Short answer: Optimal control tools such as GRAPE can find pulse shapes that remove coherent gate error in a numerical model, but a 2025 simulation preprint finds that a well-calibrated analytical DRAG pulse already sits close to the decoherence floor at 20 ns gate time. The same study finds DRAG more robust to qubit frequency detuning and GRAPE more robust to amplitude error. Everything in it is simulation, with no hardware run.

The control problem

Quantum optimal control asks two things: whether a system is controllable, and how to find control amplitudes that drive it to a target. The QuTiP documentation says controllability is determined by the commutability of the dynamics generators, formalised as the Lie Algebra Rank Criterion. For a quantum computer the most important use is gate synthesis, which means finding controls that produce a target unitary.

What GRAPE does

GRAPE stands for Gradient Ascent Pulse Engineering. The QuTiP guide explains that Schrodinger's equation for a time-dependent Hamiltonian generally has no analytical solution, so the evolution time is split into timeslots in which each control amplitude is assumed constant. The algorithm then adjusts the amplitude in each slot to improve the fidelity of the target operation.

A simulated comparison

The 2025 preprint (arXiv 2511.12799) compares Gaussian, DRAG and GRAPE pulses for single-qubit gates on a three-level transmon model, with parameters taken from an IQM Garnet device (T1 = 37 microseconds, T2 = 9.6 microseconds, anharmonicity of -200 MHz divided by 2 pi). Its reported findings are:

  • At 20 ns, GRAPE removes all coherent error, with infidelity below 10^-15 in the model.
  • DRAG at 20 ns has a coherent error of 4.9 x 10^-4, and 8.4 x 10^-4 with full decoherence, which is about 1.2 times GRAPE's decoherence-limited performance.
  • Over a plus or minus 5 MHz detuning range, the minimum fidelity is 0.990 for DRAG and 0.931 for GRAPE.
  • For amplitude error, GRAPE's minimum fidelity is 0.994 against 0.990 for DRAG.
  • GRAPE is the only route to guaranteed zero coherent error, which the authors say matters at gate times of roughly 15 ns or less, where perturbative corrections break down.

The authors read this to mean that properly calibrated DRAG already operates near the decoherence floor, and that qubit frequency detuning is the dominant calibration uncertainty in charge-noise-limited transmons.

Caveats

This is a preprint based on a single transmon model, and the numbers depend on its parameters. A related open-source repository describes a simulation pipeline for the same comparison and states that no circuits were run on physical hardware. Results on real devices may differ.

How to read the comparison

The preprint does not say that numerical optimisation is unnecessary. Its claim is narrower: for the single-qubit gate and the transmon parameters it models, a calibrated analytical pulse gets most of the way to the decoherence limit at 20 ns, and the remaining gap from GRAPE is small. At shorter gate times the picture changes, and robustness to the dominant calibration error counts as well as the nominal fidelity. A different qubit design, noise model or gate could change the ranking, so the figures are a worked example, not a general rule.

FAQ

What is GRAPE?

Gradient Ascent Pulse Engineering, a numerical method that adjusts piecewise constant control amplitudes to maximise gate fidelity.

Is DRAG always worse than GRAPE?

No. In the preprint's model, DRAG at 20 ns is within about 1.2 times of the decoherence-limited result and is more robust to detuning.

When does GRAPE help most?

The preprint says at short gate times, around 15 ns or below, and where zero coherent error is required.

Were these pulses run on hardware?

No. The study and the related repository describe simulation only.

What is gate synthesis?

Finding controls that produce a chosen unitary operation.

All field notes