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Paper 1
Quantum Error Correction near the Coding Theoretical Bound
Daiki Komoto, Kenta Kasai
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2412.21171
- arXiv
- 2412.21171
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits, necessitating highly scalable quantum error correction. In classical information theory, low-density parity-check (LDPC) codes can approach channel capacity efficiently. Yet, no quantum error-correcting codes with efficient decoding have been shown to approach the hashing bound - a fundamental limit on quantum capacity - despite decades of research. Here, we present quantum LDPC codes that not only approach the hashing bound but also allow decoding with computational cost linear in the number of physical qubits. This breakthrough paves the way for large-scale, fault-tolerant quantum computation. Combined with emerging hardware that manages many qubits, our approach brings quantum solutions to important real-world problems significantly closer to reality.
Open paperPaper 2
Synthesis of Arbitrary Quantum Circuits to Topological Assembly: Systematic, Online and Compact
Alexandru Paler, Austin G. Fowler, Robert Wille
- Year
- 2017
- Journal
- arXiv preprint
- DOI
- arXiv:1711.01387
- arXiv
- 1711.01387
It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduces a greedy scheduler generating compact box placements. The implemented software, whose source code is available online, is used to illustrate and discuss synthesis examples. Synthesis and optimisation improvements are proposed.
Open paper