Quantum advantage from effective $200$-qubit holographic random circuit sampling

Abstract: Quantum computers hold the promise of outperforming classical computers in solving certain problems. While large-scale quantum algorithms will require fault-tolerant devices, near-term demonstrations of quantum advantage on existing devices can provide important milestones. Random circuit sampling has emerged as a leading candidate for such demonstrations. However, existing implementations often underutilize circuit depth, limiting the achievable advantage. We introduce a holographic random circuit sampling algorithm that substantially increases the sampling complexity by leveraging repeated interactions and mid-circuit measurements. This approach scales the effective sampling dimension with the circuit depth, ultimately leading to an exponential growth in sampling complexity. With merely 20 physical qubits on IBM quantum devices, we experimentally demonstrate the effective sampling of up to 200 qubits, with a cross-entropy benchmark fidelity of $0.0593$, establishing a new route to scalable quantum advantage through the combined use of spatial and temporal quantum resources.