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Paper 1

Q-Pandora Unboxed: Characterizing Noise Resilience of Quantum Error Correction Codes

Avimita Chatterjee, Subrata Das, Swaroop Ghosh

Year

2023

Journal

arXiv preprint

DOI

arXiv:2308.02769

arXiv

2308.02769

Quantum error correction codes (QECCs) are critical for realizing reliable quantum computing by protecting fragile quantum states against noise and errors. However, limited research has analyzed the noise resilience of QECCs to help select optimal codes. This paper conducts a comprehensive study analyzing two QECCs - rotated and unrotated surface codes - under different error types and noise models using simulations. Among them, rotated surface codes perform best with higher thresholds attributed to simplicity and lower qubit overhead. The noise threshold, or the point at which QECCs become ineffective, surpasses the error rate found in contemporary quantum processors. When confronting quantum hardware where a specific error or noise model is dominant, a discernible hierarchy emerges for surface code implementation in terms of resource demand. This ordering is consistently observed across unrotated, and rotated surface codes. Our noise model analysis ranks the code-capacity model as the most pessimistic and circuit-level model as the most realistic. The study maps error thresholds, revealing surface code's advantage over modern quantum processors. It also shows higher code distances and rounds consistently improve performance. However, excessive distances needlessly increase qubit overhead. By matching target logical error rates and feasible number of qubits to optimal surface code parameters, our study demonstrates the necessity of tailoring these codes to balance reliability and qubit resources. Conclusively, we underscore the significance of addressing the notable challenges associated with surface code overheads and qubit improvements.

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Paper 2

Quantum optimization with arbitrary connectivity using Rydberg atom arrays

Minh-Thi Nguyen, Jin-Guo Liu, Jonathan Wurtz, Mikhail D. Lukin, Sheng-Tao Wang, Hannes Pichler

Year

2022

Journal

arXiv preprint

DOI

arXiv:2209.03965

arXiv

2209.03965

Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.

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