Shortened pulse sequences could make geometric quantum gates more resilient

Geometry with room for correction

Cheng-Yun Ding and colleagues propose a method for implementing geometric quantum gates with shortened composite pulses. Their study, submitted to arXiv on November 8, 2026, combines mathematical gate construction with numerical simulations of superconducting transmon qubits. It reports a proposed implementation, not a new hardware experiment; the supplied record does not establish peer review.

Geometric gates use a phase associated with a quantum state's closed path through its possible configurations. On the Bloch sphere—a representation of a two-level quantum system—that phase is related to the solid angle enclosed by the path. Nonadiabatic geometric control avoids the requirement that this evolution proceed slowly.

But geometry alone does not eliminate control errors. Different paths producing the same intended gate can respond differently to an inaccurate pulse amplitude or a drifting qubit frequency. Longer protective sequences also leave more time for decoherence, the loss of quantum information through interaction with the environment.

The question is therefore practical: can a path provide useful error resistance without an excessive time penalty?

Nine segments, adjustable paths

The proposed construction divides the evolution into nine segments, tracing two triangle-cap-shaped structures on the Bloch sphere. The segments follow longitude and latitude lines, with control settings chosen to cancel the accumulated dynamical phase, leaving the desired geometric contribution.

Three adjustable path parameters provide freedom to change the route without changing the target operation. For most numerical examples, the researchers simplify the search by setting two of these parameters equal.

The controls use zero detuning on longitude segments and constant detuning on latitude segments. The pulse envelope can take a simple sine-squared form. This does not mean the entire control sequence is constant: the required microwave phase also follows the prescribed evolution.

The authors examine the Hadamard, S and T single-qubit gates, alongside a two-qubit controlled-phase gate. Together, single-qubit control and an entangling operation supply the ingredients for universal quantum computation.

What the simulations show

The main robustness tests introduce a systematic pulse-amplitude error: the applied amplitude is multiplied by one plus an error fraction. After optimizing the path parameters, the proposed gates show better resistance than two conventional single-loop geometric configurations over the tested error range, from minus 10% to plus 10%.

For the amplitude-error-optimized Hadamard, S and T examples, the total pulse areas are approximately 3.01π, 1.87π and 1.71π. Each is below the 4π reference used for conventional composite geometric schemes. Pulse area measures integrated drive amplitude; its translation into duration depends on the pulse envelope and available drive strength. These results do not mean every proposed gate is faster than a single-loop alternative.

The more hardware-specific simulations include transmon energy levels outside the computational pair, along with relaxation and dephasing. A derivative-based pulse correction reduces leakage into unwanted levels. Under the selected parameters, the reported fidelities are 99.94% for Hadamard, 99.91% for S and 99.95% for T, with respective durations of 86, 24 and 24 nanoseconds.

For two qubits, the proposal modulates one transmon's frequency to control an interaction involving the joint states containing two excitations. A controlled-phase example reaches about 99.9% simulated fidelity in 63.7 nanoseconds.

What remains unproven

Those percentages describe the paper's numerical fidelity measures, not measured hardware performance. The single-qubit calculation averages over 1,001 initial states with real coefficients. The two-qubit calculation averages over products of similarly parameterized states. Neither should be presented as an unrestricted average over all possible quantum inputs.

The appendix also reports improved suppression of detuning errors and residual ZZ crosstalk for a Hadamard gate, using different optimized paths for each error type. That supports adaptability, rather than demonstrating one fixed setting that simultaneously suppresses every error. Broader simultaneous suppression is discussed as a possibility enabled by additional free parameters.

There is also a remaining speed–robustness tradeoff: the authors note that the longer Hadamard evolution slightly reduces its highest fidelity in one comparison because of decoherence.

The contribution is therefore a flexible theoretical control design with encouraging simulations. Whether its advantages survive experimental calibration, device imperfections and combined error sources remains to be established.