Flag Gadgets Based on Classical Codes

Journal Article · 09 December 2024 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.5.040340 · OSTI ID:2480748

Anker, Benjamin; Marvian, Milad

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 $(2t+1)t\lceil {\log }_2\left(w\right)\rceil$ flag qubits to fault-tolerantly measure a weight- $w$ 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. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• OSTI ID: 2480748
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 4 Vol. 5; ISSN 2691-3399; ISSN PQRUAG
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English