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Entropy Production as an Operational Boundary for Quantum Reset in Superconducting Processors

Fernando Cesar Coelho Coutinho

Published Dec 27, 2025• 0 citations
Publisher

Abstract

Quantum information reset is an intrinsically irreversible process constrained by the second law of thermodynamics. In contemporary superconducting processors, dissipation during qubit reset is frequently dominated not only by quantum limits but by a classical energy floor on the order of 10^{-21} J. In contrast, the entropic bound T \Delta S at dilution refrigerator temperatures (\sim 15 mK) corresponds to a lower energy scale of approximately 10^{-23} J, establishing entropy production as the organizing physical principle that limits both the efficiency and the speed of reset operations. We introduce an entropy-limited efficiency estimator, \eta_S = 1 - (T \Delta S / W_{\rm diss}), which quantifies the thermodynamic distance from the entropic (Landauer) limit. By construction, \eta_S = 0 corresponds to the saturation of the entropy production limit, while \eta_S \to 1 indicates dissipation dominated by non-entropic (classical) contributions. Maximizing \eta_S is equivalent to a constrained variational problem in which dissipated work is minimized subject to the second law of thermodynamics. For typical superconducting qubits (\omega_q/2\pi \sim 5 GHz, T_1 \sim 50–100 \mus, T \sim 15 mK), the entropic bound T \Delta S \sim 10^{-23} J lies two orders of magnitude below the experimentally observed classical dissipation floor W_{\rm floor} \sim 10^{-21} J. Figures 1 and 2 were generated using the provided scripts_generate_figures.py script, using parameters: \omega_q/2\pi = 5 GHz, T_1 = 80 \mus, and T = 15 mK.

DOI
10.5281/zenodo.18064062

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Quantum information reset is an intrinsically irreversible process constrained by the second law of thermodynamics. In contemporary superconducting processors, dissipation during qubit reset is frequently dominated not only by quantum limits but by a classical energy floor on the order of 10^{-21} J. In contrast, the entropic bound T \Delta S at dilution refrigerator temperatures (\sim 15 mK) corresponds to a lower energy scale of approximately 10^{-23} J, establishing entropy production as the organizing physical principle that limits both the efficiency and the speed of reset operations. We introduce an entropy-limited efficiency estimator, \eta_S = 1 - (T \Delta S / W_{\rm diss}), which quantifies the thermodynamic distance from the entropic (Landauer) limit. By construction, \eta_S = 0 corresponds to the saturation of the entropy production limit, while \eta_S \to 1 indicates dissipation dominated by non-entropic (classical) contributions. Maximizing \eta_S is equivalent to a constrained variational problem in which dissipated work is minimized subject to the second law of thermodynamics. For typical superconducting qubits (\omega_q/2\pi \sim 5 GHz, T_1 \sim 50–100 \mus, T \sim 15 mK), the entropic bound T \Delta S \sim 10^{-23} J lies two orders of magnitude below the experimentally observed classical dissipation floor W_{\rm floor} \sim 10^{-21} J. Figures 1 and 2 were generated using the provided scripts_generate_figures.py script, using parameters: \omega_q/2\pi = 5 GHz, T_1 = 80 \mus, and T = 15 mK.
We derive an operationally defined lower bound on the physical time Δt \Delta t Δtrequired to execute any information-processing task, based on the total entropy produced ΔΣ \Delta\Sigma ΔΣ. The central result, Δt≥τΣΔΣ \Delta t \geq \tau_{\Sigma} \Delta\Sigma Δt≥τΣ​ΔΣ, introduces the Process-Dependent Dissipation Timescale τΣ≡1/⟨Σ˙⟩max \tau_{\Sigma} \equiv 1/\langle \dot{\Sigma} \rangle_{\text{max}} τΣ​≡1/⟨Σ˙⟩max​, which quantifies the maximum achievable entropy production rate for a given physical platform. We derive τΣ \tau_{\Sigma} τΣ​ from microscopic system-bath models and validate our framework against experimental data from superconducting qubit platforms. Crucially, we obtain a Measurement Entropic Time Bound:Δtmeas≥τΣkB[H(P)−S(ρ)] \Delta t_{\text{meas}} \geq \tau_{\Sigma} k_{\text{B}}[H(P) - S(\rho)] Δtmeas​≥τΣ​kB​[H(P)−S(ρ)], relating measurement time to information gained. Comparison with IBM and Google quantum processors shows agreement within experimental uncertainties. This framework provides a thermodynamic interpretation of quantum advantage as reduced entropy production per logical inference and suggests concrete optimization strategies for quantum hardware design.
The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for every initial state (except possibly the single minimally dissipative input) for any reliable reset mechanism. Since local heating threatens rapid decoherence, this issue is of substantial importance beyond mere energy efficiency. For the case of qubit reset, we find the minimally dissipative state analytically for any reliable reset protocol, in terms of the entropy-flow vector introduced here. This allows us to verify a recent theorem about initial-state dependence of entropy production for any finite-time transformation, as it pertains to quantum state preparation.
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.
In practice, qubit reset must be operated in an extremely short time, which incurs a thermodynamic cost within multiple orders of magnitude above the Landauer bound. We present a general framework to determine the minimal thermodynamic cost and the corresponding optimal protocol for memory erasure under arbitrary erasure speeds. Our study reveals the divergent behavior of minimal entropy production in the short-time limit depends on the convergence and divergence of the jump operator. There is an inherent trade-off between the minimal required time and the set error probability for the convergent class. Moreover, we find the optimal protocol exhibits general features in the fast-driving regime. To illustrate these findings, we employ fermionic and bosonic baths as examples. Our results suggest that the super-Ohmic bosonic heat bath is suitable for qubit reset.
Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process’s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n -qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state in our model, via a complexity-constrained process, is quantified by the state’s . The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the . The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer’s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy. In a random circuit—a simple model for quantum chaotic dynamics—the complexity entropy transitions from zero to its maximal value around the time corresponding to the observer’s computational-power limit. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a , which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of , as quantified by .
This research establishes an operational lower bound on entropy production induced by mass gaps in quantum systems. Using completely positive trace-preserving (CPTP) dynamics, the study demonstrates that any physical reset of a system with a minimal spectral gap \delta_{min}=mc^{2} incurs a minimum entropy production defined by the relation \Sigma\ge mc^{2}/T. Unlike Landauer's principle, this bound follows purely from thermodynamic admissibility and spectral structure rather than logical irreversibility or information-theoretic arguments. Key Features of the Study: ELQR Framework: The research utilizes the Entropy-Limited Quantum Reset (ELQR) framework to model reset as a constrained CPTP control problem. Reinforcement Learning Validation: Optimization using RL agents (specifically PPO) shows that the theoretical bound emerges as a robust dynamical attractor under unconstrained control optimization. Hawking Emission Application: When applied to black-hole horizons, the bound implies a minimal entropic cost for Hawking emission per particle of mass m that is independent of information loss or Page-curve considerations. Many-Body Systems: Validated through tensor-network simulations (TeNPy) of short Heisenberg chains, confirming that the operational bound is robust even in correlated systems. Non-Markovian Extensions: Preliminary simulations of qubits coupled to memory show that while transient backflow occurs, the envelope remains consistent with the mass-induced limit.