Original title: Convolution absorbing boundaries for explicit-circuit quantum simulation of the wave equation
Hoang Anh Nguyen, Ali Tura · September 2026
When scientists simulate waves on a quantum computer, waves hit the boundary of the simulation grid and bounce right back. In the real world, waves often leave and never return. The authors fixed this bounce problem by adding absorbing boundaries that swallow outgoing waves. Because quantum computers normally preserve energy and cannot naturally absorb waves, the team used a mathematical trick called Schrodingerisation. This converts non-absorbing systems into larger quantum systems that can absorb signals. They tested this method on quantum circuits using seventeen to twenty-one qubits. The simulations matched exact references to within a tenth of a percent to a percent. However, they found that the simplest absorption method makes the success rate crash exponentially over time. To solve this, they added a precomputed tool called a Lyapunov symmetrizer. This fix eliminated the exponential penalty, cutting simulation costs by four to twenty-six orders of magnitude over longer runs.
When you shout in a long tunnel, the sound echoes because it bounces off the walls. In wave simulations, artificial edges cause reflections that aren't part of the real system, distorting results. In this paper, the absorbing boundaries act like acoustic foam that absorbs the sound at the edges, preventing echoes. The symmetrizer is like a pre-planned adjustment that keeps the sound clear without wasting energy.
This matters because quantum simulations of waves model real phenomena like sound or light, but they were stuck in closed boxes with artificial reflections. By adding absorbing boundaries, simulations can mimic open spaces, making results more accurate for physics and engineering. The new method avoids exponential costs, so simulations can run longer without failing.
The abstract doesn't claim how this method scales to very large quantum systems or different wave equations. The tests were done on grids up to 4000 unknowns and circuits with 17-21 qubits, so performance on bigger problems isn't established. Also, the precomputed symmetrizer might have its own computational costs not discussed here.
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Convolution absorbing boundaries for explicit-circuit quantum simulation of the wave equation — Hoang Anh Nguyen, Ali Tura
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.