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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