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

• URL: http://arxiv.org/abs/2207.08826v2
• Date: Wed, 24 Aug 2022 20:19:09 GMT
• Title: Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Authors: Hayata Yamasaki, Masato Koashi
• Abstract summary: Protocols for fault-tolerant quantum computation (FTQC) demand excessive space overhead of physical qubits per logical qubit. We introduce an alternative approach using a concatenation of multiple small-size quantum codes for the constant-space-overhead FTQC. Our protocol accomplishes FTQC even if a decoder has non-constant runtime, unlike the existing constant-space-overhead protocol.
• Score: 5.33024001730262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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