Thermodynamic limitations on fault-tolerant quantum computing

• URL: http://arxiv.org/abs/2411.12805v2
• Date: Tue, 31 Dec 2024 21:34:05 GMT
• Title: Thermodynamic limitations on fault-tolerant quantum computing
• Authors: Mykhailo Bilokur, Sarang Gopalakrishnan, Shayan Majidy,
• Abstract summary: We introduce a model that characterizes heat generation and dissipation for arrays of qubits weakly coupled to a refrigerator.<n>We find that current experimental parameters place the system in the bounded-error phase.<n>Our results indicate that, while inherent heating can become significant, this thermodynamic constraint should not limit scalable fault tolerance if current hardware capabilities are maintained as systems scale.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the thermodynamic limits on scaling fault-tolerant quantum computers due to heating from quantum error correction (QEC). Quantum computers require error correction, which accounts for 99.9% of the qubit demand and generates heat through information-erasing processes. This heating increases the error rate, necessitating more rounds of error correction. We introduce a dynamical model that characterizes heat generation and dissipation for arrays of qubits weakly coupled to a refrigerator and identify a dynamical phase transition between two operational regimes: a bounded-error phase, where temperature stabilizes and error rates remain below fault-tolerance thresholds, and an unbounded-error phase, where rising temperatures drive error rates beyond sustainable levels, making fault tolerance infeasible. Applying our model to a superconducting qubit system performing Shor's algorithm to factor 2048-bit RSA integers, we find that current experimental parameters place the system in the bounded-error phase. Our results indicate that, while inherent heating can become significant, this thermodynamic constraint should not limit scalable fault tolerance if current hardware capabilities are maintained as systems scale.

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