Time Optimal Synthesis of Gates for Markovian Open Qudits
Abstract
Coherent control protocols enabling fast and accurate implementations of logical gates is a key issue in quantum computing. This work deals with the optimal implementation of quantum gates in a mean-squared sense subject to experimental constraints on the multi-chromatic electromagnetic control pulses. Our assumptions encapsulate open qudits of arbitrary finite dimension subject to decoherence models in accordance with the markovian Gorini-Kossakowski-Sudarshan-Lindblad formalism. Given a unitary gate we show the existence of a time-minimal protocol minimizing the error. We derive universal and easily computable a priori lower and upper bounds on both the minimal time and minimal error. These bounds are not sharp but depend only on the dimension of the qudit, the experimental constraints, the decoherence time and strength of the coupling between the qudit and its environment. The wide applicability of these estimates helps in quantifying a posteriori the distance to optimality of numerically calculated control protocols.
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BibTeX
@misc{lutz2026time,
title = {{Time Optimal Synthesis of Gates for Markovian Open Qudits}},
author = {Killian Lutz and Yannick Privat},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05176524v3},
note = {CC BY-ND 4.0},
}
RIS
TY - UNPB
TI - Time Optimal Synthesis of Gates for Markovian Open Qudits
AU - Killian Lutz
AU - Yannick Privat
PY - 2026
DA - 2026/09/29
PB - HAL
UR - https://hal.science/hal-05176524v3
AB - Coherent control protocols enabling fast and accurate implementations of logical gates is a key issue in quantum computing. This work deals with the optimal implementation of quantum gates in a mean-squared sense subject to experimental constraints on the multi-chromatic electromagnetic control pulses. Our assumptions encapsulate open qudits of arbitrary finite dimension subject to decoherence models in accordance with the markovian Gorini-Kossakowski-Sudarshan-Lindblad formalism. Given a unitary gate we show the existence of a time-minimal protocol minimizing the error. We derive universal and easily computable a priori lower and upper bounds on both the minimal time and minimal error. These bounds are not sharp but depend only on the dimension of the qudit, the experimental constraints, the decoherence time and strength of the coupling between the qudit and its environment. The wide applicability of these estimates helps in quantifying a posteriori the distance to optimality of numerically calculated control protocols.
ER -