Standard quantum computing models often assume that error correction can scale indefinitely regardless of operating temperature. However, the thermodynamic constraints on nanoscale systems create a fundamental energy scale mismatch at room temperature that remains unsolved by algorithmic optimizations. Here, a consilience of theoretical thermodynamics, decoherence dynamics, and experimental validation is introduced to delineate the absolute physical boundaries of quantum feasibility. By integrating the Caldeira-Leggett model with relativistic causality constraints, it is demonstrated that atomic-precision quantum computing is thermodynamically impossible above 20 Kelvin. Furthermore, it is identified that while ultra-cryogenic operation (0.1K) offers theoretical scalability, it faces severe engineering bottlenecks from wiring heat loads and thermal boundary resistance (Kapitza resistance). This finding redefines the strategic landscape of quantum computing, establishing cryogenic operation not as an engineering choice but as an immutable physical mandate constrained by thermal logistics.
Standard quantum computing models often assume that error correction can scale indefinitely regardless of operating temperature. However, the thermodynamic constraints on nanoscale systems create a fundamental energy scale mismatch at room temperature that remains unsolved by algorithmic optimizations. Here, a consilience of theoretical thermodynamics, decoherence dynamics, and experimental validation is introduced to delineate the absolute physical boundaries of quantum feasibility. By integrating the Caldeira-Leggett model with relativistic causality constraints, it is demonstrated that atomic-precision quantum computing is thermodynamically impossible above 20 Kelvin. Furthermore, it is identified that while ultra-cryogenic operation (0.1K) offers theoretical scalability, it faces severe engineering bottlenecks from wiring heat loads and thermal boundary resistance (Kapitza resistance). This finding redefines the strategic landscape of quantum computing, establishing cryogenic operation not as an engineering choice but as an immutable physical mandate constrained by thermal logistics.
The central tension in quantum computing lies between the exponential scaling of quantum information density and the polynomial limits of cryogenic heat extraction. This thermodynamic bottleneck mandates a paradigm shift from maximizing coherence at millikelvin temperatures to optimizing system-level efficiency through an architectural inversion, where control and readout systems are offloaded to higher-temperature stages. This work validates the physical viability of this approach through a detailed numerical analysis of a quantum unit cell. Grounding the simulation in a realistic noise model and a measurable engineering parameter—the Two-Level System loss tangent—we demonstrate that the systematic improvement of dielectric material quality is the key enabling factor for robust, high-fidelity quantum operations at 4 Kelvin. Our results show that by transitioning from standard amorphous dielectrics to state-of-the-art crystalline materials, the decoherence-limited single-qubit gate fidelity at 4 Kelvin can exceed 99.96%, becoming nearly indistinguishable from the performance at 10 millikelvin. This provides a quantitative, materials-driven roadmap for overcoming the thermodynamic constraints on scalable quantum information systems.
The promise of fault-tolerant quantum computation rests on its ability to solve certain intractable problems exponentially faster than classical computers. However, this theoretical promise is challenged by a cascade of interconnected physical bottlenecks, where the act of scaling quantum resources to suppress errors creates insurmountable thermal and classical processing loads. This paper develops an integrated thermal equilibrium model that quantitatively links physical gate fidelity, quantum error correction (QEC) overhead, and cryogenic cooling capacity to determine the viability of a large-scale system. Through numerical analysis of a system designed to execute Shor’s algorithm, the model demonstrates that even under optimistic technological assumptions, the required physical resources—in terms of qubit count, cooling power, and classical decoding speed—remain orders of magnitude beyond plausible near-term capabilities. The findings indicate that the primary barrier to scalable quantum computation is not a single engineering challenge but a systemic, multi-physics resource gap, where the polynomial scaling of classical support systems fails to keep pace with the exponential demands of the quantum core. This suggests that progress requires a holistic co-design of algorithms, hardware, and control systems rather than isolated improvements in qubit count alone.
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.
Abstract In the near future, one of the major challenges in the realization of large-scale quantum computers operating at low temperatures is the management of harmful heat loads owing to thermal conduction of cabling and dissipation at cryogenic components. This naturally raises the question that what are the fundamental limitations of energy consumption in scalable quantum computing. In this work, we derive the greatest lower bound for the gate error induced by a single application of a bosonic drive mode of given energy. Previously, such an error type has been considered to be inversely proportional to the total driving power, but we show that this limitation can be circumvented by introducing a qubit driving scheme which reuses and corrects drive pulses. Specifically, our method serves to reduce the average energy consumption per gate operation without increasing the average gate error. Thus our work shows that precise, scalable control of quantum systems can, in principle, be implemented without the introduction of excessive heat or decoherence.
The standard Landauer bound W≥kBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system-bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime-finite-time syndrome extraction, strong coupling to cryogenic environments, and non-equilibrium dynamics. Here, we develop a unified thermodynamic framework for fault-tolerant quantum computing that incorporates corrections beyond the ideal Landauer limit. We derive a generalized bound on the heat dissipation per QEC cycle: Qmin≥kBTln2+kBTΔISB+ℏτ, and scaling this result to large-scale quantum computers, we find that the total heat load grows polynomially with code distance but remains in the nanowatt range for million-qubit systems-well within the cooling power of modern dilution refrigerators. Applying our model to superconducting qubit architectures, we show that while strong coupling can add up to ∼20% to the ideal cost, finite-time effects contribute approximately 0.55% at 100 ns and 5.5% at 10 ns reset operations. Our results establish that the true thermodynamic cost of fault tolerance, while exceeding the naive Landauer estimate, does not pose a fundamental obstacle to scalability; the dominant engineering challenges lie in the heat load of control electronics and wiring, not in the fundamental dissipation of qubit reset.
Abstract: This analysis argues that Shor’s algorithm, while mathematically elegant, functions as a theoretical artifact defined under physically unrealizable conditions—perfect coherence, infinite precision, and unbounded resources—rendering it a mathematical trap that has misdirected the field toward infeasible engineering goals. In contrast, Landauer’s principle—that “information is physical”—provides a necessary foundation for evaluating computation within thermodynamic and material constraints. Empirical evidence reveals a fundamental scaling phase transition: beyond current scales, quantum error correction fails to suppress errors due to correlated failures, operator imprecision, and material defects, causing system reliability to degrade. The resulting divergence in resource requirements makes commercial-scale quantum computing physically infeasible. A constructive path forward requires abandoning idealized models of exponential speedup and developing computational paradigms intrinsically grounded in physical law. Keywords: Quantum computing; Shor’s algorithm; Landauer’s principle; Quantum error correction; Computational scalability; Fault-tolerant quantum computing; Physical limits of computation; Decoherence; Two-level systems; Operator imprecision; Phase transition in quantum systems; Quantum hardware; Information theory; Thermodynamics of computation; Quantum supremacy