Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2506.20318

Computed tomography of propagating microwave photons

Qiming Chen, Aarne Keränen, Aashish Sah, Mikko Möttönen

Published Jun 25, 2025• 0 citations
arXivHTMLPDF

Abstract

Propagating photons serve as essential links for distributing quantum information and entanglement across distant nodes. Knowledge of their Wigner functions not only enables their deployment as active information carriers but also provides error diagnostics when photons passively leak from a quantum processing unit. While well-established for standing waves, characterizing propagating microwave photons requires post-processing of room-temperature signals with excessive amplification noise. Here, we demonstrate amplification-free Wigner function tomography of propagating microwave photons using a superconductor--normal-metal--superconductor bolometer based on the resistive heating effect of absorbed radiation. By introducing two-field interference in power detection, the bolometer acts as a sensitive and broadband quadrature detector that samples the input field at selected angles at millikelvin with no added noise. Adapting the principles of computed tomography (CT) in medical imaging, we implement Wigner function CT by combining quadrature histograms across different projection angles and demonstrate it for Gaussian states at the single-photon level. Compressed sensing and neural networks further reduce the projections to three without compromising the reconstruction quality. These results address the long-standing challenge of characterizing propagating microwave photons in a superconducting quantum network and establish a new avenue for real-time quantum error diagnostics and correction.

DOI
10.48550/arxiv.2506.20318

Related papers

Experimental State Tomography of Itinerant Single Microwave Photons

Christopher Eichler, Deniz Bozyigit, Claus Lang +3 more

A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.

arXiv:1011.6668•Physical Review Letters•Jun 1, 2011•200 citations

Vaihemoduloitujen fotoneiden bolometrinen mittaus

Lukkari, Santtu

Propagating microwave photons have gained great interest due to their potential being used in the applications of the quantum technology, such as communication and sensing. The use of propagating microwave photons as information carriers requires methodology that is able to characterize the incoming photon signals. Since the signal could consist of only a few photons, the signal detection is truly a challenging task. Amplifying a weak microwave signal to room temperature would cause excessive noise and cover the signal. Previously, amplification-free signals have been measured with qubit-based photon detection, which relies on excitation of the qubit. This method is limited by a narrow bandwidth, since the qubit can absorb only a few discrete energies. However, a bolometer utilizing resistive absorption of the photons offers a broad bandwidth and enables the measurement without amplification. This thesis examines the use of bolometer as a phase and amplitude sensitive detector for propagating microwave signals. The phase sensitivity of the bolometer is enabled by homodyne detection, where the measurement signal is combined with a strong local oscillator signal. The combining of these signals is implemented with a beam splitter. Amplitude sensitivity is studied by repeating the measurement with multiple signal powers, and phase sensitivity is studied using a phase modulated measurement signal with different modulation amplitudes. The data is extracted from the bolometer by assuming a linear dependency between the average resonance frequency and the average photon number. Similarly, a linear dependency is assumed between the variances. This thesis demonstrates that the bolometer is able to detect changes in the measurement signal power and phase by measuring the average photon number and variance. The average photon number and variance oscillate, meaning that the phase modulation is detected. The oscillation amplitudes increase as a function of power indicating the amplitude sensitivity. A strong local oscillator signal allows the detection of weak signals without amplification, and thus the measurement can be conducted with minimal added noise. These results together show, that the bolometer is a versatile microwave detector and a promising candidate for quantum technology applications in the microwave region.

•Dec 2, 2025•0 citations

Characterizing quantum microwave radiation and its entanglement with superconducting qubits using linear detectors

Christopher Eichler, Deniz Bozyigit, Andreas J. Wallraff

Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasiprobability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.

arXiv:1206.3405•Physical Review A•Sep 10, 2012•134 citations

Generation and Efficient Measurement of Single Photons Using Superconducting Circuits

William Kindel

In this thesis, I demonstrate and evaluate an on-demand source of single propagating microwaves photons. Working in the context of a quantum network, nodes are connected via propagating, nonclassical states of the electromagnetic field. As such, preparing and detecting propagating quantum states is an essential task. I work with one particular node consisting of a microfabricated, effective two level system coupled to a microwave resonator and study its ability to produce propagating nonclassical states, such as single photon states. In principle, states generated by this node could be sent to other such nodes. However, I send them into a Josephson parametric amplifier (JPA) to characterize the source. In particular, I discuss how to design and couple the two components that form my source: a fixed frequency transmon qubit and a 3D superconducting waveguide cavity. I demonstrate the ability to control of the dynamics of this combined system and implement a single photon generation protocol, which utilizes a single microwave control field that is far detuned from the photon emission frequency. To characterize the generation, I perform tomography on the propagating photon state to determine its density matrix ρ. I perform repeated JPA-backed, linear measurements of the propagating state. Based on the histograms of my measurements, I infer a maximum single photon component ρ₁₁ = 0.36 ± 0.01. I characterize the imperfections of the photon generation and detection, including detection inefficiency and measurement backaction. I find that within uncertainty my measurements match my expectation.

•Jan 1, 2015•0 citations

Hong-Ou-Mandel Interference with Microwave Photons: Doing Quantum Optics Experiments using Superconducting Circuits

Andreas J. Wallraff

Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.

Bulletin of the American Physical Society•Jun 3, 2014•0 citations

Correlation measurement of propagating microwave photons at millikelvin

Aarne Keränen, Qiming Chen, András Gunyhó +5 more

Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number $$\langle \hat{n}\rangle$$ ⟨ n ̂ ⟩ and reveal the expected photon number variance $${(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)$$ ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.

arXiv:2407.05147•Nature Communications•Apr 24, 2025•5 citations
Propagating photons serve as essential links for distributing quantum information and entanglement across distant nodes. Knowledge of their Wigner functions not only enables their deployment as active information carriers but also provides error diagnostics when photons passively leak from a quantum processing unit. While well-established for standing waves, characterizing propagating microwave photons requires post-processing of room-temperature signals with excessive amplification noise. Here, we demonstrate amplification-free Wigner function tomography of propagating microwave photons using a superconductor--normal-metal--superconductor bolometer based on the resistive heating effect of absorbed radiation. By introducing two-field interference in power detection, the bolometer acts as a sensitive and broadband quadrature detector that samples the input field at selected angles at millikelvin with no added noise. Adapting the principles of computed tomography (CT) in medical imaging, we implement Wigner function CT by combining quadrature histograms across different projection angles and demonstrate it for Gaussian states at the single-photon level. Compressed sensing and neural networks further reduce the projections to three without compromising the reconstruction quality. These results address the long-standing challenge of characterizing propagating microwave photons in a superconducting quantum network and establish a new avenue for real-time quantum error diagnostics and correction.
A wide range of experiments studying microwave photons localized in superconducting cavities have made important contributions to our understanding of the quantum properties of radiation. Propagating microwave photons, however, have so far been studied much less intensely. Here we present measurements in which we reconstruct the quantum state of itinerant single photon Fock states and their superposition with the vacuum by analyzing moments of the measured amplitude distribution up to fourth order. Using linear amplifiers and quadrature amplitude detectors, we have developed efficient methods to separate the detected single photon signal from the noise added by the amplifier. From our measurement data we have also reconstructed the corresponding Wigner function.
Propagating microwave photons have gained great interest due to their potential being used in the applications of the quantum technology, such as communication and sensing. The use of propagating microwave photons as information carriers requires methodology that is able to characterize the incoming photon signals. Since the signal could consist of only a few photons, the signal detection is truly a challenging task. Amplifying a weak microwave signal to room temperature would cause excessive noise and cover the signal. Previously, amplification-free signals have been measured with qubit-based photon detection, which relies on excitation of the qubit. This method is limited by a narrow bandwidth, since the qubit can absorb only a few discrete energies. However, a bolometer utilizing resistive absorption of the photons offers a broad bandwidth and enables the measurement without amplification. This thesis examines the use of bolometer as a phase and amplitude sensitive detector for propagating microwave signals. The phase sensitivity of the bolometer is enabled by homodyne detection, where the measurement signal is combined with a strong local oscillator signal. The combining of these signals is implemented with a beam splitter. Amplitude sensitivity is studied by repeating the measurement with multiple signal powers, and phase sensitivity is studied using a phase modulated measurement signal with different modulation amplitudes. The data is extracted from the bolometer by assuming a linear dependency between the average resonance frequency and the average photon number. Similarly, a linear dependency is assumed between the variances. This thesis demonstrates that the bolometer is able to detect changes in the measurement signal power and phase by measuring the average photon number and variance. The average photon number and variance oscillate, meaning that the phase modulation is detected. The oscillation amplitudes increase as a function of power indicating the amplitude sensitivity. A strong local oscillator signal allows the detection of weak signals without amplification, and thus the measurement can be conducted with minimal added noise. These results together show, that the bolometer is a versatile microwave detector and a promising candidate for quantum technology applications in the microwave region.
Recent progress in the development of superconducting circuits has enabled the realization of interesting sources of nonclassical radiation at microwave frequencies. Here, we discuss field quadrature detection schemes for the experimental characterization of itinerant microwave photon fields and their entanglement correlations with stationary qubits. In particular, we present joint state tomography methods of a radiation field mode and a two-level system. Including the case of finite quantum detection efficiency, we relate measured photon field statistics to generalized quasiprobability distributions and statistical moments for one-channel and two-channel detection. We also present maximum-likelihood methods to reconstruct density matrices from measured field quadrature histograms. Our theoretical investigations are supported by the presentation of experimental data, for which microwave quantum fields beyond the single-photon and Gaussian level have been prepared and reconstructed.
In this thesis, I demonstrate and evaluate an on-demand source of single propagating microwaves photons. Working in the context of a quantum network, nodes are connected via propagating, nonclassical states of the electromagnetic field. As such, preparing and detecting propagating quantum states is an essential task. I work with one particular node consisting of a microfabricated, effective two level system coupled to a microwave resonator and study its ability to produce propagating nonclassical states, such as single photon states. In principle, states generated by this node could be sent to other such nodes. However, I send them into a Josephson parametric amplifier (JPA) to characterize the source. In particular, I discuss how to design and couple the two components that form my source: a fixed frequency transmon qubit and a 3D superconducting waveguide cavity. I demonstrate the ability to control of the dynamics of this combined system and implement a single photon generation protocol, which utilizes a single microwave control field that is far detuned from the photon emission frequency. To characterize the generation, I perform tomography on the propagating photon state to determine its density matrix ρ. I perform repeated JPA-backed, linear measurements of the propagating state. Based on the histograms of my measurements, I infer a maximum single photon component ρ₁₁ = 0.36 ± 0.01. I characterize the imperfections of the photon generation and detection, including detection inefficiency and measurement backaction. I find that within uncertainty my measurements match my expectation.
Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number ⟨n^⟩\langle \hat{n}\rangle⟨n^⟩ ⟨ n ̂ ⟩ and reveal the expected photon number variance (Δn)2=⟨n^⟩(⟨n^⟩+1){(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)(Δn)2=⟨n^⟩(⟨n^⟩+1) ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.