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Paper 1

Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries

Adam Paetznick, Krysta M. Svore

Year

2013

Journal

arXiv preprint

DOI

arXiv:1311.1074

arXiv

1311.1074

We present a decomposition technique that uses non-deterministic circuits to approximate an arbitrary single-qubit unitary to within distance $ε$ and requires significantly fewer non-Clifford gates than existing techniques. We develop "Repeat-Until-Success" (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit $Z$-axis rotation to within distance $ε$, where the number of $T$ gates scales as $1.26\log_2(1/ε) - 3.53$, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of $2.4\log_2(1/ε) - 3.28$ can be achieved for arbitrary unitaries and a small range of $ε$, which is roughly twice as good as optimal deterministic decomposition methods.

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Paper 2

ADaPT: Adaptive-window Decoding for Practical fault-Tolerance

Tina Oberoi, Joshua Viszlai, Frederic T. Chong

Year

2026

Journal

arXiv preprint

DOI

arXiv:2605.01149

arXiv

2605.01149

Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through parallelization and reducing reaction time via speculation on window boundaries. However, these methods use a fixed window size d, paying a fixed decoding time overhead for each window. In practice, we find this overhead of a fixed window size unnecessary in many cases due to the sparsity of average-case errors in QEC. Leveraging this insight, in this paper we propose an adaptive window decoding technique based on decoder confidence. This technique reduces the overhead in decoding time thus reducing reaction time without compromising on logical error rates. We benchmark adaptive window decoding across different codes and hardware inspired noise models. Our results show that this adaptive technique reaches the target error rate while maintaining a low decoding time overhead across different codes, and under different noise models.

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