Impacts of Decoder Latency on Utility-Scale Quantum Computer Architectures

The speed of a fault-tolerant quantum computer is dictated by the reaction time of its classical electronics, that is, the total time required by decoders and controllers to determine the outcome of a logical measurement and execute subsequent conditional logical operations. Despite its importance, the reaction time and its impact on the design of the logical microarchitecture of a quantum computer are not well understood. In this work, we build, for a surface code based architecture, a model for the reaction time in which the decoder latency is based on parallel space- and time-window decoding methods, and communication latencies are drawn from our envisioned quantum execution environment comprising a high-speed network of quantum processing units, controllers, decoders, and high-performance computing nodes. We use this model to estimate the increase in the logical error rate of magic state injections as a function of the reaction time. Next, we show how the logical microarchitecture can be optimized with respect to the reaction time, and then present detailed full-system quantum and classical resource estimates for executing utility-scale quantum circuits based on realistic hardware noise parameters and state-of-the-art decoding times. For circuits with $10^{6}$--$10^{11}$ $T$ gates involving 200--2000 logical qubits, under a $\Lambda=9.3$ hardware model representative of a realistic target for superconducting quantum processors operating at a 2.86 MHz stabilization frequency, we show that even decoding at a sub-microsecond per stabilization round speed introduces substantial resource overheads: approximately 100k--250k additional physical qubits for correction qubit storage in the magic state factory; 300k--1.75M extra physical qubits in the core processor due to the code distance increase of $d$ to $d+4$ for extra memory protection; and a longer runtime by roughly a factor of 100.