Efficient Long-Range Entanglement using Dynamic Circuits (2308.13065v2)

Abstract: Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by non-unitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: CNOT gate teleportation between up to 101 qubits by feeding forward 99 mid-circuit measurement outcomes, and the preparation of Greenberger-Horne-Zeilinger (GHZ) states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices.

• The paper shows that dynamic circuits enable high-fidelity CNOT teleportation across 101 qubits, outperforming traditional unitary methods as qubit count increases.
• It employs mid-circuit measurements and conditional feed-forward operations to reduce circuit depth, thereby mitigating errors on NISQ hardware.
• An error budget analysis in GHZ state preparation offers a clear roadmap for future enhancements in dynamic circuit architecture.

Efficient Long-Range Entanglement Using Dynamic Circuits: An Overview

Introduction

The paper "Efficient Long-Range Entanglement using Dynamic Circuits" presents an exploration into the utility of dynamic circuits for generating long-range entanglement on large-scale quantum devices. Dynamic circuits, characterized by their ability to incorporate mid-circuit measurements and conditional feed-forward operations, are posited as a means to surpass the limitations inherent in unitary quantum circuits, particularly in the context of near-term quantum hardware with limited connectivity.

Key Contributions

The paper focuses on two primary tasks: CNOT gate teleportation and GHZ state preparation, both utilizing dynamic circuits. In the first task, the authors demonstrate that dynamic circuits can achieve high-fidelity CNOT gate teleportation over distances spanning up to 101 qubits in a linear chain. This result is enabled by efficiently managing mid-circuit measurements and conditional operations to reduce circuit depth—a critical factor in mitigating errors on noisy quantum devices. The paper shows a crossover point where dynamic circuits outperform traditional unitary circuits in terms of fidelity as the qubit count increases.

The second task involves preparing GHZ states using dynamic circuits. While the implementation does not yet provide a clear advantage over unitary-based approaches due to current experimental constraints, the authors present an error budget analysis detailing the challenges involved. This serves as a roadmap for further improvements, suggesting that, with advancements in fidelity of mid-circuit measurements and more efficient feed-forward operations, dynamic circuits could indeed become the preferable approach for preparing large-scale, entangled quantum states.

Theoretical Implications

Theoretical implications of this work include a refined understanding of the complexity associated with implementing long-range entanglement on noisy quantum hardware. The paper highlights how dynamic circuits offer a potentially more scalable solution by providing constant-depth circuit implementations. This addresses fundamental issues related to the spread of entanglement within a quantum system constrained by its information light cone, thus limiting the depth required for long-range gates in traditionally implemented unitary circuits to quadratic growth.

Practical Implications

On the practical side, this work suggests pathways for improving quantum computational efficiencies through enhanced circuit design. The ability to implement effectively all-to-all connectivity on a hardware platform with sparse qubit interconnections is a significant step forward. Moreover, the implications for quantum error correction are substantial, as dynamic circuits could significantly improve the implementation of fault-tolerant quantum computing by reducing the reliance on deep circuits and enhancing error correction feedback mechanisms.

Future Directions

Future directions for research include the extension of these concepts to more complex multi-qubit gates, as discussed in the extrapolation to teleportation of Toffoli or CCZ gates. Additionally, advancements in hardware that improve the efficiency and fidelity of mid-circuit measurements and feed-forward logic will be crucial for realizing the full potential of dynamic circuits. There is also scope for exploring the integration of dynamic circuit techniques into larger quantum algorithms, where high-fidelity, long-range entanglement remains a bottleneck.

Conclusion

In conclusion, this paper underscores the promising utility of dynamic circuits for quantum information processing, particularly for tasks requiring long-range entanglement. While current experimental setups have not yet fully realized the expected advantages for tasks like GHZ state preparation, the detailed analysis provided enhances our understanding of the necessary technological advancements. Dynamic circuits represent a viable path toward overcoming connectivity limitations in quantum hardware, with significant implications for both theoretical quantum computing and practical implementation on noisy intermediate-scale quantum (NISQ) devices.