A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time complexity slightly higher than O(d3). We report a distributed version of the UF decoder that exploits parallel computing resources for further speedup. Using an FPGA-based implementation, we empirically show that this distributed UF decoder has a sublinear average time complexity with regard to d, given O(d3) parallel computing resources. The decoding time per measurement round decreases as d increases, a first time for a quantum error decoder. The implementation employs a scalable architecture called Helios that organizes parallel computing resources into a hybrid tree-grid structure. We are able to implement d up to 21 with a Xilinx VCU129 FPGA, for which an average decoding time is 11.5 ns per measurement round under phenomenological noise of 0.1%, significantly faster than any existing decoder implementation. Since the decoding time per measurement round of Helios decreases with d, Helios can decode a surface code of arbitrarily large d without a growing backlog.
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FPGA-Based Distributed Union-Find Decoder for Surface Codes
A fault-tolerant quantum computer must decode and correct errors faster than they appear to prevent exponential slowdown due to error correction. The Union-Find (UF) decoder is promising with an average time complexity slightly higher than $O(d^3)$. We report a distributed version of the UF decoder that exploits parallel computing resources for further speedup. Using an FPGA-based implementation, we empirically show that this distributed UF decoder has a sublinear average time complexity with regard to $d$, given $O(d^3)$ parallel computing resources. The decoding time per measurement round decreases as $d$ increases, the first time for a quantum error decoder. The implementation employs a scalable architecture called Helios that organizes parallel computing resources into a hybrid tree-grid structure. Using a Xilinx VCU129 FPGA, we successfully implement $d$ up to 21 with an average decoding time of 11.5 ns per measurement round under 0.1\% phenomenological noise, and 23.7 ns for $d=17$ under equivalent circuit-level noise. This performance is significantly faster than any existing decoder implementation. Furthermore, we show that \name can optimize for resource efficiency by decoding $d=51$ on a Xilinx VCU129 FPGA with an average latency of 544 ns per measurement round.
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- Award ID(s):
- 2216030
- PAR ID:
- 10553492
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Quantum Engineering
- Volume:
- 5
- ISSN:
- 2689-1808
- Page Range / eLocation ID:
- 1 to 18
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1109/TQE.2024.3467271
