Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation

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• Hayata Yamasaki, University of Tokyo
• Thursday 28 September 2023, 14:15-15:30
• MR9 (Ground Floor Pavillion B).

If you have a question about this talk, please contact Subhayan Roy Moulik.

Scalable realization of quantum computing to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation (FTQC) demand excessive space overhead of physical qubits per logical qubit. A more recent protocol to achieve constant-space-overhead FTQC using quantum low-density parity-check (LDPC) codes thus attracts considerable attention but suffers from another drawback: it incurs polynomially long time overhead. To address these problems, we here introduce an alternative approach using a concatenation of multiple small-size quantum codes for the constant-space-overhead FTQC rather than a single large-size quantum LDPC code. We develop techniques for concatenating different quantum Hamming codes with growing sizes. As a result, we construct a low-overhead protocol to achieve constant space overhead and only quasi-polylogarithmic time overhead simultaneously. Our protocol accomplishes FTQC even if a decoder has non-constant runtime, unlike the existing constant-space-overhead protocol. These results establish a foundation for FTQC realizing a large class of quantum speedups within feasibly bounded space overhead yet negligibly short time overhead. This achievement opens a promising avenue for the low-overhead FTQC based on code concatenation.

The talk is based on the following paper.

https://arxiv.org/abs/2207.08826

This talk is part of the CQIF Seminar series.

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