=2).circuit6()
en_vqe, _, _ = HS.run_vqe(var_form=circ, backend="statevector_simulator")

More reps makes the ansatz more expressive (lower energy) but deeper — and, on real hardware, noisier. See Methods for the trade-offs.

Pauli decomposition of \(H(k)\)¶

Any Hermitian matrix can be written as a weighted sum of Pauli strings — exactly what a quantum computer measures:

from jarvis.io.qiskit.inputs import decompose_Hamiltonian

op = decompose_Hamiltonian(hk)   # qiskit SparsePauliOp
print("Number of Pauli terms:", len(op))

Full bandstructure (VQD)¶

VQE returns only the lowest eigenvalue. A bandstructure needs all eigenvalues of \(H(k)\) at every \(k\); VQD finds excited states by re-running VQE with an orthogonality penalty. get_bandstruct does this along a high-symmetry \(k\)-path:

from jarvis.db.figshare import get_wann_electron
from jarvis.io.qiskit.inputs import get_bandstruct

w, ef, atoms = get_wann_electron(jid="JVASP-816")
out = get_bandstruct(w=w, atoms=atoms, line_density=1, savefig=True)
# out["eigvals_q"]  -> quantum (VQD) eigenvalues along the k-path
# out["eigvals_np"] -> classical reference eigenvalues

Use line_density=1 for a quick, crude plot; raise it (and the ansatz reps) for a publication-quality figure.

Back ends¶

run_vqe / run_vqd accept a backend argument:

"statevector_simulator" — exact, noiseless (default; best for learning).
"aer_simulator*" — Qiskit Aer shot-based simulators.
an IBM backend name (e.g. "ibm_brisbane") — real hardware, requires qiskit-ibm-runtime and a saved IBM Quantum token.

A couple of materials to try¶

Material	JARVIS ID
Al (FCC metal)	`JVASP-816`
Si (semiconductor)	`JVASP-1002`

Swap the JID into get_wann_electron(...) and re-run.