Signal-to-noise problems in fault-tolerant quantum computation

@misc{oh2026signaltonoise,
  title = {{Signal-to-noise problems in fault-tolerant quantum computation}},
  author = {Hyunwoo Oh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15210},
  eprint = {2610.15210},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15210},
}

TY  - UNPB
TI  - Signal-to-noise problems in fault-tolerant quantum computation
AU  - Hyunwoo Oh
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.15210
UR  - https://arxiv.org/abs/2610.15210
AB  - Quantum computation offers a promising alternative to classical Monte Carlo methods by naturally avoiding sign problems through unitary evolution. A common misconception follows from this: because quantum simulation sidesteps the sign problem, it is often assumed to be an essentially perfect substitute for classical sampling. This is false---quantum measurements are intrinsically stochastic, and estimating observables often requires a number of samples that grows exponentially with system size, time separation, or inverse temperature, exactly as in the classical signal-to-noise problem. In this work, we analyze the origin and structure of signal-to-noise problems in quantum computation, drawing parallels with classical Monte Carlo, and demonstrate that such noise persists even in sign-problem-free regimes. We discuss strategies to mitigate it, in particular a quantum generalization of Stein control variates construction, in which unbiased estimators are built from operator commutators [X,A] and their discrete diagonal counterparts, and validate the approach with exactly solvable numerical examples that quantify the achievable variance reduction. Our results underscore that variance reduction, not merely sign-problem avoidance, is required to make quantum algorithms practically viable for many-body physics.
ER  -