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Paper 1

Simplified circuit-level decoding using Knill error correction

Ewan Murphy, Subhayan Sahu, Michael Vasmer

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.05320

arXiv

2603.05320

Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be supplemented with a fast and accurate classical decoding algorithm. Standard techniques for measuring the parity-check operators of a quantum error-correcting code involve repeated measurements, which both increases the amount of data that needs to be processed by the decoder, and changes the nature of the decoding problem. Knill error correction is a technique that replaces repeated syndrome measurements with a single round of measurements, but requires an auxiliary logical Bell state. Here, we provide a theoretical and numerical investigation into Knill error correction from the perspective of decoding. We give a self-contained description of the protocol, prove its fault tolerance under locally decaying (circuit-level) noise, and numerically benchmark its performance for quantum low-density parity-check codes. We show analytically and numerically that the time-constrained decoding problem for Knill error correction can be solved using the same decoder used for the simpler code-capacity noise model, illustrating that Knill error correction may alleviate the stringent requirements on classical control required for building a large-scale quantum computer.

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Paper 2

Mechanisms for Quantum Advantage in Global Optimization of Nonconvex Functions

Dylan Herman, Guneykan Ozgul, Anuj Apte, Junhyung Lyle Kim, Anupam Prakash, Jiayu Shen, Shouvanik Chakrabarti

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03385

arXiv

2510.03385

We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we demonstrate a rigorous correspondence between the spectral properties of Schrödinger operators and the mixing times of classical Langevin diffusion. This correspondence motivates a mechanism for separation on functions with unique global minimum: while quantum algorithms operate on the original potential, classical diffusions correspond to a Schrödinger operators with a WKB potential having nearly degenerate global minima. We formalize these ideas by proving that a real-space adiabatic quantum algorithm (RsAA) achieves provably polynomial-time optimization for broad families of nonconvex functions. First, for block-separable functions, we show that RsAA maintains polynomial runtime while known off-the-shelf algorithms require exponential time and structure-aware algorithms exhibit arbitrarily large polynomial runtimes. These results leverage novel non-asymptotic results in semiclassical analysis. Second, we use recent advances in the theory of intrinsic hypercontractivity to demonstrate polynomial runtimes for RsAA on appropriately perturbed strongly convex functions that lack global structure, while off-the-shelf algorithms remain exponentially bottlenecked. In contrast to prior works based on quantum tunneling, these separations do not depend on the geometry of barriers between local minima. Our theoretical claims about classical algorithm runtimes are supported by rigorous analysis and comprehensive numerical benchmarking. These findings establish a rigorous theoretical foundation for quantum advantage in continuous optimization and open new research directions connecting quantum algorithms, stochastic processes, and semiclassical analysis.

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