Efficient Classical Simulation of Heuristic Peaked Quantum Circuits

TL;DR

This paper demonstrates that peaked quantum circuits, previously thought to be classically intractable, can be efficiently simulated using tensor network methods, challenging claims of quantum advantage.

Contribution

The authors develop a tensor network-based classical simulation method that efficiently contracts peaked quantum circuits, including those with obfuscated permutations, in about one hour.

Findings

Classical simulation of peaked circuits is feasible within hours.

The method can extract the peak bitstring with high accuracy.

It challenges previous claims of quantum advantage for these circuits.

Abstract

Peaked quantum circuits, whose output distribution is sharply concentrated on a single bitstring, have emerged as a promising candidate for verifiable quantum advantage, as the correctness of the quantum output can be checked by simply comparing against the known peak. Recent work by Gharibyan et al. arXiv:2510.25838 claimed heuristic quantum advantage using peaked circuits executed on Quantinuum's 56-qubit H2 processor. These peaked circuits concentrate their output on a single hidden bitstring by training a shallow simulable circuit variationally and inserting an obfuscated permutation to increase the depth to a level that makes classical simulation intractable, with estimated runtimes of years for the largest instances. We show that these circuits can be efficiently simulated classically. We describe a method that efficiently performs a full tensor network contraction, allowing near-exact sampling and extraction of the peaked bitstring. The method exploits the mirrored structure of the circuit and iteratively cancels both halves into a Matrix Product Operator (MPO), and avoids the obfuscated permutation by greedily reducing the MPO bond dimension through a process we call unswapping. The method can fully contract and extract the peak of the largest circuit in approximately one hour on a single GPU, around half the time it took to run on the quantum hardware.