The paper discusses the computational power of random quantum circuits in arbitrary geometries, focusing on the advancements in hardware and the challenges faced by classical simulations. The authors describe recent upgrades to Quantinuum's H2 quantum computer, which now supports up to 56 qubits with arbitrary connectivity and a high two-qubit gate fidelity of 99.843(5)%. The study highlights the importance of connectivity, fidelity, and clock speed in determining the computational power of quantum computers compared to classical computers. The H2 quantum computer's flexible connectivity enables the execution of circuits that are extremely challenging to simulate classically, even at relatively low circuit depths. The high gate fidelities achieved on the H2 quantum computer allow for sampling from classically difficult circuits with unprecedented fidelity, demonstrating that the computational power of the H2 quantum computer is strongly limited by the number of qubits rather than fidelity or clock speed. The paper also explores the complexity of exact tensor network contraction for the circuits run on the H2 quantum computer, showing that the contraction cost grows extremely quickly with depth. The results suggest that the separation between the computational power of quantum computers and classical computers will continue to grow rapidly as the number of qubits increases. Overall, the study provides empirical evidence for the computational advantage of quantum computers over classical computers in random circuit sampling tasks, particularly in highly connected geometries.The paper discusses the computational power of random quantum circuits in arbitrary geometries, focusing on the advancements in hardware and the challenges faced by classical simulations. The authors describe recent upgrades to Quantinuum's H2 quantum computer, which now supports up to 56 qubits with arbitrary connectivity and a high two-qubit gate fidelity of 99.843(5)%. The study highlights the importance of connectivity, fidelity, and clock speed in determining the computational power of quantum computers compared to classical computers. The H2 quantum computer's flexible connectivity enables the execution of circuits that are extremely challenging to simulate classically, even at relatively low circuit depths. The high gate fidelities achieved on the H2 quantum computer allow for sampling from classically difficult circuits with unprecedented fidelity, demonstrating that the computational power of the H2 quantum computer is strongly limited by the number of qubits rather than fidelity or clock speed. The paper also explores the complexity of exact tensor network contraction for the circuits run on the H2 quantum computer, showing that the contraction cost grows extremely quickly with depth. The results suggest that the separation between the computational power of quantum computers and classical computers will continue to grow rapidly as the number of qubits increases. Overall, the study provides empirical evidence for the computational advantage of quantum computers over classical computers in random circuit sampling tasks, particularly in highly connected geometries.