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Squeezed_Superconducting_Qubit_Magnetic_Sensor

Walter Ayala

Published Sep 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22943297

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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.
This work presents a theoretical, technical, statistical, and experimental framework for aquantum metrology system based on collective spin squeezing. The objective is to determineexperimentally whether an atomic ensemble can be prepared in a spin-squeezed state andwhether the resulting state provides a measurable metrological advantage for estimation of aweak physical parameter, such as a magnetic field.The central quantity is the Wineland spin-squeezing parameter, denoted here by ξ2R,ξ2R =N(∆S⊥)2|⟨S⟩|2,where S⊥ is the collective-spin component along the optimally squeezed transverse direc-tion. Values ξ2R < 1 indicate metrologically useful spin squeezing under the assumptions ofthe corresponding Ramsey-type measurement protocol.The v2.1 framework explicitly separates three concepts that are sometimes conflated: re-duction of collective-spin variance, metrological spin squeezing, and experimentally demon-strated parameter-estimation gain. It also distinguishes the quantum Fisher information of astate from the classical Fisher information obtained by a particular measurement.The protocol contains baseline characterization, squeezing generation, tomography of thetransverse covariance matrix, calibration of detection efficiency, estimation of systematic un-certainties, independent metrological testing, and reproducibility measurements. Negativecontrols are included to distinguish genuine quantum-projection-noise reduction from ordi-nary technical-noise suppression.The proposal is falsifiable. A failure to obtain a confidence interval for ξ2R below unity,failure to reproduce the effect on independent runs, or failure to demonstrate a sensitivityimprovement under a matched experimental comparison constitutes a negative result for thecorresponding hypothesis.No experimental result is claimed.
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A measurement of a single-qubit quantum sensor reveals at most 1 bit of information about the signal that was sensed. To perform a classification task on the signal, the conventional approach is to repeat a sensing protocol many times, averaging the measurement results to obtain a high-precision estimate of the sensed signal, and then to apply classical postprocessing. Quantum computational sensing (QCS) is an alternative approach that breaks with the paradigm of first obtaining a classical estimate of the signal and then computing a function of the estimated signal in postprocessing. QCS instead combines quantum sensing with quantum computing to concentrate information about the signal relevant to the task into the solitary bit revealed by each measurement. Here, we report on the experimental demonstration of QCS where sensing and computing were both performed by the same single superconducting transmon qubit. We consider various binary classification tasks based on static and oscillating magnetic fields induced by current through a flux line. The fields were sensed through a double-junction superconducting quantum interference device (SQUID) loop that was part of the qubit. We used a protocol based on quantum signal processing to preprocess the sensed signals in the quantum domain prior to measurement. For tasks on static magnetic fields, our protocol outperformed the conventional baseline of Ramsey-based phase estimation by as much as 15 percentage points. For tasks on oscillating magnetic fields, we classified signal amplitude and frequency with up to 20 and 15 percentage points higher accuracy, respectively, compared to the conventional baseline of optimized dynamical-decoupling protocols. Our results illustrate how quantum computing can enhance quantum sensing even with a minimally sized quantum system subject to the practical limitations of decoherence and error-prone operations.
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The performance of superconducting-qubit magnetometers depends not only on magnetic-field encoding during Ramsey interrogation, but also on how efficiently the encoded information is recovered during readout. Squeezed microwaves provide a promising route to improve information extraction by suppressing readout noise, yet how such readout enhancement translates into accessible information for magnetic-field estimation remains unclear. Here we develop an effective detected-mode framework linking projected quadrature noise, state-assignment error, and the classical Fisher information accessible from binary readout outcomes. A finite mismatch between the squeezed quadrature and the discrimination axis produces an optimal squeezing strength through the competition between squeezed and anti-squeezed fluctuations. We further show that squeezed readout improves the readout-limited magnetic-field sensitivity by recovering information otherwise lost during state assignment, with the enhancement remaining robust against quadrature mismatch, transmission loss, and added noise. These results establish a quantitative connection between squeezed-microwave readout and measurement-stage information recovery in superconducting quantum sensing.
In a quantum computer, the information carriers, which are bits in ordinary computers, are implemented as devices that exhibit coherent superpositions of physical states and entanglement. Such components, known as quantum bits or qubits, can be realized with various different types of two-state quantum systems. Quantum computers will be built for computational speed, with hoped for applications especially in cryptography and in other tasks where classical computers remain inefficient. Circuit quantum electrodynamics (cQED) is a quantum-computer architecture which employs superconducting electronic components and microwave photon fields as building blocks. Compared to cavity quantum electrodynamics (CQED), where atoms are trapped in physical cavities, cQED is more attractive in that its qubits are tunable and conveniently integrable with the electronics already in use. This architecture has shown some of the most promising qubit designs, despite their coherence times reaching tens of microseconds, are still below the state of the art with spin qubits, which reach milliseconds. Coherence times are historically the most relevant parameters describing the fitness of a qubit, although these days not necessarily the limiting factor. This thesis presents a comprehensive set of theoretical and experimental methods for measuring the characteristic parameters of superconducting qubits. We especially study transmission-line-shunted plasma oscillation qubits, or transmons, and presents experimental results for a single sample. Transmon capacitively couples a superconducting quantum interference device (SQUID) with a coplanar waveguide (CPW) resonator, often with added frequency tunability utilizing an external magnet. The number of superconducting charge carriers tunnelled through a junction in the SQUID are used as qubit degrees of freedom. Readout of the qubit state is carried out by measuring transmission through the CPW. A cryogenic setup is employed with measurement and driving pulses delivered from microwave sources. Steady-state spectroscopy is employed to determine the resonance frequencies of the qubit and the resonator, qubit-resonator coupling constants, and the energy parameters of the qubit. Pulse-modulated measurements are employed to determine the coherence times of the qubit. The related analysis- and simulation programs and scripts are collected togithub.com/patomaki.