Title: Quantum Error Correction using Generalized Surface Codes
Speaker: Dr. Pavithran Iyer, Xanadu, Toronto
Abstract: Noise presents a significant challenge to quantum computing hardware, limiting the complexity of problems that can be tackled beyond just a few qubits. Quantum Error Correction (QEC) offers a theoretical framework that guarantees reliable quantum computation in the presence of noise. In this talk, I will focus on a popular class of QEC codes called Surface Codes, where quantum information is encoded in an entangled state of many physical qubits that are arranged on a 2D lattice. Several experimental implementations of QEC using surface codes have been realized on superconducting, semiconductor, and optical platforms. Furthermore, Surface codes serve as a testbed for developing and experimentally testing QEC strategies that extend beyond 2D architectures.
Surface codes were initially developed as a conceptual demonstration of QEC; however, they require a substantial overhead in the number of physical qubits per logical qubit. Reducing this overhead is essential in the NISQ era, where the number of qubits is limited. Achieving this could enable the realization of 50-100 logical qubits, supporting small quantum algorithms with technologies expected in the near future. In this talk, I will introduce a generalized framework for surface codes on 2D lattices, based on [1], which enables the encoding of more quantum information than previously known approaches. I will demonstrate an efficient technique for calculating the number of logical qubits using topological properties of graphs. I will also discuss optimal connectivity for physical qubits in a 2D architecture to maximize both the encoded logical information and noise resilience. Furthermore, drawing on results from [2], I will show how to benchmark the performance of generalized surface codes under the quantum erasure model, which captures noise from physical effects that cause quantum information to leak from the qubit’s subspace -- such as photon loss in optical waveguides or charge leakage in quantum dots. Beyond quantum computing applications, QEC tools for erasure noise help determine percolation thresholds for the many-body system corresponding to a surface code. Additionally, evaluating QEC performance against erasure noise provides valuable insights into resilience against broader decoherence effects. Finally, I will introduce an open-source software tool from [3] that enables the design and analysis of generalized surface codes.
[1]: https://arxiv.org/abs/1606.07116