This version develops a rigorous experimental framework for spatial thermal diagnosticsusing superconducting qubits as distributed sensing elements. The central methodologicalchange relative to a simple frequency-to-temperature conversion is the introduction of anexplicit measurement model separating thermal and non-thermal contributions to the observedqubit-frequency shift.For sensor i,δωobsi = δωthi + δωfluxi + δωqpi + δωTLSi + δωroi + δωotheri.Only after characterization of these contributions is a temperature estimate formed. Thelocal thermal response is represented by a calibrated coefficientαi(T0) = ∂ωq,i∂T⃓⃓⃓⃓T0,with explicit uncertainty and possible nonlinear correction.The spatial inverse problem is formulated through a response matrix, a point-spreadfunction (PSF), and regularized reconstruction. Spatial resolution is therefore not identifiedsimply with sensor spacing.The protocol introduces independent reference thermometry, blocked test data, blind lo-calized thermal perturbations, cross-validation, uncertainty propagation, hierarchical analysisacross cooldowns, and predefined falsification criteria. The primary endpoint is the inde-pendently evaluated reconstruction error of the thermal field. Secondary endpoints includeeffective spatial resolution, temperature resolution, localized perturbation detection, calibrationstability, and cross-cooldown reproducibility.The proposal remains exploratory and falsifiable. It does not claim experimental validation,universal thermometry, or superiority over conventional thermal sensors.
This version develops a rigorous experimental framework for spatial thermal diagnosticsusing superconducting qubits as distributed sensing elements. The central methodologicalchange relative to a simple frequency-to-temperature conversion is the introduction of anexplicit measurement model separating thermal and non-thermal contributions to the observedqubit-frequency shift.For sensor i,δωobsi = δωthi + δωfluxi + δωqpi + δωTLSi + δωroi + δωotheri.Only after characterization of these contributions is a temperature estimate formed. Thelocal thermal response is represented by a calibrated coefficientαi(T0) = ∂ωq,i∂T⃓⃓⃓⃓T0,with explicit uncertainty and possible nonlinear correction.The spatial inverse problem is formulated through a response matrix, a point-spreadfunction (PSF), and regularized reconstruction. Spatial resolution is therefore not identifiedsimply with sensor spacing.The protocol introduces independent reference thermometry, blocked test data, blind lo-calized thermal perturbations, cross-validation, uncertainty propagation, hierarchical analysisacross cooldowns, and predefined falsification criteria. The primary endpoint is the inde-pendently evaluated reconstruction error of the thermal field. Secondary endpoints includeeffective spatial resolution, temperature resolution, localized perturbation detection, calibrationstability, and cross-cooldown reproducibility.The proposal remains exploratory and falsifiable. It does not claim experimental validation,universal thermometry, or superiority over conventional thermal sensors.
This work proposes an experimentally falsifiable framework for incorporating real-timethermal information into quantum error correction for superconducting qubits. The centralidea is not to assume a universal thermal error law, but to determine experimentally whetherlocal temperature, thermal gradients, and related thermal observables contain predictive in-formation about physical error probabilities.Version 3.1 replaces the previous additive phenomenological error expression with a boundedstatistical model based on conditional error probabilities. For each physical error channel a,the model has the generic formp(a)i(t) = logit−1[︂β(a)0 + β(a)TδTi(t) + β(a)∇T Gi(t) + β(a)τδτ (t) + β(a)·xi(t)]︂,where Gi represents a normalized local temperature-gradient observable and xi containsoptional control variables. A physically motivated thermal occupation term may be includedas a covariate, but it is not imposed as the complete error model.Three operating modes are compared:1. Mode A: fixed-rate baseline decoder;2. Mode B: thermal-information-aware decoder with fixed cycle duration;3. Mode C: thermal-information-aware decoder with bounded adaptive cycle duration.The primary endpoint is the logical error-rate ratio between Mode B and Mode A undermatched experimental conditions. The secondary endpoint compares Mode C with Mode B.The protocol incorporates calibration, cross-validation, pre-registration of the primaryendpoint, paired experimental blocks, bootstrap confidence intervals, multiple-comparisoncontrol, systematic-error analysis, placebo tests, latency characterization, and independentcooldown reproducibility.No experimental result is claimed.
This document develops a theoretical, technical, and experimental framework for activethermal compensation of quantum-control pulses in superconducting qubits. The centralproposal is to measure a temperature-related control variable and use that information toadapt the microwave control amplitude so that the realized gate rotation is less sensitive toslow or reproducible thermal variations.Version 2.0 makes an important distinction between established physical relations andphenomenological assumptions. In particular, no universal linear dependence of the Rabifrequency on temperature is assumed. Instead, the temperature-to-control response is rep-resented by experimentally identifiable transfer functions and local calibration coefficients.Possible microscopic contributions from quasiparticles, thermal photons, two-level systems,dielectric loss, and other environmental channels are treated as candidate mechanisms ratherthan as a universal additive law.The control problem is formulated using a driven two-level Hamiltonian with both am-plitude and detuning errors. A thermal sensitivity coefficient is introduced through theexperimentally measurable derivative of the effective Rabi frequency with respect to tem-perature. The compensation law is derived from this measured response. Finite sensor andactuator bandwidth are incorporated through a causal filter and an explicit latency term.The experimental protocol combines Rabi calibration, thermal characterization, random-ized benchmarking, interleaved randomized benchmarking, and independent measurementsof T1 and T∗2. The primary experimental question is whether active thermal compensationproduces a statistically and experimentally resolvable reduction of gate error under controlledthermal perturbations.The proposal does not assume a predetermined improvement in fidelity, and it does notassume that amplitude compensation automatically suppresses all thermal decoherence. Allnumerical coefficients introduced in this document are design parameters or initial experi-mental ranges unless explicitly identified as measured quantities. No experimental result isclaimed.
This work presents a theoretical, engineering, and experimental framework for a multi-stagecryogenic architecture with programmable thermal conductance. The objective is to inves-tigate whether dynamically controlled thermal links can modify the low-frequency thermalenvironment experienced by a superconducting quantum device without introducing compen-sating noise or instability.The architecture is represented as a lumped thermal network containing nodes with heat ca-pacities, thermal conductances, external heat loads, and stochastic heat-current sources. Thisformulation replaces a single-stage temperature-noise expression with a matrix description ofthermal fluctuations and transfer functions. For a linear network, the temperature fluctuationspectrum is obtained from the thermal susceptibility matrix and the spectral-density matrixof the dissipative heat-current sources.A central methodological distinction is made between (i) mean temperature, (ii) tempera-ture fluctuations, (iii) electromagnetic noise, (iv) mechanical/vibrational noise, and (v) qubitdecoherence. These quantities are not assumed to be equivalent.The programmable element is modeled as a controllable thermal conductance Gi(u, t).Its effect is evaluated together with the noise associated with the control mechanism, pos-sible electromagnetic coupling, mechanical coupling, and transient thermal response. Theexperimental protocol therefore contains matched passive and programmable conditions, ran-domized measurement order, independent calibration, thermal settling criteria, control-bandmeasurements, and reproducibility across cooldowns.The primary endpoint is a pre-registered, band-limited reduction in the temperature-noisepower spectral density at the quantum device stage. Secondary endpoints include integratedtemperature variance, qubit T1, qubit T∗2, and randomized-benchmarking metrics. The pro-posal does not assume that any secondary endpoint must improve.The framework is explicitly falsifiable. A programmable architecture can fail to provide anet benefit if it produces additional noise, thermal gradients, control instability, electromag-netic interference, mechanical coupling, excessive settling time, or no reproducible reductionin the predefined thermal-noise metric.
This document presents Version 6.1 of a proposed quantum magnetic sensor based on acollectively prepared, spin-squeezed ensemble of superconducting qubits.The central objective is to determine, experimentally and reproducibly, whether quantumstate preparation can improve magnetic-field estimation relative to a matched unsqueezedsuperconducting-qubit reference operated with the same device, readout chain, resource budget,and total cycle time.A critical physical refinement of the present version is that a superconducting qubit is notassumed to couple to magnetic field through the bare electron gyromagnetic ratio.Instead, the magnetic transduction coefficient is defined operationally asκB,i =⃓⃓⃓⃓∂ωi∂B⃓⃓⃓⃓,or, for flux-mediated devices,κB,i =⃓⃓⃓⃓∂ωi∂Φi⃓⃓⃓⃓Mi,where Miis the effective field-to-flux coupling coefficient.This formulation permits transmon, SQUID-loop, fluxonium, or related architectures withoutconflating artificial-qubit dynamics with physical electron-spin Zeeman coupling.The quantum-state resource is characterized using the optimized Wineland spin-squeezingparameterξ2R =N minn⊥ Var(Sn⊥ )|⟨S⟩|2.Values below unity constitute a metrological spin-squeezing criterion under the statedcollective-spin model.The primary metrological endpoint is not ξ−1R alone.Instead, the proposed experiment directly compares the measured magnetic-field sensitivityper square root bandwidth of the squeezed protocol against a matched coherent/unsqueezedprotocol:Gpair =ηB,cohηB,sq. The principal confirmatory criterion is that the preregistered 95% confidence interval forthe paired gain exclude unity after accounting for preparation overhead, contrast, decoherence,readout noise, calibration uncertainty, device-to-device variation, and cooldown-to-cooldownvariation.The framework includes Hamiltonian modeling, collective squeezing, Ramsey interferometry,classical and quantum Fisher information, open-system dynamics, magnetic transductioncalibration, null tests, blind analysis, preregistration, hierarchical statistics, uncertainty budgets,replication criteria, falsification rules, data schemas, and a reproducible Python referenceimplementation.No experimental result is claimed.
Accurate knowledge of the on-chip temperature is essential for understanding and optimizing the performance of superconducting qubits, yet direct thermometry at millikelvin temperatures remains challenging. While qubits themselves are sensitive to the temperature of their environment, other factors may affect the qubits` effective temperature, and using them as thermometers with any accuracy requires specialized measurement protocols and qubit designs, limiting their practicality for routine diagnostics and adding complex infrastructure to any hardware testing apparatus. Here we demonstrate a complementary on-chip thermometry method based on superconducting Dayem bridges that are integrated on the same chip as transmon qubits. By extracting the critical current of the Dayem bridge from I-V measurements, we obtain a local, quantitative measure of the chip temperature without the need for microwave calibration or qubit-specific control sequences. To demonstrate the utility of the Dayem bridges as thermometers, we fabricate them in-situ with qubits on the same chip, calibrate the Dayem bridge critical current as a function of temperature, and characterize its resolution and stability at cryogenic temperatures. We additionally perform simultaneous measurements of the Dayem bridge thermometer and qubit excited-state population, and show agreement over the relevant temperature range, validating the method against established qubit thermometry. Furthermore, we correlate the independently measured chip temperature with qubit energy relaxation and dephasing times, demonstrating the utility of this approach for diagnosing temperature-dependent decoherence mechanisms. These results establish integrated Dayem bridges as a simple, non-invasive, and scalable tool for cryogenic hardware development, and on chip thermometry in superconducting quantum circuits.
Quantum thermometry has long promised sensitivities beyond classical limits, with recent paradigms highlighting quantum coherence as a primary driver of precision. While most studies focus on single-point temperature estimation, we extend this framework to the spatial domain. We consider a probe two-level system (TLS) coupled asymmetrically to an auxiliary TLS that equilibrates with a sample of profile T(x). The reduced probe state carries coherence in its local basis that remains temperature-sensitive after the probe transition has frozen out, yielding a Fisher information exponentially larger at low temperature than that of a population-only readout. An exact reparametrization converts the thermometric precision into a local spatial distinguishability bound; its validity requires only a sufficiently small relative temperature uncertainty and yields an explicit measurement budget. Adding auxiliary TLSs shifts the array's optimal working temperature upward and broadens the useful sensing window, with the achievable gain ultimately limited by the total available coupling rather than by an indefinite scaling law. Finally, we propose a microwave Mach-Zehnder interferometer that maps the temperature-dependent probe coherence onto an experimentally accessible quadrature observable.