Singular Quantum Molecular Rotation Algorithm & RUS Parity Verification
Classical atom coordinates are mapped onto continuous trapped-ion vibrational modes. Regardless of whether the molecule contains 10 or 1,000 atoms, the quantum representation compresses into an invariant 4-phase register.
Continuous Harmonic Lie Algebra Pipeline on Quantinuum H2 Trapped Ions
Rather than treating qubits as static binary switches, Q-Rotate embeds continuous spatial coordinates directly into continuous vibrational motional modes and continuous single-qubit Lie group rotations.
Regardless of whether the target biomolecule contains 10 atoms or 10,000 atoms, the entire system compresses into 4 pocket qubits, 4 ligand qubits, and 1 spectator ancilla qubit (O(1) space).
Proprietary pharmaceutical drug structures and target active site pockets never disclose their 3D coordinates. Interference occurs in quantum superposition, measuring only a single-bit parity ancilla.
Classical HPC computes center-of-mass angular distributions in milliseconds. The Quantinuum H2 quantum processor then evaluates the multi-dimensional conformational overlap in a single continuous unitary rotation — bypassing grid discretization entirely.
Encodes the electrostatic and steric profile of the enzyme binding cavity (e.g. COVID Mpro catalytic dyad Cys145/His41 or Rhodopsin Lys296).
Encodes the drug molecule / chromophore conformation. The angular difference ΔΦ between the two rings represents conformational mismatch.
As the evolution parameter τ sweeps from 0 to 1, the ligand's quantum state rotates smoothly through Hilbert space. On the oscilloscope, the Cyan wave slides along the time axis toward the stationary Gold pocket waveform.
Constructive quantum interference! The ligand and pocket wavefunctions are in perfect geometric and electrostatic resonance. Fidelities ≥ 98%.
Destructive interference. The conformational overlap is low, indicating steric clash or electrostatic repulsion.
Neither data register is ever measured! The observer only learns the scalar parity bit P(|0⟩). The underlying 3D structural coordinates remain strictly unexposed inside the quantum coherence sphere.
The ancilla is measured mid-circuit while the data registers retain their quantum coherence.
If mismatch occurs, hardware classical control updates the laser pulse frequency and applies phase dampening in real time.
Within 3 to 5 iterations, the system converges into the global energy minimum, locking in the drug-pocket binding conformation.
\text{HQC} = 5 + \left[ N_{1q} + 10 \times N_{2q} + 5 \times N_m \right] \times \frac{N_{\text{shots}}}{5000}
Gate counts come from the compiled circuit. Nm counts state preps plus measurements. Each RUS iteration is a separate run, so the total is runs × per-circuit cost. This is an estimate, not a billed job.
@guppy.comptime
def guppy_qrotate_rus_demo() -> None:
# 1. Allocate Trapped-Ion Registers
q_pocket = qubit()
q_ligand = qubit()
ancilla = qubit()
# 2. Continuous Phase Encoding Rz(Φ)
h(q_pocket); rz(q_pocket, angle(0.25))
h(q_ligand); rz(q_ligand, angle(0.40))
# 3. Apply Continuous Lie Evolution U_tube(τ)
ry(q_ligand, angle(0.15))
rz(q_ligand, angle(0.10))
# 4. Coordinate-Free Blind Parity SWAP
h(ancilla)
cx(q_ligand, q_pocket)
toffoli(ancilla, q_pocket, q_ligand) # 3x Native ZZPhase
cx(q_ligand, q_pocket)
h(ancilla)
# 5. Mid-Circuit Measurement & FPGA Reset
m_parity = measure(ancilla)
if m_parity == 1:
reset(ancilla) # RUS Loop Trigger
output("parity_error", m_parity)Superconducting chips have planar grid connectivity (heavy SWAP routing overhead). Quantinuum physically shuttles ions across 32 zones with zero routing penalty for the 4 Controlled-SWAP pairs.
High-depth continuous rotation circuits require ultra-high fidelity. H2 barium/ytterbium ions deliver the fidelity necessary for deep conformational verification.
Continuous parameters τ and φ_m map directly to laser phase shifts with zero gate synthesis decomposition overhead.