Quantum Beaker(a martinqq.com project)
Hartree–Fock pretends each electron moves in the average field of all the others, which turns an impossible many-electron problem into a small matrix problem, iterated until it stops changing (the SCF loop). Orbitals are built from Gaussian functions: the STO-3G basis set, fetched live from the Basis Set Exchange. What it misses is the correlation energy, electrons dodging each other instantaneously: small, but it decides bonds and reaction barriers. Node 1 hands its orbitals and Hamiltonian to Nodes 2–4, so every curve starts at the HF energy; for big molecules it freezes the core and passes only an active space of frontier orbitals (e.g. 6 orbitals = 12 qubits).
Each molecular orbital counts twice, once per spin, and each of these spin orbitals gets one qubit: |1⟩ occupied, |0⟩ empty. The Jordan–Wigner mapping rewrites the electronic Hamiltonian as a weighted sum of Pauli strings (products of I, X, Y, Z), with strings of Z gates that keep the fermionic sign right: H₂ gives 15 strings, water about 1,100. The Hartree–Fock state is simply the first N qubits set to |1⟩, one per electron.
Starting from Hartree–Fock, the circuit applies UCC excitations: rotations by an angle θ that move one electron (single) or two (double) from occupied to empty orbitals. Each is a product of Pauli-string rotations (2 for a single, 8 for a double), and each rotation is a textbook block: a basis change (H, or S†·H) turning X and Y into Z, a CNOT ladder gathering the parity onto one qubit, Rz(θ), then the ladder and basis change undone. Those CNOT ladders are why circuit depth, and simulation cost, grow as ADAPT adds excitations.
VQE rests on the variational principle: the energy of any state is at or above the true ground-state energy, so a classical optimiser (BFGS) can push the circuit's angles downhill while the simulator evaluates energies. ADAPT grows the circuit one excitation at a time: screen every candidate's energy gradient, add the largest, re-optimise all the angles, and stop once the gradient norm falls below the tolerance. Qiskit (Node 2), NVIDIA CUDA-Q (Node 3) and Quantum Rings (Node 4) do this concurrently from the same warm start: every point on the chart is one optimiser iteration, and the three curves reach the same energy at different speeds.
After every ADAPT round the current circuit is exported as OpenQASM 2.0 (Copy QASM). Our Quantathon runtime model predicts how long Quantum Rings' simulator takes to run it at thresholds 16, 64 and 512, and Node 4 measures the same circuit, so the panel shows predicted next to measured. Each pair is scored with the challenge metric: score = max(0, 1 − |log10(predicted / measured)| / 2).
Full write-up, with equations, numbers and code pointers: docs/how-it-works.md
docs/how-it-works.md
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Click to place C
click atom: select · click again: attach · drag: move / place · drag space: rotate · ⌫ delete · ⌘Z undo ?
