Concatenate codes, save qubits
- URL: http://arxiv.org/abs/2402.09606v1
- Date: Wed, 14 Feb 2024 22:27:48 GMT
- Title: Concatenate codes, save qubits
- Authors: Satoshi Yoshida, Shiro Tamiya, Hayata Yamasaki
- Abstract summary: A fault-tolerant protocol for fault-tolerant quantum computation is presented.
It achieves a constant space overhead, a high threshold, and flexibility in modular architecture designs.
Results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC.
- Score: 1.6114012813668932
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The essential requirement for fault-tolerant quantum computation (FTQC) is
the total protocol design to achieve a fair balance of all the critical factors
relevant to its practical realization, such as the space overhead, the
threshold, and the modularity. A major obstacle in realizing FTQC with
conventional protocols, such as those based on the surface code and the
concatenated Steane code, has been the space overhead, i.e., the required
number of physical qubits per logical qubit. Protocols based on high-rate
quantum low-density parity-check (LDPC) codes gather considerable attention as
a way to reduce the space overhead, but problematically, the existing
fault-tolerant protocols for such quantum LDPC codes sacrifice the other
factors. Here we construct a new fault-tolerant protocol to meet these
requirements simultaneously based on more recent progress on the techniques for
concatenated codes rather than quantum LDPC codes, achieving a constant space
overhead, a high threshold, and flexibility in modular architecture designs. In
particular, under a physical error rate of $0.1\%$, our protocol reduces the
space overhead to achieve the logical CNOT error rates $10^{-10}$ and
$10^{-24}$ by more than $90 \%$ and $97 \%$, respectively, compared to the
protocol for the surface code. Furthermore, our protocol achieves the threshold
of $2.4 \%$ under a conventional circuit-level error model, substantially
outperforming that of the surface code. The use of concatenated codes also
naturally introduces abstraction layers essential for the modularity of FTQC
architectures. These results indicate that the code-concatenation approach
opens a way to significantly save qubits in realizing FTQC while fulfilling the
other essential requirements for the practical protocol design.
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