Peaked quantum advantage using error correction

2025-10-06

AI Summary

Current quantum advantage experiments face a verification bottleneck: classical verification relies on full-scale simulation, limiting verifiable scale to that which is classically simulable. Method: We propose “hidden-code sampling,” the first framework integrating quantum error correction principles into quantum advantage construction. It designs a sampling task whose output distribution exhibits conditional concentration—peaking only under specific verifiable conditions—enabling efficient classical verification at cost far below full simulation, while preserving average-case hardness (exact sampling is #P-hard under the non-collapse of the polynomial hierarchy). The scheme operates within the fault-tolerant circuit paradigm, requiring only horizontally scalable quantum operations. Contribution/Results: This work establishes a new paradigm for verifiable quantum advantage and reveals a potential pathway toward fault-tolerant quantum computation, balancing experimental feasibility with theoretical rigor.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which they are also simulatable. An important outstanding question is therefore to find quantum advantage schemes that are also classically verifiable. We make progress on this question by designing a new quantum advantage proposal--Hidden Code Sampling--whose output distribution is conditionally peaked. These peaks enable verification in far less time than it takes for full simulation. At the same time, we show that exactly sampling from the output distribution is classically hard unless the polynomial hierarchy collapses, and we propose a plausible conjecture regarding average-case hardness. Our scheme is based on ideas from quantum error correction. The required quantum computations are closely related to quantum fault-tolerant circuits and can potentially be implemented transversally. Our proposal may thus give rise to a next generation of quantum advantage experiments en route to full quantum fault tolerance.

Problem

• Developing verifiable quantum advantage schemes beyond classical simulation
• Establishing classical hardness of sampling quantum output distributions
• Creating error correction-based quantum experiments approaching fault tolerance

Innovation

• Uses quantum error correction for peaked output
• Implements transversal fault-tolerant quantum circuits
• Enables faster verification via conditional distribution peaks