Flag Gadgets based on Classical Codes
- URL: http://arxiv.org/abs/2212.10738v2
- Date: Tue, 20 Feb 2024 23:34:24 GMT
- Title: Flag Gadgets based on Classical Codes
- Authors: Benjamin Anker and Milad Marvian
- Abstract summary: We develop a framework to design flag gadgets using classical codes.
We show how to perform fault-tolerant syndrome extraction for any stabilizer code with arbitrary distance.
These small examples may be relevant to near-term experiments on small-scale quantum computers.
- Score: 1.30536490219656
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Fault-tolerant syndrome extraction is a key ingredient in implementing
fault-tolerant quantum computations. While conventional methods use a number of
extra qubits linear in the weight of the syndrome, several improvements have
been introduced using flag gadgets. In this work, we develop a framework to
design flag gadgets using classical codes. Using this framework we show how to
perform fault-tolerant syndrome extraction for any stabilizer code with
arbitrary distance using exponentially fewer qubits than conventional methods
when qubit measurement and reset are relatively slow compared to a round of
error correction. We further take advantage of the saving provided by our
construction to fault-tolerantly measure multiple stabilizers using a single
gadget, and show that it maintains the same exponential advantage when it is
used to fault-tolerantly extract the syndrome of quantum LDPC codes. Using the
developed framework we perform computer-assisted search to find several small
examples where our constructions reduce the number of qubits required. These
small examples may be relevant to near-term experiments on small-scale quantum
computers.
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