The computational power of random quantum circuits in arbitrary geometries is explored through experiments that sample output distributions of two-dimensional quantum circuits, highlighting a gap between classical and quantum computing capabilities. Classical simulations using tensor network techniques have limitations, emphasizing the need for improvements in quantum hardware to frustrate classical simulation. Quantum computers with over 50 qubits are vulnerable to classical simulation due to gate fidelity and connectivity constraints. Recent hardware upgrades to Quantinuum's H2 quantum computer enable operation with up to 56 qubits, arbitrary connectivity, and high two-qubit gate fidelity. Data from random circuit sampling in highly connected geometries are presented at unprecedented fidelities and scale, surpassing state-of-the-art classical algorithms. The difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture. Quantum error correction is essential for realizing quantum computing power, but current architectures lack the required properties for large-scale error correction. Quantum computing technologies are maturing, and researchers are exploring whether quantum computational advantage can be achieved without error correction. Random circuit sampling (RCS) is a task that highlights the difficulty of simulating quantum computers on classical systems. The separation between quantum and classical computational power for RCS is determined by speed, connectivity, fidelity, and size. Tensor-network methods allow classical simulations with imperfect fidelity, with fidelity dependent on circuit connectivity. Increasing quantum computer connectivity, fidelity, or both can frustrate such simulations. Quantinuum's H2 trapped-ion QCCD quantum computer has been upgraded to operate with up to 56 qubits, arbitrary connectivity, and high two-qubit gate fidelity. This enables random circuit sampling in highly connected geometries at unprecedented fidelities and scale. The H2 quantum computer's capabilities are tested through RCS in randomly assigned geometries. The arbitrary connectivity of H2 enables the execution of flexibly programmed circuits that are extremely challenging to simulate classically even at relatively low circuit depths. The combination of low depth requirements and high gate fidelities allows sampling from classically-challenging circuits at unprecedented fidelity. The high fidelities achieved in this work close the loophole in the claim that RCS is classically hard. The H2 quantum computer's performance is evaluated through benchmarking results for primitive operations, showing that the fidelity of these operations has not degraded. The primary challenge in scaling from N=32 to N=56 was developing transport waveforms for a larger number of potential wells. The new waveforms use the same basic primitives to rearrange qubits but with reconfigured trajectories and spacing. The fidelity of primitive operations has improved, with the average error of the native perfect entangler reduced. The primary detrimental impact of loading more qubits is increased execution time and memory error per qubit per layer. Random circuit sampling (RCS) is a computational task designed to highlight the difficulty of simulating quantum computers on classical systems. The separation between classical andThe computational power of random quantum circuits in arbitrary geometries is explored through experiments that sample output distributions of two-dimensional quantum circuits, highlighting a gap between classical and quantum computing capabilities. Classical simulations using tensor network techniques have limitations, emphasizing the need for improvements in quantum hardware to frustrate classical simulation. Quantum computers with over 50 qubits are vulnerable to classical simulation due to gate fidelity and connectivity constraints. Recent hardware upgrades to Quantinuum's H2 quantum computer enable operation with up to 56 qubits, arbitrary connectivity, and high two-qubit gate fidelity. Data from random circuit sampling in highly connected geometries are presented at unprecedented fidelities and scale, surpassing state-of-the-art classical algorithms. The difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture. Quantum error correction is essential for realizing quantum computing power, but current architectures lack the required properties for large-scale error correction. Quantum computing technologies are maturing, and researchers are exploring whether quantum computational advantage can be achieved without error correction. Random circuit sampling (RCS) is a task that highlights the difficulty of simulating quantum computers on classical systems. The separation between quantum and classical computational power for RCS is determined by speed, connectivity, fidelity, and size. Tensor-network methods allow classical simulations with imperfect fidelity, with fidelity dependent on circuit connectivity. Increasing quantum computer connectivity, fidelity, or both can frustrate such simulations. Quantinuum's H2 trapped-ion QCCD quantum computer has been upgraded to operate with up to 56 qubits, arbitrary connectivity, and high two-qubit gate fidelity. This enables random circuit sampling in highly connected geometries at unprecedented fidelities and scale. The H2 quantum computer's capabilities are tested through RCS in randomly assigned geometries. The arbitrary connectivity of H2 enables the execution of flexibly programmed circuits that are extremely challenging to simulate classically even at relatively low circuit depths. The combination of low depth requirements and high gate fidelities allows sampling from classically-challenging circuits at unprecedented fidelity. The high fidelities achieved in this work close the loophole in the claim that RCS is classically hard. The H2 quantum computer's performance is evaluated through benchmarking results for primitive operations, showing that the fidelity of these operations has not degraded. The primary challenge in scaling from N=32 to N=56 was developing transport waveforms for a larger number of potential wells. The new waveforms use the same basic primitives to rearrange qubits but with reconfigured trajectories and spacing. The fidelity of primitive operations has improved, with the average error of the native perfect entangler reduced. The primary detrimental impact of loading more qubits is increased execution time and memory error per qubit per layer. Random circuit sampling (RCS) is a computational task designed to highlight the difficulty of simulating quantum computers on classical systems. The separation between classical and