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Exponentially Reduced Circuit Depths Using Trotter Error Mitigation

Date & Time

November 14, 2024, 11:30am

Where to Attend

PSC 2136

Zoom

Speaker

James WatsonQuICS

Event Type

RQS Seminar

Abstract: Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by use of these formulae. This work provides an improved, rigorous analysis of these techniques for the task of calculating time-evolved expectation values. We demonstrate that, to achieve error ϵ in a simulation of time T using a pth-order product formula with extrapolation, circuits depths of O(T1+1/ppolylog(1/ϵ)) are sufficient -- an exponential improvement in the precision over product formulae alone. Furthermore, we achieve commutator scaling, improve the complexity with T, and do not require fractional implementations of Trotter steps. Our results provide a more accurate characterisation of the algorithmic error mitigation techniques currently proposed to reduce Trotter error.

Lunch will be provided.

*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*