Experimentally Testable Quantum Advantage in Shallow Circuits

2026-09-29

AI Summary

This study addresses the absence of explicit classical bounds for shallow-circuit quantum advantage at finite sizes by proposing a single-processor, two-round testing protocol. By integrating multi-copy disjoint-player repeated games with random-position teleportation, the protocol linearizes the classical soundness bound with respect to the number of players, thereby enabling the construction of constant-depth quantum strategies. The authors rigorously prove that the classical winning probability asymptotically approaches zero as the system size increases, achieving an arbitrarily small classical success rate. Based on these theoretical guarantees, the work further presents a feasible experimental scheme requiring only 99 qubits. This research establishes a clear theoretical and experimental pathway for verifying quantum advantage in shallow circuits.

Abstract

Experimental tests of shallow-circuit quantum advantage require explicit classical bounds at finite circuit sizes. We refine the finite-size classical soundness bound of Aasnaess's graph-distributed construction to depend linearly on the number of players. Combined with standard disjoint-player repetition, this gives a two-round test on a single processor for any finite nonlocal game with a finite-dimensional perfect quantum strategy and classical winning probability $γ<1$, with arbitrarily small classical success. The method is based on playing $m$ copies with disjoint players and teleporting each player's register to a uniformly random one of $N$ sites before the questions are revealed. Each answer bit of a depth-$D$, fan-in-$K$ classical response with fixed wiring depends on at most $K^D$ question wires, making cross-player dependencies unlikely when $N$ is large. The quantum implementation has constant depth per round and wins with certainty. A classical device wins with probability at most $γ^m+O(mK^D/N)$, which vanishes as $O(\log N/N)$ for $m=\lceil\log_{1/γ}N\rceil$ at fixed $D$ and $K$. We present an explicit proposal for an experimentally testable quantum advantage with 99 qubits.

Problem

• quantum advantage
• shallow circuits
• finite-size classical bounds
• nonlocal game

Innovation

• shallow circuits
• quantum advantage
• nonlocal game
• graph-distributed construction
• constant depth