Thermodynamic limitations on fault-tolerant quantum computing

TL;DR

This paper explores the thermodynamic constraints on fault-tolerant quantum computing, showing that heat generated during error correction can limit scalability but current systems are within safe operational regimes.

Contribution

The authors develop a dynamical model linking heat generation and error rates, identifying a phase transition that impacts fault tolerance in quantum computers.

Findings

Current superconducting qubit systems are in the bounded-error phase.

Thermodynamic heating can become significant but is not a fundamental scalability limit.

Maintaining current hardware capabilities ensures fault tolerance remains feasible.

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.