What Do the Opcodes Look Like as Physical Pulses?

Plain-language explainer for doi:10.5281/zenodo.20680609 (#411)

The central idea in one sentence

Every Origami ISA opcode is a shaped microwave or laser pulse, DRAG is the ISA type checker, and G₂ holonomic gates are topologically protected in a way that SU(2) gates are not.

Bridging two communities

The Origami ISA programme specifies what a gate should do algebraically. The optimal control community (GRAPE, DRAG, randomised benchmarking) optimises how to shape the pulse to implement it. These two communities have not previously spoken the same language. This paper bridges them.

The three results

DRAG is the ISA type checker. In a transmon qubit, the $\lvert 2\rangle$ state (second excited level) is always present. A TWIST pulse that leaks amplitude into $\lvert 2\rangle$ is, in ISA terms, an ill-typed operation — TWIST should stay within the computational subspace ${\lvert 0\rangle, \lvert 1\rangle}$. DRAG (Derivative Removal via Adiabatic Gate) suppresses this leakage by adding a derivative term to the pulse envelope. DRAG is the pulse-level implementation of the ISA typing rule. ISA-augmented GRAPE reduces leakage by 63% vs standard GRAPE.

SPIN costs 12 CNOTs as a permutation, then hits an obstruction. The SPIN opcode (G₂ triality) acts on 7 Fano-point qubits as a permutation of order 3. As a permutation, it costs exactly 12 CNOTs. But its phase component — $i\sqrt{7}/2$ — is not a root of unity, so it cannot be implemented exactly by any standard gate set. This is the hardware signature of associamancy.

G₂ holonomic gates have discrete Berry phases. The Weyl group of G₂ is $D_6$ (dihedral, order 12). All closed loops in G₂ parameter space give holonomies in this discrete group — 12 possible values, not a continuous angle. This discreteness gives topological protection: small perturbations to the control path that stay within one Weyl chamber leave the gate exactly unchanged. SU(2) holonomic gates have no such protection.

For the full technical treatment, see doi:10.5281/zenodo.20680609