I formalize the energy–information invariant Ñt for superconducting qubits in circuit QED (cQED) and show how it can serve as a practical, measurable criterion for operation near Landauer efficiency. The central idea is that stable coherence emerges when the energy cost per acquired bit approaches the Landauer bound; not because dissipation vanishes, but because it is minimized relative to information gain. (i) I define the information rate via the Shannon–Hartley capacity with explicit discussion of quantum limits (Holevo bound); (ii) I establish a reference plane for power P and rigorously define Tₑff either as the noise temperature of the readout chain or via cavity photon occupancy; and (iii) I clarify that İ in the denominator of Ñt must approximate the maximally achievable rate for the given SNR and bandwidth, without penalizing software postprocessing. With these specifications, the hypothesis is: stable coherence is achieved in the asymptotic limit Ñt → 1.
I formalize the energy–information invariant Ñt for superconducting qubits in circuit QED (cQED) and show how it can serve as a practical, measurable criterion for operation near Landauer efficiency. The central idea is that stable coherence emerges when the energy cost per acquired bit approaches the Landauer bound; not because dissipation vanishes, but because it is minimized relative to information gain. (i) I define the information rate via the Shannon–Hartley capacity with explicit discussion of quantum limits (Holevo bound); (ii) I establish a reference plane for power P and rigorously define Tₑff either as the noise temperature of the readout chain or via cavity photon occupancy; and (iii) I clarify that İ in the denominator of Ñt must approximate the maximally achievable rate for the given SNR and bandwidth, without penalizing software postprocessing. With these specifications, the hypothesis is: stable coherence is achieved in the asymptotic limit Ñt → 1.
Abstract Computation requires energy. Landauer’s principle establishes that erasing one bit of information irreversibly dissipates at least kBT ln 2 of thermal energy. Modern computers operate 10^6 to 10^9 times above this fundamental bound. In 1973, Bennett demonstrated that any computation can be made thermodynamically reversible through procedures that preserve information, thereby approaching the Landauer limit. However, a critical question remained unanswered for fifty years: how quickly does reversible compilation converge to the theoretical minimum, and what ensemble size achieves practical energy savings? We resolve this problem through the Fluctuation-Dissipation Compilation Theorem, which provides the first explicit convergence rate for thermodynamically optimal computing. Reversible compilation of any algorithm dissipates average energy equal to the thermal energy scale multiplied by the logical entropy change, plus corrections that decrease as the inverse square root of the ensemble size. This N^(−1/2) convergence rate, derived by combining fluctuation theorems from statistical mechanics with the central limit theorem, is provably optimal—no compilation strategy can achieve faster convergence. The proof unifies three historically independent disciplines: statistical mechanics through the Jarzynski equality and Crooks fluctuation theorem, information theory through Shannon entropy bounds, and compilation theory through Bennett’s reversible computing framework. By formulating thermodynamic compilation as a rigorous resource theory, we establish that reversible transformations exactly conserve entropy while irreversible erasure operations incur fundamental energy costs bounded by information-theoretic limits. Critically, we provide finite-ensemble performance guarantees essential for practical implementations, characterizing not just average energy dissipation but complete statistical distributions including fluctuations and tail probabilities. Numerical experiments on Grover search and quantum Fourier transforms validate our predictions. Simulations confirm the predicted N^(−1/2) convergence rate within 3% error and demonstrate energy reductions exceeding 99.9% compared to irreversible implementations. These results establish that thermodynamically optimal compilation is achievable with realistic ensemble sizes for near-term quantum hardware operating under thermal constraints. This framework bridges fundamental physics and practical computing. Applications span quantum processors cooled to millikelvin temperatures where every picojoule of dissipation limits performance, battery-powered Internet-of-Things sensors requiring decade-long autonomous operation, data centers consuming one percent of global electricity where incremental efficiency improvements yield billion-dollar savings, and deep-space missions operating on hundred-watt radioisotope generators where every watt conserved enables additional science. By establishing thermodynamic compilation as a rigorous engineering discipline with explicit finite-size guarantees, this work transforms Bennett’s asymptotic theoretical insight into a practical methodology for approaching fundamental physical limits in real computing systems
Preprint: This paper derives quantitative bounds on measurement windows for finite-capacity observers extracting information from decohering quantum systems, extending standard decoherence theory to realistic experimental constraints. Main Result: For Gaussian-Markovian decoherence with exponential information decay I(t) = I₀ exp(-2Γt), bounded-capacity observers lose access to system distinctions when mutual information drops below detection threshold ε, yielding measurement window: τ_c = (1/2Γ) log(α C_A / ε) where Γ is decoherence rate [s⁻¹], C_A is observer capacity [bits] defined via Shannon formula (bandwidth × log₂(SNR) × integration time), ε is detection threshold [bits], and α ~ 0.1-1 is a model-dependent constant from spectral decomposition of environmental information. This establishes logarithmic capacity-scaling: doubling detector quality extends measurement windows by only ~0.35/Γ seconds, implying diminishing returns from capacity improvements. Experimental Predictions: For state-of-the-art circuit QED (superconducting transmon qubits, T₁ = 100 μs, bandwidth Δf = 10 MHz, SNR = 10), the framework predicts τ_c ~ 4-10 μs. Varying bandwidth from 1-30 MHz (capacity C_A ∈ [3, 90] bits) produces measurable Δτ_c ≈ 1.7 μs variation (5-10% of coherence time). Five experimental tests discriminate capacity-scaling from standard decoherence: ∙ Tests 1-3: Verify logarithmic capacity-scaling, inverse rate-dependence, threshold-dependence ∙ Test 4: Multi-observer non-redundancy (at most one narrowband detector succeeds) ∙ Test 5: Capacity-dependent redundancy buildup (primary discriminating signature) Key Contributions: ∙ First quantitative analysis of Zurek's pre-objective phase under explicit finite-resource constraints ∙ Capacity-scaling law connecting Shannon information theory to quantum measurement dynamics ∙ Operational definitions ensuring falsifiability (capacity, threshold, mutual information defined via measurement protocols) ∙ Concrete numerical predictions for three platforms (circuit QED, spin qubits, optomechanics) with resource estimates ∙ Design principle: environmental shielding (linear benefit in τ_c) outperforms detector improvement (logarithmic benefit) when both options available Technical Approach: The bound follows from threshold-crossing analysis of exponential decay with capacity-limited initial information I₀ = α C_A, justified via spectral decomposition of environmental information under flat-spectrum approximation for narrowband observation. All parameters (Γ, C_A, ε) are operationally defined and independently measurable, avoiding circularity. Extensions to non-Markovian dynamics (memory kernels), scrambling systems (black holes, many-body chaos), and non-Gaussian noise (Lévy flights, 1/f noise) are discussed with conjectured scaling laws. Scope: The bound applies specifically to Gaussian-Markovian systems (harmonic oscillators, qubits in dispersive limit, weak continuous measurement with memoryless baths). Circuit QED provides optimal testbed due to tunable Purcell filters (bandwidth control), high coherence times (T₁ > 300 μs achieved), and multiplexed readout infrastructure (5+ independent detectors demonstrated). Validity requires α C_A > ε (initial information exceeds threshold); domain violations occur when capacity too small, threshold too high, or coupling too weak. Relation to Prior Work: Zurek's Quantum Darwinism (2003-2009) explains asymptotic objectivity emergence through environmental redundancy but assumes unbounded observers (C_A → ∞, t → ∞). This work analyzes the complementary finite-resource regime (C_A < ∞, t ~ τ_c), providing first capacity-parameterized bound on pre-objective phase duration. Framework is interpretation-neutral—compatible with Copenhagen, Many-Worlds, Bohmian mechanics, and relational quantum mechanics. Philosophical implications (process ontology, observer-dependent reality, impermanence) are explored but clearly separated from testable predictions. Methods: Open quantum systems theory, Shannon information theory, operational quantum measurement, circuit QED experimental physics, numerical prediction for realistic parameters. Content: Complete 90-page manuscript with axiomatic framework (§2), narrowband observation model (§3), main theorem with proof (§4), numerical predictions (§5), five experimental falsification tests (§6), detailed Quantum Darwinism comparison (§7), extensions and limitations (§8), interpretive options (§9), and honest assessment (§10). Includes 77 references and operational definitions for all information-theoretic quantities. Target Audience: Quantum foundations researchers, experimental quantum physicists (circuit QED, trapped ions, quantum dots), quantum information theorists, philosophers of physics interested in measurement and objectivity.
Cryogenic quantum computers require classical control electronics operating at room temperature (T_room ≈ 300 K) to interface with qubits at milliKelvin (T_qubit ≈ 10 mK). Information erasure in room-temperature logic incurs a Landauer-limit cost, E_Landauer = k_B T_room ln 2 per bit. Refrigeration to maintain T_qubit introduces additional energy dissipation, quantified via Carnot efficiency: COP = T_qubit / (T_room − T_qubit). This work computes the total energy floor as E_total = E_Landauer + E_refrigeration, where E_refrigeration = Q_cold / COP and Q_cold = k_B T_qubit ln 2 per bit. A JPCUB normalization is proposed to partition dissipation between controller and qubit subsystems, enabling targeted optimization. For T_qubit = 10 mK, E_refrigeration ≈ 10^4 × E_Landauer, indicating controller-side dissipation dominates. [to verify] JPCUB ratios quantify trade-offs, guiding thermal management in scalable quantum architectures. ## 1. Introduction Quantum computing systems face dual thermodynamic challenges: information erasure in classical control electronics and refrigeration to maintain qubit coherence. Landauer's principle establishes E_Landauer = k_B T ln 2 per bit as the minimum energy cost for information loss [Landauer, 1961, DOI:10.1103/RevModPhys.29.544]. However, cryogenic qubits necessitate refrigeration from room temperature, introducing a Carnot efficiency overhead [Kittel, 2008, DOI:10.1002/9783527618132]. This paper derives the combined energy floor for control electronics, accounting for both effects, and introduces a normalization framework (JPCUB) to separate controller and qubit dissipation. ## 2. Background Landauer's principle links information theory and thermodynamics, asserting that erasing a bit of information requires energy E = k_B T ln 2 [Landauer, 1961]. For cryogenic systems, this applies to room-temperature logic, while qubit operation demands refrigeration. The coefficient of performance (COP) for a Carnot refrigerator is COP =
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.
Standard physics correctly predicts that an excited electron decays to a lower orbital and emitsa photon, yet its explanatory nucleus is tautological: “the system minimizes energy.” Energyis treated as primitive, and the reason the Universe exports energy to the vacuum is delegatedto spontaneous emission postulates or to an external reservoir, without an information-theoreticaccounting of the discarded degrees of freedom. Building on MetaTime Modelo 3, where theStandard Model is formulated as a boundary open effective field theory (open-EFT) with a causal nonMarkovian influence functional characterized by a running latency ΓL(µ), we propose a mechanisticreinterpretation: an excited orbital is not merely “higher energy” but a state of higher algorithmiccomplexity—a larger bulk entanglement wedge footprint required to stabilize its boundary geometryagainst vacuum noise. Orbital relaxation is a compression event that erases a definite informationbudget ∆I into the traced-out bath. By Landauer’s principle, erasing ∆I bits must dissipate energyE ≥ kBTeff ln 2 ∆I. We identify the emitted photon as this mandatory Landauer export and treat itsfrequency ω as the bath’s erasure clock rate, yielding the exchange relation Eγ ≃ ℏω ≃ kBTeff ln 2 ∆I.The Planck relation thus emerges as an informational exchange rate: Planck’s constant is the “priceof a bit” evaluated at the vacuum’s effective erasure temperature. For the hydrogen Lyman-αtransition 2p → 1s in free vacuum, defining ∆I via a Jensen–Shannon information metric on orbitalprobability densities gives ∆I2p→1s = 0.64079 bits and implies an effective erasure temperatureTeff ≃ 2.66 × 105 K. We outline falsifiable extensions in which Teff and ΓL become environmentallytunable (cavity QED, dense media), producing correlated deviations in line shapes and relaxationpathways beyond standard QED vacuum fluctuations.
The Landauer principle states that any logically irreversible information processing must be accompanied by dissipation into the environment. In this Letter, we investigate the heat dissipation associated with finite-time information erasure and the effect of quantum coherence in such processes. By considering a scenario wherein information is encoded in an open quantum system whose dynamics are described by the Markovian Lindblad equation, we show that the dissipated heat is lower bounded by the conventional Landauer cost, as well as a correction term inversely proportional to the operational time. To clarify the relation between quantum coherence and dissipation, we derive a lower bound for heat dissipation in terms of quantum coherence. This bound quantitatively implies that the creation of quantum coherence in the energy eigenbasis during the erasure process inevitably leads to additional heat costs. The obtained bounds hold for arbitrary operational time and control protocol. By following an optimal control theory, we numerically present an optimal protocol and illustrate our findings by using a single-qubit system.