The reduced state space approximation in Magnetic Resonance is the observation that many spin states (particu-larly in large spin systems in liquids) either remain unpopulated altogether or do not contribute to the observable magnetization dynamics in any way [1-5]. Such states may be excluded from consideration – the result is a family of very efficient simulation algorithms that were under development for the last six years [1-11] and are presently implemented in our Spinach library [7]. Importantly, the reduced matrices are a different representation of the same Lie algebra, meaning that all existing Magnetic Resonance simulation machinery (relaxation theories, exponential propagators, diagonalization methods, average Hamiltonian theories, etc.) remains unchanged – the only differ-ence is smaller matrices [3]. We recently started to implement standard NMR, EPR, DNP and Spin Chemistry experiments in the Spinach library [7,11]. Spinach is a well-commented and well-documented open-source Matlab library [7] available for download at http://spindynamics.org. The recent version is capable of simulating almost any type of spin dynamics in NMR, EPR, DNP or Spin Chemistry. Spinach includes an Optimal Control waveform design module [12] as well as inter-action visualization and trajectory analysis tools [13].

Literature
[1] I. Kuprov, N. Wagner-Rundell, P.J. Hore, Journal of Magnetic Resonance, 184 (2007) 196-206.
[2] I. Kuprov, N. Wagner-Rundell, P.J. Hore, Journal of Magnetic Resonance, 189 (2007) 241-250.
[3] I. Kuprov, Journal of Magnetic Resonance, 195 (2008) 45-51.
[4] H.J. Hogben, P.J. Hore, I. Kuprov, Journal of Chemical Physics, 132 (2010) 174101.
[5] A. Karabanov et al., Journal of Chemical Physics, 135 (2011) 084106.
[6] I. Kuprov, Journal of Magnetic Resonance, 209 (2011) 31-38.
[7] H.J. Hogben et al., Journal of Magnetic Resonance, 208 (2011) 179-194.
[8] M. Krzystyniak, L.J. Edwards, I. Kuprov, Journal of Magnetic Resonance, 210 (2011) 228-232. 
[9] H.J. Hogben, P.J. Hore, I. Kuprov, Journal of Magnetic Resonance, 211 (2011) 217-220.
[10] L.J. Edwards, I Kuprov, Journal of Chemical Physics, 136 (2012) 044108.
[11] A. Karabanov, A. van der Drift, L.J. Edwards, I Kuprov, W. Köckenberger, PCCP, 14 (2012) 2658-2668.
[12] P. de Fouquieres, S.G. Schirmer, S.J. Glaser, I. Kuprov, J. Magn. Reson., 212 (2011) 412-417.
[13] I. Kuprov, Journal of Magnetic Resonance, submitted [http://arxiv.org/abs/1212.4454].

Dr. Ilya Kuprov is Associate Professor of Chemical Physics within Chemistry at the University of Southampton, having previously been an EPSRC Research Fellow (2009 - 2014), a Lecturer in Physical Chemistry at the University of Durham (2007 - 2009), and a Fellow by Examination at Magdalen College, Oxford (2005 - 2010). The area of expertise of Dr Kuprov's research group is Quantum Theory: we are working on quantum mechanical models of magnetic processes, such as those encountered in Nuclear Magnetic Resonance, Electron Spin Resonance, Magnetic Resonance Imaging, Spin Chemistry and related areas. Applications of our research span a huge range of topics, from photosynthesis to parallel computing to quantum control theory.