Efficient Simulation of Leakage Errors in Quantum Error Correcting Codes Using Tensor Network Methods

Leakage errors, in which a qubit is excited to a level outside the qubit subspace, represent a significant obstacle in the development of robust quantum computers. We present a computationally efficient simulation methodology for studying leakage errors in quantum error correcting codes (QECCs) using tensor network methods, specifically Matrix Product States (MPS). Our approach enables the simulation of various leakage processes, including thermal noise and coherent errors, without approximations (such as the Pauli twirling approximation) that can lead to errors in the estimation of the logical error rate. We apply our method to two QECCs: the one-dimensional (1D) repetition code and a thin $3\times d$ surface code. By leveraging the small amount of entanglement generated during the error correction process, we are able to study large systems, up to a few hundred qudits, over many code cycles. We consider a realistic noise model of leakage relevant to superconducting qubits to evaluate code performance and a variety of leakage removal strategies. Our numerical results suggest that appropriate leakage removal is crucial, especially when the code distance is large.Comment: 14 pages, 12 figure

Quantum Circuit Simulation by SGEMM Emulation on Tensor Cores and Automatic Precision Selection

Quantum circuit simulation provides the foundation for the development of quantum algorithms and the verification of quantum supremacy. Among the various methods for quantum circuit simulation, tensor network contraction has been increasing in popularity due to its ability to simulate a larger number of qubits. During tensor contraction, the input tensors are reshaped to matrices and computed by a GEMM operation, where these GEMM operations could reach up to 90\% of the total calculation time. GEMM throughput can be improved by utilizing mixed-precision hardware such as Tensor Cores, but straightforward implementation results in insufficient fidelity for deep and large quantum circuits. Prior work has demonstrated that compensated summation with special care of the rounding mode can fully recover the FP32 precision of SGEMM even when using TF32 or FP16 Tensor Cores. The exponent range is a critical issue when applying such techniques to quantum circuit simulation. While TF32 supports almost the same exponent range as FP32, FP16 supports a much smaller exponent range. In this work, we use the exponent range statistics of input tensor elements to select which Tensor Cores we use for the GEMM. We evaluate our method on Random Circuit Sampling (RCS), including Sycamore's quantum circuit, and show that the throughput is 1.86 times higher at maximum while maintaining accuracy.Comment: This paper has been accepted to ISC'2

Entanglement distillation towards minimal bond cut surface in tensor networks

We propose that a minimal bond cut surface is characterized by entanglement distillation in tensor networks. Our proposal is not only consistent with the holographic models of perfect or tree tensor networks, but also can be applied for several different classes of tensor networks including matrix product states and multi-scale entanglement renormalization ansatz. We confirmed our proposal by a numerical simulation based on the random tensor network. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography.Comment: 8 pages, 9 figure