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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. 

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. 

This paper describes an operating system (OS) called The- seus. Theseus is the result of multi-year experimentation to redesign and improve OS modularity by reducing the states one component holds for another, and to leverage a safe programming language, namely Rust, to shift as many OS responsibilities as possible to the compiler. Theseus embodies two primary contributions. First, an OS structure in which many tiny components with clearly-defined, runtime-persistent bounds interact without holding states for each other. Second, an intralingual approach that realizes the OS itself using language-level mechanisms such that the compiler can enforce invariants about OS semantics. Theseus’s structure, intralingual design, and state manage- ment realize live evolution and fault recovery for core OS components in ways beyond that of existing works.