The paper introduces an MCMC-based technique to determine the digitization effects in a class of bosonic systems with Hamiltonians of the form (2), using the coordinate-basis truncation scheme. This allows estimating expectation values of various operators at finite temperature, including their digitization errors, by dialing the temperature to study different energy scales.
As a demonstration, the method is applied to the (2+1)-dimensional scalar quantum field theory regularized on a lattice. The key points are:
The coordinate-basis truncation scheme is introduced for single-boson and multi-boson systems. This scheme admits MCMC simulations without a sign problem.
The MCMC formulation and algorithm are presented, leveraging the fact that the weights in the partition function are non-negative under certain conditions. This allows efficient computations compared to exact diagonalization.
Numerical results are shown for a single boson and the 2D scalar QFT on a 4x4 lattice. The digitization errors are found to decay exponentially as the digitization spacing adig is reduced, matching the expected behavior.
Even without analytical results, the digitization errors can be determined by fitting the numerical data at finite adig values. This provides a way to estimate the resources needed for realistic quantum simulations of bosonic theories, and to cross-check the validity of quantum simulation results.
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by Masanori Han... kl. arxiv.org 04-03-2024
https://arxiv.org/pdf/2212.08546.pdfDybere Forespørgsler