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UID:pretalx-juliacon-2026-H9MULV@pretalx.com
DTSTART;TZID=CET:20260814T100000
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DESCRIPTION:We report on recent progress in the numerical optimisation of q
 uantum control systems using [OptimalControl.jl](https://github.com/contro
 l-toolbox/OptimalControl.jl). Although the package is designed to optimise
  general control systems governed by ordinary differential equations\, it 
 naturally accommodates quantum problems described by finite-dimensional Sc
 hrödinger equations evolving on Lie groups — specifically\, bilinear dy
 namical systems whose state trajectories lie on unitary groups and are exp
 ressed compactly in terms of tensor products of complex matrices.\n\nA wel
 l-established Julia ecosystem for quantum optimal control already exists\,
  with packages such as `QuantumControl.jl`\, `Krotov.jl`\, and `GRAPE.jl` 
 providing mature\, quantum-tailored implementations of the GRAPE and Kroto
 v algorithms. These methods are effective for a broad class of problems an
 d can accommodate extensions such as free final time or path constraints o
 n controls and states\, typically via penalisation of the cost functional.
  However\, penalisation-based approaches offer no rigorous guarantee of co
 nstraint satisfaction and can introduce significant ill-conditioning. Our 
 motivation is complementary: to leverage state-of-the-art nonlinear progra
 mming solvers that treat such constraints directly\, as genuine algebraic 
 equalities and inequalities arising from the transcription of the continuo
 us-time optimal control problem — including additional optimisation vari
 ables such as free final time or parameters of the system.\n\n`OptimalCont
 rol.jl` offers a high-level\, expressive modelling interface that allows u
 sers to specify dynamics\, objectives\, and constraints in a form close to
  mathematical notation\, with no compromise on performance. Problems are t
 ranscribed via direct methods into large-scale sparse nonlinear programmes
 \, which are solved using interior-point methods on both CPU and GPU\, exp
 loiting automatic differentiation through `ExaModels.jl` and `MadNLP.jl`. 
 Crucially\, the framework also supports the combination of direct and indi
 rect methods: direct transcription is used first to identify the qualitati
 ve structure of the optimal solution\, after which indirect shooting metho
 ds — based on the Pontryagin Maximum Principle — can be applied to ref
 ine the solution to arbitrary numerical precision.\n\nWe present prelimina
 ry results on the optimisation of small quantum systems modelling nitrogen
 -vacancy (NV) centres in diamond. These systems\, comprising an electron s
 pin coupled to one or more nuclear spins via hyperfine interaction\, are n
 aturally described with bilinear dynamics driven by bounded microwave cont
 rols. The combination of hard amplitude constraints\, partial controllabil
 ity (nuclear spins are driven only indirectly through the electron spin)\,
  and the need for various costs functionals for gate synthesis makes NV ce
 ntres a compelling benchmark for our approach. We discuss the formulation 
 of these problems within `OptimalControl.jl`\, and compare the results and
  computational performance against existing quantum-specific methods.
DTSTAMP:20260502T093454Z
LOCATION:Room 3
SUMMARY:Optimising Quantum Control Systems: Application to NV Centres - Jea
 n-Baptiste Caillau\, David Tinoco
URL:https://pretalx.com/juliacon-2026/talk/H9MULV/
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