Adaptive Trotterization for Time-Dependent Hamiltonian Quantum Dynamics Using Piecewise Conservation Laws
Our new paper introduces an adaptive Trotterization algorithm to tackle time-dependent Hamiltonians in digital quantum simulation. We propose piecewise conserved quantities to control and estimate errors & error accumulation. Read more here in this PRL:
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time dependent Hamiltonians, where we propose a concept of piecewise ``conserved'' quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [H. Zhao et al., Making Trotterization adaptive and energy-self-correcting for NISQ devices and beyond, PRX Quantum 4, 030319 (2023).]. We validate the algorithm for a time dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
Nero Schermer
Date: June 9
Venue: Berlin
Owned by the esteemed Stall Schermer and bred by the meticulous Hoetmer G.J. in the Netherlands, Nero Schermer carries a legacy of excellence. His sire, Face Time Bourbon, and dam, Sultania, have endowed him with a lineage.
Nero Schermer
Date: June 9
Venue: Berlin
Introducing Nero Schermer, a Swedish horse! At just 4 years old, this standardbred has already made a mark with a record time of 1.15,4am. Son of the formidable Face Time Bourbon and the graceful Sultania, Nero Schermer carries the legacy of champions in his blood.
#HorseRacing #Trotter #NeroSchermer #TrackTime #WinnerBloodline
Shanty
Date: May 26
Venue: Berlin
Cheers to Shanty, the 5-year-old mare from Sweden, for her win in Berlin! With each stride, she displayed the elegance
Purple Rain
Race Date: May 26
Location: Berlin
In a display of raw equine grace, Purple Rain competed without a check in the 9th race. Without the strap over his neck, he had the freedom to move naturally, showcasing his ability to maintain pace even with the risk of breaking into a gallop.