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arXiv:2606.28313

Diameter truncated operator evolution

Tom Holden-Dye, Max Marvell, Joel Mills, Christoper J. Turner, Arijeet Pal

quant-phcond-mat.stat-mechSubmitted Jun 26, 2026• Announced Jun 29, 2026• 0 citations
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Abstract

We present a method for simulating operator dynamics in out-of-equilibrium quantum systems. Due to the rapid growth of complexity in these systems, this is typically speaking an intractable task. However, exceptional progress has been made in recent years to sidestep this barrier, with the introduction of a number of methods that make use of a truncation of the simulation to low-weight (the number of non-trivial terms in a Pauli string basis expansion) observables, which turns out to be a good approximation for many dynamical quantities of interest, e.g., two-point infinite-temperature correlation functions between local operators. In this work, we extend this idea to a leaner truncation protocol, truncating operators based on their diameter - that is, the size of the region on the lattice on which they are non-trivially supported. Using existing analysis for generic circuits we argue that this kind of truncation protocol is physically well-motivated, and show via extensive numerical simulations for a number of systems of interest (here, the kicked Ising model and the Heisenberg XXZ model) that it is effective, and allows us to efficiently and accurately extract local correlation functions and transport properties.

Comments
11 pages, 6 figures

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We introduce a propagation-based approach to thermal state simulation by adapting Pauli and Majorana propagation to imaginary-time evolution in the Schrödinger picture. Our key observation is that high-temperature states can be sparse in the Pauli or Majorana bases, approaching the identity at infinite temperature. By formulating imaginary-time evolution directly in these operator bases and evolving from the maximally mixed state, we access a continuum of temperatures where the state remains efficiently representable. We provide analytic guarantees for small-coefficient truncation and Pauli-weight (Majorana-length) truncation strategies by quantifying the error growth and the impact of backflow. Large-scale numerics on the 1D J1-J2 model (energies) and the triangular-lattice Hubbard model (static correlations) validate efficiency at high temperatures.
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