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Title: Flag Gadgets Based on Classical Codes
Fault-tolerant syndrome extraction is a key ingredient in implementing fault-tolerant quantum computation. While conventional methods use a number of extra qubits that are 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. In particular, our method requires only ?? flag qubits to fault-tolerantly measure a weight ? stabilizer. 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 syndromes of quantum low-density parity-check 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.  more » « less
Award ID(s):
2237356
PAR ID:
10572894
Author(s) / Creator(s):
;
Publisher / Repository:
American Physical Society
Date Published:
Journal Name:
PRX Quantum
Volume:
5
Issue:
4
ISSN:
2691-3399
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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