The Gate — Winding-Class Holonomic Gates

In plain terms AT-001 is a new way to control a qubit in superposition. In a conventional gate, the qubit performs whatever imperfect pulse the control electronics deliver. AT-001 moves the operation out of the pulse and into the circuit geometry: the gate is set by how the superconducting phase winds through the device. Because the result depends on an integer winding number rather than precise pulse amplitude, the operation becomes more stable against control error.

AT-001 breaks that link. The operation is not defined by the exact height or shape of the pulse, but by an integer winding number: how many times the superconducting phase winds through a physical loop. The gate is implemented as a Wilczek–Zee holonomy in a zero-energy dark subspace, so the result depends on the winding class of the path, not on the fine details of the waveform.

The pulse can flex. The integer cannot. As long as the winding is enforced and the evolution remains adiabatic, a whole class of control-amplitude error cancels by construction. An integer is hard to get a little bit wrong.

This is not a claim of topological fault tolerance. The winding still has to be driven correctly, and adiabaticity, fabrication tolerance, leakage, and disorder still matter. The claim is narrower and more useful for near-term hardware: the gate is winding-class robust. It moves the burden from perfect pulse amplitude to circuit geometry and path class.

It also pairs naturally with AT-002. The gate needs clean flux bias; the quiet coil supplies it. By confining the bias field near the qubit, the coil helps the winding-class advantage survive as qubits are packed closer together instead of being washed out by crosstalk.

The logical qubit lives in a pair of zero-energy dark states; the gate angle is set by the integer winding number ν as the phase winds through the loop, while the quiet coil (AT-002) supplies the bias and keeps the field local.

Provisional filed — App. 64/017,790. Analytically derived and simulation-validated; not yet silicon-proven.

Inside the gate

The dark subspace

The logical qubit is encoded in two zero-energy dark states, |D₁⟩ and |D₂⟩. These states are decoupled from the lossy excited level and separated from the bright sector by a dark–bright gap above ~420 MHz. That gap raises the cost of erasure: thermal and TLS processes have to cross it before they can spoil the distinction the qubit is holding open.

Winding-class control

A flux sweep with winding number ν = 1 sets the gate angle, θ = 2πνλ. The path can deform and the waveform can vary, but if the winding number is unchanged, the gate angle is unchanged to first order. That is the core move: the operation is carried by a winding class, not by pulse amplitude.

What it buys

First-order amplitude-error immunity. The gate angle is an integer winding number times a fixed geometric constant; control-amplitude error largely cancels by construction, verified analytically and numerically by two independent methods to 0.1%.
Universal control. A three-handle device gives two independent generators; finite winding sequences are dense in SU(2), so arbitrary single-qubit rotations compile via Solovay–Kitaev.
Gap protection. The dark subspace is separated from the bright states by a gap above ~420 MHz, reducing the ability of thermal and TLS processes to erase the distinction.
A different robustness axis. Not the best isolated single-gate fidelity number, but a gate less dependent on perfect analog pulse delivery — and therefore more stable as the processor scales.

Reference

Reference E. S. Brooke, "Universal Holonomic Quantum Gates via Winding-Class-Indexed Dark-State Connections in Multi-Loop Superconducting Circuits" (2026). Gate = exp(i·2πν·A_φ), set by the integer winding number ν.

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