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ACM/IEEE Design Automation Conference (DAC)

Late Breaking Results: An Efficient Bridge-based Compression Algorithm for Topologically Quantum Error Corrected Circuits

Wei-Hsiang Tseng, Yao‐Wen Chang

Published Jul 9, 2023• 1 citation
Publisher

Abstract

Topological quantum error correction (TQEC) is a promising method for fault-tolerant quantum circuits. A TQEC circuit can be visualized as the defect movement along the time axis and modeled as a 3D space-time volume to estimate the required resource. A quantum algorithm must minimize the space-time volume for a feasible physical qubit number and computational time, especially for large-scale designs. Previous work presents quadratic-time simultaneous primal and dual bridge compression for a TQEC circuit, which is infeasible for large-scale problems. This paper presents an efficient divide-and-conquer approach to primal and dual bridge compression, which can support different code distances between qubits. Compared with the previous work, experimental results show that our algorithm is effective and efficient even for large-scale problems.

DOI
10.1109/dac56929.2023.10247656

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Topological quantum error correction (TQEC) is a promising method for fault-tolerant quantum circuits. A TQEC circuit can be visualized as the defect movement along the time axis and modeled as a 3D space-time volume to estimate the required resource. A quantum algorithm must minimize the space-time volume for a feasible physical qubit number and computational time, especially for large-scale designs. Previous work presents quadratic-time simultaneous primal and dual bridge compression for a TQEC circuit, which is infeasible for large-scale problems. This paper presents an efficient divide-and-conquer approach to primal and dual bridge compression, which can support different code distances between qubits. Compared with the previous work, experimental results show that our algorithm is effective and efficient even for large-scale problems.
Topological quantum error correction (TQEC) using the surface code is among the most promising techniques for fault-tolerant quantum circuits. The required resource of a TQEC circuit can be modeled as a space-time volume of a three-dimensional diagram by describing the defect movement along the time axis. For large-scale complex problems, it is crucial to minimize the space-time volume for a quantum algorithm with a reasonable physical qubit number and computation time. Previous work proposed an automated tool to perform bridge compression on a large-scale TQEC circuit. However, the existing automated bridging compression is only for dual defects and not for primal defects. This paper presents an algorithm to perform bridge compression on primal and dual defects simultaneously. In addition, the automatic compression algorithm performs initialization/measurement simplification and flipping to improve the compression. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 47%.
Topological quantum error correction (TQEC) using the surface code is among the most promising techniques for fault-tolerant quantum circuits. The required resource of a TQEC circuit can be modeled as a space-time volume of a three-dimensional diagram by describing the defect movement along the time axis. For large-scale complex problems, it is crucial to minimize the space-time volume for a quantum algorithm with a reasonable physical qubit number and computation time. Previous work proposed an automated tool for bridge compression on a large-scale TQEC circuit. However, the existing automated bridge compression is only for dual defects and not for primal defects. This paper presents an algorithm to simultaneously perform bridge compression on primal and dual defects. In addition, the automatic compression algorithm performs initialization/measurement simplification and flipping to improve the compression. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 53%.
Topological quantum error correction (TQEC) is promising for scalable fault-tolerant quantum computation. The required resource of a TQEC circuit can be modeled as its space-time volume of a three-dimensional geometric description. Implementing a quantum algorithm with a reasonable physical qubit number and computation time is challenging for large-scale complex problems. Therefore, it is desirable to minimize the space-time volume for large-scale TQEC circuits. Previous work proposed bridge compression, which can significantly compress a TQEC circuit, but it was performed manually. This article presents the first automated tool that can perform bridge compression on a large-scale TQEC circuit. Our proposed algorithm applies the bridge compression technique to compactify TQEC circuits with modularization. Besides, we offer a time-ordering-aware 2.5-D placement for compacting TQEC circuits and satisfying time-ordered measurement constraints. On the other hand, we suggest friend net-aware routing to effectively reduce the required routing resource under topological deformation. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 84%.
The topological quantum error correction (TQEC) scheme is promising for scalable and reliable quantum computing. A TQEC circuit can be modeled by a three-dimensional diagram, and the implementation resource of a TQEC circuit is abstracted to its space-time volume. Implementing a quantum algorithm with a reasonable physical qubit number and reasonable computation time is challenging for large-scale practical problems. Therefore, minimizing the space-time volume of a TQEC circuit becomes a crucial issue. Previous work shows that bridge compression can greatly compress TQEC circuits, but it was performed only manually. It is desirable to develop automated compression techniques for TQEC circuits to achieve low-overhead, large-scale quantum computations. In this paper, we present the first work that can automatically perform bridge compression on TQEC circuits. Compared with the state-of-the-art method, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 83%.
Quantum computing has raised great interests for its potential to achieve an asymptotic speedup on specific problems. Current quantum devices suffer from noise which needs robust and scalable error-correcting schemes. Topological quantum error correction (TQEC) is among the most promising error-correcting techniques with exponential suppression of error with linear increase of space-time complexity. In this paper, we present the first work to explore space-time optimization between 1-D and 2-D architectures for TQEC circuits. We prove the NP-hardness of the qubit routing problem in the layout synthesis and propose an efficient algorithm to optimize space-time volumes for both 1-D and 2-D qubit architectures with promising experimental results.
Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future. However, these near-term quantum processors will only contain a small amount of noisy qubits and allow limited qubit connectivity. Fault-tolerant schemes that not only have low qubit overhead but also comply with geometrical interaction constraints are therefore necessary. In this work, we combine flag fault tolerance with quantum circuit mapping, to enable an efficient flag-bridge approach to implement FT QEC on near-term devices. We further show an example of performing the Steane code error correction on two current superconducting processors and numerically analyze their performance with circuit level noise. The simulation results show that the QEC circuits that measure more stabilizers in parallel have lower logical error rates. We also observe that the Steane code can outperform the distance-3 surface code using flag-bridge error correction. In addition, we foresee potential applications of the flag-bridge approach such as FT computation using lattice surgery and code deformation techniques.