Single-qubit gate teleportation provides a quantum advantage

TL;DR

This paper demonstrates that simulating single-qubit gate teleportation circuits classically is computationally hard, even under weak simulation criteria, highlighting a fundamental quantum advantage in these simple circuits.

Contribution

It proves that constant-depth classical circuits cannot efficiently simulate single-qubit Clifford-gate-teleportation circuits, establishing a strong form of quantum advantage.

Findings

Classical constant-depth circuits cannot simulate these quantum circuits.

Unconditional proof based on classical circuit complexity.

Simulation difficulty persists even for weak, possibilistic scenarios.

Abstract

Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation [Phys. Rev. A 106, 062430 (2022)], a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.