A Square-Root Barrier to Quantum Gate Speed under Linear Coupling
Abstract
Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff.
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BibTeX
@misc{gaviria2026squareroot,
title = {{A Square-Root Barrier to Quantum Gate Speed under Linear Coupling}},
author = {Pablo Restrepo Gaviria and Mischa P. Woods},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19280},
eprint = {2609.19280},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19280},
}
RIS
TY - UNPB
TI - A Square-Root Barrier to Quantum Gate Speed under Linear Coupling
AU - Pablo Restrepo Gaviria
AU - Mischa P. Woods
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19280
UR - https://arxiv.org/abs/2609.19280
AB - Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff.
ER -