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References: Breakthroughs Required for Viability

  1. Quantum error correction - Wikipedia - Explains surface codes, threshold theorems, and the nonlinear relationship between physical error rates and overhead ratios, central to this chapter's analysis of why error rates must drop 100-10,000x.

  2. Fault-tolerant quantum computation - Wikipedia - Describes the conditions for fault tolerance including independent error assumptions and threshold requirements, relevant to this chapter's catalog of why all ten breakthroughs must occur simultaneously.

  3. Joint probability - Wikipedia - Explains joint probability for independent and dependent events, the mathematical framework this chapter uses to demonstrate that the collective likelihood of all required breakthroughs is vanishingly small.

  4. Quantum Error Correction (2013) - Daniel A. Lidar and Todd A. Brun, Editors - Cambridge University Press - Comprehensive treatment of error correction overhead calculations and threshold requirements, providing the technical foundation for this chapter's analysis of breakthroughs 1 and 8.

  5. Quantum Computing: An Applied Approach (2nd Edition, 2021) - Jack D. Hidary - Springer - Includes resource estimates for fault-tolerant algorithms showing million-qubit requirements, supporting this chapter's enumeration of the scale of breakthroughs needed across all ten dimensions.

  6. How to Factor 2048 Bit RSA Integers in 8 Hours Using 20 Million Noisy Qubits - Gidney and Ekera, arXiv (2019) - Provides the most cited resource estimate for practical quantum computation, establishing the 20 million qubit target that underlies this chapter's 1,000x scaling requirement.

  7. Suppressing Quantum Errors by Scaling a Surface Code Logical Qubit - Google Quantum AI, Nature (2023) - Reports on the current state of error suppression using surface codes, providing empirical data on where we stand relative to the error rate breakthroughs this chapter identifies as necessary.

  8. The Quantum Computing Bubble - Sankar Das Sarma, arXiv (2024) - Catalogs the gap between current quantum hardware capabilities and the requirements for useful computation, independently corroborating the ten-breakthrough framework developed in this chapter.

  9. Quantum Computing: Progress and Prospects (2019) - National Academies of Sciences - Independent assessment identifying multiple simultaneous breakthroughs needed for viable quantum computing, supporting this chapter's joint probability analysis of collective success.

  10. Low-Overhead Fault-Tolerant Quantum Computing - Gidney et al., arXiv (2023) - Explores reduced-overhead approaches to fault tolerance that still require dramatic improvements across multiple dimensions, demonstrating that even optimistic scenarios require most of the breakthroughs cataloged in this chapter.