The computational power of random quantum circuits in arbitrary geometries (2406.02501v3)

Abstract: Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

• The paper shows that random circuit sampling on the H2 quantum computer significantly challenges classical simulation by leveraging arbitrary qubit connectivity.
• The study employs advanced techniques like mirror benchmarking and XEB to validate the high two-qubit gate fidelity (99.843%) of 56-qubit operations.
• The findings suggest that quantum circuits with complex, non-rectilinear geometries can achieve quantum advantage at lower depths compared to traditional 2D grids.

The Computational Power of Random Quantum Circuits in Arbitrary Geometries

The paper discusses the integration of recent advancements in quantum computing, particularly focusing on the development and performance evaluation of Quantinuum's H2 quantum computer. The paper is primarily centered on elucidating the computational capabilities of random quantum circuits, highlighting the challenges and solutions in bridging the computational gap between classical and quantum computing methodologies using different geometrical configurations.

Overview of the Research

The primary objective of this work is to demonstrate the increased computational capabilities of quantum computers over classical counterparts through the execution of random circuit sampling (RCS). Random circuit sampling serves as a benchmark to assess the quantum advantage by implementing specific quantum circuits and comparing the computational load with that of classical simulations. The research is anchored in observing the behavior of quantum circuits in a non-rectilinear, randomly connected setup, which is shown to exacerbate the difficulty of classical simulation.

Experimental Setup and Advancements

The experimental core of the paper is the Quantinuum H2 quantum computer, which has been upgraded to perform operations involving up to 56 qubits. It features arbitrary connectivity and achieves a high two-qubit gate fidelity of 99.843%. This high fidelity, coupled with a quantum charged-coupled device (QCCD) architecture, ensures flexible configurations of quantum circuits. The researchers showcase the machine's capability through random circuit sampling in highly connected geometries, achieving levels of fidelity and scale previously unattainable by standard classical algorithms.

Key Findings

1. Increased Difficulty for Classical Simulations: The paper illustrates that the flexibility in connectivity, combined with high fidelity of gates, renders classical simulation significantly challenging, particularly as the number of qubits exceeds 50. Chain loose bonds in large-scale computations are highlighted by the reduced efficacy of tensor network techniques used in classical simulations.
2. Complexity Density in Random Geometries: A unique aspect of this paper is the focus on the complexity density of quantum circuits in random geometries. It has been established that these configurations maintain their complexity density even for larger qubit systems. This aspect is contrasted with 2D geometries where complexity grows with circuit depth, indicating the robustness of random geometries against increasing circuit sizes.
3. Achievable Circuit Depth: The research quantifies the relation of circuit depth to qubit number, demonstrating that the connectivity of the H2 system allows for quantum supremacy at relatively low depths in comparison to 2D grid configurations. This emphasizes the potential of highly connected architectures in practicing random circuit sampling.
4. Validation Through Mirror-Benchmarking and XEB: Validation of the fidelity of quantum circuits run on H2 was carried out using mirror benchmarking techniques and the linear cross-entropy benchmark (XEB), both confirming the experimental results with high accuracy.

Implications and Future Directions

The implications of this research have substantial depth both in the foundation of theoretical physics and in practical computational chemistry, as they suggest that quantum computers, by harnessing unique connectivity options, could harness a distinct advantage over classical systems without necessarily expanding qubit count dramatically. As for future developments, the quantum systems can focus on error reduction and increased connectivity, which could further elevate the computational prowess, potentially linking them to other complex quantum phenomena and solving intricate algorithmic challenges. The research hints that understanding the exponential growth in the computational complexity of randomly generated circuits could steer quantum development towards more nuanced quantum applications.

As quantum hardware continues to evolve, integrating such highly flexible architectures with efficient quantum error correction mechanisms will be pivotal in expanding the applicability of quantum computing outside experimental laboratories and into industries where computational efficiency is paramount.