Parallel window decoding enables scalable fault tolerant quantum computation

Abstract

Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 μs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today’s leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.

A Cryo-CMOS DAC-Based 40-Gb/s PAM4 Wireline Transmitter for Quantum Computing

“…The frequency of data qubit measurements depends on the type of quantum algorithm. In the worst case, a correction should be applied between each cycle, but in practice, this measurement rate is always lower [28], [29], [30]. By considering Fig.…”

Evaluation of the Classical Hardware Requirements for Large-Scale Quantum Computations

“…The setup in Fig. 7 achieves high decoding accuracy in practice [26]. shown on the left panel and averaged over 500 shots.…”

“…The middle d cycles of the blue windows are committed in round A, with the outer d cycles on the left and right acting as a buffer zone. In round B the intermediate windows are decoded and stitched together with the committed windows of round A to recover the full syndrome history[26].…”

Spanning Tree Matching Decoder for Quantum Surface Codes

“…This decoder results in large threshold error rates, but in practice, its polynomial time complexity introduces a latency that can be a bottleneck for fault-tolerant quantum computing architectures [5], [14], [15]. Considerable efforts have been invested in optimizing the performance of this decoder [16], [17]. Suboptimal algorithms based on the union-find (UF) decoder have also been proposed, achieving almost linear time in code length [18], [19].…”