Superconducting Quantum Sensors

• Superconducting quantum sensors are devices that use Josephson interference, quasiparticle dynamics, and coherent circuit effects to transduce physical parameters into measurable signals.
• They include dc- and rf-SQUIDs, TESs, STJs, and SNSPDs, offering sensitivities such as nΦ0/√Hz magnetometry and eV-scale energy resolution for calorimetric detection.
• Applications span photonic quantum communication, rare-event searches, and material characterization, highlighting their role in advancing both research and quantum technology.

Superconducting quantum sensors are measurement devices in which superconducting order, Josephson interference, quasiparticle generation and transport, or coherent superconducting-circuit dynamics provide the transduction mechanism from an external parameter to a measurable electrical, optical, or microwave signal. The field spans dc- and rf-SQUID magnetometers, transition-edge sensors (TESs), superconducting tunnel junctions (STJs), superconducting nanowire single-photon detectors (SNSPDs), and qubit- or resonator-based circuit-QED sensors, with applications ranging from photonic quantum communication and rare-event searches to charge sensing, thermometry, magnetometry, strain metrology, and characterization of magnons and superconducting circuitry (Danilin et al., 2021).

1. Device classes and defining mechanisms

Historically, superconducting sensors began with Superconducting Quantum Interference Devices (SQUIDs), in which Josephson junctions embedded in a superconducting loop convert magnetic flux into a change in critical current or voltage. The perspective on superconducting-circuit sensing distinguishes dc-SQUIDs, rf-SQUIDs, transmon, flux qubit, gatemon, and qudit architectures, and frames their sensing role through parameter-dependent energy levels $E_i(\lambda)$ and phase accumulation in interferometric protocols such as Ramsey sensing and phase estimation algorithms (Danilin et al., 2021).

A second major class consists of calorimetric and quasiparticle-based detectors. TESs operate on the sharp resistance change at the superconducting transition and are used as ultra-sensitive microcalorimetric photon detectors, while STJs convert deposited energy into quasiparticles that tunnel across an insulating barrier to produce a current pulse proportional to absorbed energy. SNSPDs use a narrow superconducting wire whose local superconducting state is destabilized by photon absorption, vortex processes, or electrothermal dynamics (Smith et al., 2011). A more recent extension is the proposed Superconducting Quasiparticle-Amplifying Transmon, or SQUAT, which combines a transmon architecture with a quasiparticle trapping and multiplication stage to detect meV-scale phonons and single THz photons (Fink et al., 2023).

A third class uses coherent superconducting circuits directly as quantum probes. Examples in the supplied literature include a SQUID-terminated parametric Kerr resonator operated near a dissipative phase transition, a MHz-frequency heavy fluxonium acting as a frequency-resolved charge sensor, entanglement-based strain metrology with superconducting qubits, and transmon-based sensing of magnons over a dynamic range of about 2000 excitations (Beaulieu et al., 2024).

2. Operating principles and performance metrics

SQUID sensing is based on flux-dependent Josephson interference. The superconducting-circuit sensing perspective reports sensitivities as low as $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$ and spatial resolution down to $\sim 50~\mathrm{nm}$ for SQUID-based devices, situating them as benchmark superconducting magnetometers (Danilin et al., 2021).

TES operation relies on a superconducting film biased at its transition edge, where minute deposited energies generate measurable resistance changes. In the steering experiment, the TESs were described as thin-film superconducting tungsten detectors held at $40$–$75~\mathrm{mK}$; a photon raises the temperature and resistance, and the resulting voltage pulse is read out. The same broad operating logic appears in optical TESs for rare-event searches, where a titanium/gold bilayer is stabilized by negative electrothermal feedback and read out with a dc SQUID (Smith et al., 2011). In STJs, by contrast, the elementary excitations are quasiparticles created by pair breaking; the number of tunneling quasiparticles is

$N=\eta \frac{E}{\epsilon},$

with $\epsilon \approx 1.7\Delta$, and the statistical energy-resolution limit is

$\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$

where $F$ is the Fano factor (Friedrich et al., 2020).

For qubit-based superconducting sensors, the basic resource is coherent phase evolution. The probability pattern for single-qubit interferometric sensing was given as

$$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$

which makes explicit how the sensed parameter enters through the phase accumulated during free evolution (Danilin et al., 2021). In entangled sensors, the same source reports an $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$0-qubit response containing $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$1, together with an $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$2-dependent decoherence penalty, thereby formalizing the standard tension between Heisenberg-limited scaling and finite coherence.

These distinct transduction mechanisms lead to distinct figures of merit. TES studies emphasize conditional detection efficiency, responsivity, noise-equivalent power, and dark-count rate; STJ studies emphasize eV-scale energy resolution and line-shape control; SNSPD studies emphasize quantum efficiency, dark count rate, magnetic-field tolerance, and mode-switchable sensitivities to magnetic field or temperature; qubit-based sensing emphasizes Fisher information, scaling with time or probe size, and coherence-limited sensitivity (Manenti et al., 2024).

3. Transition-edge sensors in photonic quantum measurement and rare-event searches

TESs have played a central role in high-efficiency photonic quantum measurement. In the loophole-free quantum steering experiment, Alice’s arm used TESs to close the detection loophole without post-selection. The experiment achieved a conditional detection efficiency $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$3, approximately $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$4, and tested the steering condition

$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$5

Using the threshold relation

$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$6

the work emphasized that for $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$7 and ideal visibility, $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$8 is required. The reported values were $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$9 with bound $\sim 50~\mathrm{nm}$0, corresponding to a $\sim 50~\mathrm{nm}$1 standard deviation violation, and $\sim 50~\mathrm{nm}$2 with bound $\sim 50~\mathrm{nm}$3, corresponding to a violation by over $\sim 50~\mathrm{nm}$4 standard deviations (Smith et al., 2011).

The same paper attributes the sensor advantage to very high intrinsic detector efficiency, photon-number resolution, and near-zero dark counts. In that setup, the TESs yielded measured detection efficiencies $\sim 50~\mathrm{nm}$5 and $\sim 50~\mathrm{nm}$6 times greater than SPADs at $\sim 50~\mathrm{nm}$7, with performance limited by fibre splicing losses rather than intrinsic detector efficiency. The reported rise time was $\sim 50~\mathrm{nm}$8 and the dead time $\sim 50~\mathrm{nm}$9, which was described as insignificant at the $40$0 count rates used, with loss due to dead time of $40$1 (Smith et al., 2011).

A distinct TES trajectory aims at relaxing cryogenic overhead. A nitrogen-cooled TES based on van der Waals heterostructures of $40$2 operated at and above liquid nitrogen temperature, with full superconductivity persisting above $40$3 and operational data up to an onset near $40$4. At $40$5 the reported responsivity was $40$6, the NEP was $40$7, the fastest observed relaxation component was $40$8, and the detector preserved full responsivity up to $40$9 while retaining significant readout into the GHz range. The device was also integrated on telecom-grade SiN waveguide chips (Seifert et al., 2020).

Low-background TES operation is equally important in rare-event searches. Optical TESs characterized for dielectric haloscopes distinguished electrical-noise, high-energy, and photonlike events through a pipeline that included Butterworth filtering, feature extraction, principal component analysis, k-means clustering, and manual review. The study isolated photonlike events in the $75~\mathrm{mK}$0–$75~\mathrm{mK}$1 range and reported a photonlike dark-count rate of $75~\mathrm{mK}$2, with $75~\mathrm{mK}$3 at $75~\mathrm{mK}$4, described as a seven order of magnitude reduction relative to the SPAD previously used in the MuDHI haloscope setup. High-energy events were experimentally verified and simulated as substrate interactions induced by cosmic rays and environmental $75~\mathrm{mK}$5 radiation, whereas the ultimate source of the residual photonlike dark counts remained unresolved (Manenti et al., 2024).

4. Nanowires, tunnel junctions, and quasiparticle-amplifying superconducting sensors

SNSPDs occupy a different regime of superconducting sensing, optimized for fast single-photon detection but also capable of multifunctional operation. The amorphous SNSPD study reported robust performance in magnetic fields up to $75~\mathrm{mK}$6, with unchanged quantum efficiency at typical bias currents and dark count rates below $75~\mathrm{mK}$7 within the quantum-efficiency plateau. By moving the bias current toward the electrothermal oscillation regime, the same device functioned as a magnetometer with sensitivity better than $75~\mathrm{mK}$8, reaching $75~\mathrm{mK}$9 at $N=\eta \frac{E}{\epsilon},$0 and $N=\eta \frac{E}{\epsilon},$1, and as a thermometer with sensitivity $N=\eta \frac{E}{\epsilon},$2 at $N=\eta \frac{E}{\epsilon},$3 and $N=\eta \frac{E}{\epsilon},$4 (Lawrie et al., 2021).

STJs are a mature high-resolution superconducting sensor platform for low-energy calorimetry. In the sterile-neutrino search based on $N=\eta \frac{E}{\epsilon},$5Be electron capture, the junction stack was Ta-Al-$N=\eta \frac{E}{\epsilon},$6-Al-Ta with surface area $N=\eta \frac{E}{\epsilon},$7 and thickness $N=\eta \frac{E}{\epsilon},$8, operated at $N=\eta \frac{E}{\epsilon},$9. Over a net total of $\epsilon \approx 1.7\Delta$0 days with a single STJ operated at low count rate, the experiment set exclusion limits for sterile neutrinos in the mass range from $\epsilon \approx 1.7\Delta$1 to $\epsilon \approx 1.7\Delta$2 and improved upon previous work by up to an order of magnitude. The kinematic observable was the daughter recoil energy

$\epsilon \approx 1.7\Delta$3

which makes the search model-independent at the level of decay kinematics (Friedrich et al., 2020).

The Monte-Carlo study for the BeEST program complements this by modeling quasiparticle production, Fano statistics, and escape-induced line-shape distortions. For bulk materials it reported $\epsilon \approx 1.7\Delta$4 and $\epsilon \approx 1.7\Delta$5, in agreement with literature values. Initial simulations of the low-energy escape tail were consistent with observations and predicted fine structure associated with discrete electron escape processes. This suggests that line-shape modeling is not a peripheral issue but part of the sensor itself, because response-function structure can mimic or obscure rare-event signatures (Bray et al., 2022).

The proposed SQUAT extends quasiparticle-based superconducting sensing into qubit hardware. It combines a transmon core with a lower-gap trap region that supports quasiparticle trapping, multiplication, and repeated tunneling. The proposal predicts sensitivity to single THz photons and to $\epsilon \approx 1.7\Delta$6 phonons in the absorber substrate on the $\epsilon \approx 1.7\Delta$7 timescale, while removing the separate readout resonator used in quantum capacitance detector architectures and reading out parity-induced frequency shifts directly from the qubit (Fink et al., 2023).

5. SQUID arrays, low-frequency circuit sensors, and integrated cryogenic readout

SQUIDs remain the canonical superconducting quantum sensor for magnetometry, but array architectures introduce additional design degrees of freedom. In two-dimensional Superconducting Quantum Interference Arrays, a central obstacle for absolute magnetometry has been the need for incommensurate loop areas. The synthetic-area-spread work showed that selectively inserted bare superconducting loops can reproduce the required non-periodic voltage–magnetic-flux response even when the SQUID loops themselves are physically identical. The formal result is an effective synthetic area vector

$\epsilon \approx 1.7\Delta$8

and arrays up to $\epsilon \approx 1.7\Delta$9 were experimentally verified to behave in alignment with this theory (Monaghan et al., 19 Nov 2025).

At the level of individual coherent circuits, heavy fluxonium demonstrates that superconducting sensing need not be confined to the GHz regime. The reported device reached a transition frequency of $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$0, the lowest stated for any superconducting qubit, and combined resolved sideband cooling with coherent manipulation and single-shot readout. The final ground-state population after sideband cooling was $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$1, corresponding to an effective temperature of $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$2, with coherence times $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$3 and $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$4. In cyclic preparation-and-interrogation sensing, the fluxonium acted as a frequency-resolved AC-charge sensor with charge sensitivity $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$5 and energy sensitivity $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$6, while remaining inherently insensitive to DC charge noise (Najera-Santos et al., 2023).

Superconducting transduction can also be embedded in cryo-CMOS. A sub-$\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$7 temperature sensor implemented in $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$8-nm FDSOI CMOS used the temperature dependence of the critical current of a superconducting thin film. The circuit comprised a $\Delta E_{\mathrm{FWHM}}=2.355\sqrt{F\epsilon E},$9-resolution current-output DAC, a transimpedance amplifier with a superconducting thin film as gain element, and a comparator; it dissipated $F$0 and operated at ambient temperatures as low as $F$1, providing variable temperature resolution reaching sub-$F$2 over a measurement range of about $F$3 to $F$4 (Olivieri et al., 2024).

Materials processing remains integral to sensor performance. The NbN deposition study used reactive dc-magnetron sputtering with target-voltage hysteresis and total-process-pressure monitoring to stabilize nitrogen consumption. By optimizing argon pressure and nitrogen flow, it reported NbN films with $F$5 and an illustrative $F$6 microstrip resonator with $F$7 at $F$8. This provides a direct link between thin-film process control and the low-loss microwave performance required for resonator-based superconducting sensors such as KIDs (Glowacka et al., 2014).

6. Quantum-enhanced sensing with superconducting qubits and resonators

The metrological interest of superconducting circuits extends beyond classical transduction into explicitly quantum-enhanced scaling. The superconducting-circuit sensing perspective distinguishes the standard quantum limit, where uncertainty scales as $F$9, from the Heisenberg limit, where it scales as $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$0, and discusses how entanglement and quantum error correction could in principle maintain Heisenberg scaling if the relevant error channels are correctable (Danilin et al., 2021).

A concrete experimental realization of criticality-enhanced sensing used a superconducting $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$1 resonator terminated by a SQUID and parametrically driven near twice the resonance frequency. The effective Hamiltonian was reported as

$$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$2

with critical detuning $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$3. Operating near the finite-component second-order dissipative phase transition, the reported frequency-estimation precision scaled quadratically with effective system size, $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$4, and each emitted photon was described as carrying more information about the estimated parameter than in a classical counterpart (Beaulieu et al., 2024).

A complementary route unifies criticality and non-equilibrium dynamics in a $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$5-qubit superconducting Stark–Wannier platform. With only computational-basis measurements and outcomes combined across several evolution times, the experiment achieved near-Heisenberg-limited precision with fitted exponents $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$6 and $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$7. The protocol also showed that sensing performance throughout the extended phase significantly outperformed the localized regime, while retaining simple initialization and readout requirements (Li et al., 20 Aug 2025).

Superconducting qubits have also been proposed for direct strain metrology. In the picostrain-sensing protocol, $$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$8 strain-sensitive qubits are collectively coupled to the momentum quadrature of a microwave resonator, and a GHZ state yields

$$P_{|1\rangle}(\Phi_{\mathrm{ext}},\tau)=\frac{1}{2}+\frac{1}{2}e^{-\Gamma \tau}\cos(\Delta \omega(\Phi_{\mathrm{ext}})\tau),$$9

together with quantum Fisher information scaling $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$00. The reported sensitivity figures were $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$01 for a single qubit and around $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$02 for $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$03 entangled qubits, with the scheme described as natively compatible with superconducting processors (Çelik, 27 Nov 2025).

Another hybrid sensing direction uses a superconducting transmon as a high-dynamic-range probe of collective excitations. In the YIG-magnon experiment, dispersive qubit–magnon coupling allowed sensing over a range of about $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$04 magnons, with few-magnon-sensitive detection and accurate resolution of magnon decay. Time-resolved decay was resolved up to about $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$05 magnons, and a parametrically activated XX interaction allowed the magnon damping rate to be mapped onto the qubit relaxation rate (Rani et al., 2024).

7. Quantum sensing of superconducting materials and circuits

A broader measurement ecosystem surrounds superconducting quantum sensors: quantum sensors that are not themselves superconducting are increasingly used to characterize superconducting materials and superconducting devices. NV centers in diamond were used with YBa$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$06Cu$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$07O$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$08 to probe the Meissner effect, the $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$09–$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$10 phase diagram, and fluorescence contours, yielding lower and upper critical fields $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$11 and $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$12 and critical current density $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$13 from a single sensing species with support from simulation and Brandt-model fitting (Ho et al., 2024).

Wide-field magnetic imaging with perfectly aligned diamond quantum sensors extended this to quantitative vortex metrology in YBa$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$14Cu$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$15O$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$16. After pixel-wise correction for strain-induced inhomogeneities, the method visualized the magnetic flux of single vortices with accuracy of $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$17. The mean radial field profile of $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$18 isolated vortices matched the theoretical model, and fitting yielded $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$19 at $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$20, while the temperature dependence was fit by

$\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$21

with $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$22 and $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$23 (Nishimura et al., 2023).

Scanning-probe NV microscopy has also been applied directly to superconducting circuitry. In an on-chip Nb resonator, single NV centers mounted on a scanning probe sensed both microwave and static magnetic fields. Rabi oscillation mapping showed that resonator-generated microwave fields could coherently control the spin sensor, with strongest fields at the resonator edges, while ODMR imaging visualized magnetic-field-induced vortex formation, evolution, and depinning. The study reported NV-to-sample distances tunable from about $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$24 to $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$25, resonator frequency near $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$26, and a typical local flux estimate per vortex of about $\sim 50~\mathrm{n}\Phi_0/\sqrt{\mathrm{Hz}}$27 (Li et al., 18 Jun 2026).

These results do not redefine superconducting quantum sensors as a category, but they do show that superconducting sensing now operates bidirectionally: superconducting devices act as quantum sensors, and quantum sensors are used in turn to diagnose superconducting films, vortices, resonators, and circuit environments. A plausible implication is that future progress will depend increasingly on this reciprocal coupling between device engineering, microscopic materials characterization, and quantum-limited readout across optical, microwave, and condensed-matter platforms.