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

Degenerate and nondegenerate Josephson parametric oscillators for quantum information applications

Andreas Bengtsson

Published Jan 1, 2017• 1 citation
OpenAlex

Abstract

Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.

Related papers

The Josephson parametric oscillator - From microscopic studies to single-shot qubit readout

Philip Krantz

Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.

•Jan 1, 2016•3 citations

Quantum information processing with tunable and low-loss superconducting circuits

Andreas Bengtsson

The perhaps most promising platform for quantum information processing is the circuit-QED architecture based on superconducting circuits representing quantum bits. These circuits must be made with low losses so that the quantum information is retained for as long as possible. We developed fabrication processes achieving state-of-the-art coherence times of over 100 µs. We identified the primary source of loss to be parasitic two-level systems by studying fluctuations of qubit relaxation times.Using our high-coherence circuits, we implemented a quantum processor built on fixed-frequency qubits and frequency-tunable couplers. The tunable couplers were lumped-element LC resonators, where the inductance came from a superconducting quantum interference device (SQUID). We achieved a controlled-phase gate with a fidelity of 99% by parametric modulation of the coupler frequency. Using this device, and another similar to it, we demonstrated two different quantum algorithms, the quantum approximate optimization algorithm, and density matrix exponentiation. We achieved high algorithmic fidelities, aided by our carefully calibrated gates.Additionally, we researched parametric oscillations using frequency-tunable resonators. Previously, degenerate parametric oscillations have been demonstrated by modulation of the resonant frequency at twice that frequency. We use this phenomenon to implement a readout method for a superconducting qubit with a fidelity of 98.7%. We demonstrated correlated radiation in nondegenerate parametric oscillations by modulating at the sum of two resonant frequencies of a multimode resonator. We showed an excellent quantitative agreement between the classical properties of the oscillations with a theoretical model. Moreover, we studied higher-order modulation at up to five times their resonant frequencies. These types of parametric oscillation states might be used as a quantum resource for continuous-variable quantum computing.

•Jan 1, 2020•2 citations

Single-shot read-out of a superconducting qubit using a Josephson parametric oscillator

Philip Krantz, Andreas Bengtsson, Michaël Simoen +6 more

We propose and demonstrate a read-out technique for a superconducting qubit by dispersively coupling it with a Josephson parametric oscillator. We employ a tunable quarter wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with 185±15 photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot read-out performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.

arXiv:1508.02886•Nature Communications•May 9, 2016•100 citations

Nondegenerate Parametric Resonance in a Tunable Superconducting Cavity

Waltraut Wustmann, Vitaly Shumeiko

Josephson parametric amplifiers continue to attract attention for monitoring and readout of superconducting qubits in quantum information processing, as well as other applications. The authors continue their research on these systems, presenting a comprehensive study of nondegenerate amplifiers that addresses nonlinear gain, parametric instability, amplification processes (two- and four-mode linear processes plus nonlinear corrections, with signal-to-noise ratios for all cases), and frequency conversion. Quantum fluctuations and squeezing are considered as well.

arXiv:1704.05083•Physical Review Applied•Aug 21, 2017•24 citations

Parametrically pumped superconducting circuits

Philip Krantz

In this licentiate thesis, I present the design, fabrication, and characterization of superconducting parametric resonators, for use in quantum information processing. These devices are quarter-wavelength coplanar waveguide resonators (~5 GHz), terminated at one end by a non-linear inductance provided by a SQUID (superconducting quantum interference device). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using on-chip transmission lines. The modulation occurs on a timescale much faster than the photon loss out of the resonator. The non-linearity provides several different regimes for operating this device. I focused on the parametric regime, in which the non-linear element was being modulated (pumped) at or near twice the resonant frequency. This pumping can lead to amplification and frequency conversion of an incoming signal. It can also give rise to instabilities and self-oscillations "parametric oscillations" - that is, the generation of an intense electric field in the resonator (the creation of photons). Parametric oscillations set in when the pumping strength exceeds a threshold value, and also depends on the pump-frequency detuning from twice the resonance and on the static flux through the SQUID. I characterized the devices over a wide parameter range by doing homodyne detection of the reflected signal or of the emitted field oscillations. In particular, I investigated the damping and two leading nonlinearities, dominating in different operating regimes, which influence the dynamics of the parametric resonator. First, I extracted the Duffing nonlinearity by studying the line width of the resonator as a function of the input signal (without pumping the SQUID). Second, with high pump amplitude, I extracted the pump-induced nonlinearity by determining the threshold parameters (pump amplitude and detuning) for the onset of parametric oscillations; this nonlinearity leads to the generation of higher-order pump terms that complicate the system dynamics, but can be mitigated now that they have been understood. My results validate a recent theoretical model for the classical, non-linear dynamics of parametric resonance, and helps determine workable design parameters. Finally, I helped develop a linearized model $-$ the "pumpistor" - describing this device in terms of a flux-controlled impedance. This will be useful when designing more complex circuits. One goal of this work is to demonstrate single-shot measurements on superconducting qubits (quantum bits of information). We will use the parametric resonator as a threshold discriminator, associating the qubit's two energy eigenstates with the parametric oscillations either turning on or not. This would be a very useful device in the quantum engineer's toolbox when designing systems for quantum information processing and communication.

•Jan 1, 2013•1 citation

Nondegenerate parametric oscillations in a tunable superconducting resonator

Andreas Bengtsson, Philip Krantz, Michaël Simoen +5 more

We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.

arXiv:1801.04566•Physical review. B./Physical review. B•Apr 4, 2018•18 citations
Parametric oscillations are well studied phenomena, with applications in amplification, quantum optics, and quantum information processing. They can occur as a parameter of a system, such as the resonant frequency, is being modulated or “pumped” by an external field. A nonlinearity of the system can then transfer power from the pumping frequency to two frequencies called signal and idler. When the signal falls within a resonance, and when the pump amplitude exceeds an instability threshold, parametric oscillations occur. When signal and idler fall within the same resonance, the pumping is called degenerate.Due to somewhat different implementations, in combination with rich nonlinear physics, the details of the parametric oscillations can differ in different systems. In this work, we expand on the research done on parametric oscillations using a superconducting microwave resonator with a tunable boundary condition. Previously, a degenerate Josephson parametric oscillator (JPO) has been demonstrated by modulation of this boundary condition at twice the resonator's resonant frequency. We further use the JPO to implement a novel read-out method for a superconducting qubit. Moreover, we demonstrate a different, nondegenerate regime of the JPO, which we denote the NJPO, by modulating the frequency at the sum of two resonant frequencies of a multimode resonator.Both the JPO qubit read-out and the NJPO have applications within quantum information processing. The perhaps most promising platform for quantum information processing is represented by the circuit-QED architecture with superconducting resonators and artificial atoms, where the two lowest atomic levels represent the qubit. We make these circuits using lithographic techniques, and control and measure them at low temperature using microwaves. The qubit's state is fragile and difficult to read out with high fidelity. To this end, we have developed a method based on the JPO, in which the qubit state is mapped onto a zero-amplitude or a large-amplitude state of the JPO. We achieved a large contrast (185±15 photons), therefore eliminating the need for a following quantum-limited parametric amplifier. Our readout fidelity was 81.5 %, and by carefully modeling we can distinguish fidelity loss from the qubit and the readout, respectively. This analysis displays an actual readout fidelity of 98.7 %.An alternative model for quantum computing is based on continuous variables, and uses harmonic oscillators instead of qubits. Entangled states, which can be used as quantum resources, can then be created, for example, by two-mode squeezing of the oscillator ground state. The state of the NJPO produces correlated oscillations in its two modes, which might be useful for continuous-variable quantum computing. In this work we fully characterize the classical properties of the NJPO, and show good quantitative agreement with a theoretical model.
Circuit quantum electrodynamics (cQED) is a prominent platform for quantum information processing, in which microwave photons are confined into resonant cavities coupled to superconducting quantum bits (qubits). The large effective dipole moment of the qubit, in combination with the high energy density of the quasi 1-D resonator allow these systems to enter the so-called strong coupling regime. The quantum state of the qubit can then be assessed by probing the frequency of the resonator, protecting the qubit from otherwise losing its energy to the environment. However, eventhough this so-called dispersive readout technique has proven useful, it is often in itself insufficient to render single-shot readout performance | one of the crucial tasks required for realizing a quantum computer. This thesis describes the demonstration of a single-shot readout technique forsuperconducting quantum bits, based on coupling the qubit to a frequency-tunable resonator. The backbone of our device is a 5 GHz quarter-wavelength coplanar waveguide resonator, terminated at one end by a non-linear inductance provided by a superconducting quantum interference device (SQUID). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using an on-chip transmission line. The modulation occurs on a timescale much faster than the photon loss out of the resonator and if the pump strength exceeds a threshold value set by the damping rate of the resonator, an intense photon field will build up inside the resonator | known as "parametric oscillations". By heterodyne detection of the output signal from the Josephson parametric oscillator (JPO), we first extracted two leading nonlinear effects of the system (dominating in different limits of applied magnetic flux). Next, we couple a qubit to the JPO and demonstrate that we can encode its quantum state onto the strong output field of the parametric oscillator (or lack thereof), rendering a signal-to-noise ratio sufficient for single-shot state detection and therefore also obviating a quantum limited parametric amplifier. The thesis also contains results from microscopic studies of the Josephson junctions, which we use to provide the necessary nonlinearities in the above mentioned devices. In particular, we show how the microstructure of the barrier layer and its atomic composition can be used to infer important electrical properties of the junctions. This knowledge allows us to better tailor the properties of Josephson-based devices.
The perhaps most promising platform for quantum information processing is the circuit-QED architecture based on superconducting circuits representing quantum bits. These circuits must be made with low losses so that the quantum information is retained for as long as possible. We developed fabrication processes achieving state-of-the-art coherence times of over 100 µs. We identified the primary source of loss to be parasitic two-level systems by studying fluctuations of qubit relaxation times.Using our high-coherence circuits, we implemented a quantum processor built on fixed-frequency qubits and frequency-tunable couplers. The tunable couplers were lumped-element LC resonators, where the inductance came from a superconducting quantum interference device (SQUID). We achieved a controlled-phase gate with a fidelity of 99% by parametric modulation of the coupler frequency. Using this device, and another similar to it, we demonstrated two different quantum algorithms, the quantum approximate optimization algorithm, and density matrix exponentiation. We achieved high algorithmic fidelities, aided by our carefully calibrated gates.Additionally, we researched parametric oscillations using frequency-tunable resonators. Previously, degenerate parametric oscillations have been demonstrated by modulation of the resonant frequency at twice that frequency. We use this phenomenon to implement a readout method for a superconducting qubit with a fidelity of 98.7%. We demonstrated correlated radiation in nondegenerate parametric oscillations by modulating at the sum of two resonant frequencies of a multimode resonator. We showed an excellent quantitative agreement between the classical properties of the oscillations with a theoretical model. Moreover, we studied higher-order modulation at up to five times their resonant frequencies. These types of parametric oscillation states might be used as a quantum resource for continuous-variable quantum computing.
We propose and demonstrate a read-out technique for a superconducting qubit by dispersively coupling it with a Josephson parametric oscillator. We employ a tunable quarter wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with 185±15 photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot read-out performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.
Josephson parametric amplifiers continue to attract attention for monitoring and readout of superconducting qubits in quantum information processing, as well as other applications. The authors continue their research on these systems, presenting a comprehensive study of nondegenerate amplifiers that addresses nonlinear gain, parametric instability, amplification processes (two- and four-mode linear processes plus nonlinear corrections, with signal-to-noise ratios for all cases), and frequency conversion. Quantum fluctuations and squeezing are considered as well.
In this licentiate thesis, I present the design, fabrication, and characterization of superconducting parametric resonators, for use in quantum information processing. These devices are quarter-wavelength coplanar waveguide resonators (~5 GHz), terminated at one end by a non-linear inductance provided by a SQUID (superconducting quantum interference device). The SQUID acts as a flux-controlled boundary condition, which effectively changes the electrical length of the resonator. This enables the modulation of the resonant frequency by coupling microwave magnetic flux into the SQUID, using on-chip transmission lines. The modulation occurs on a timescale much faster than the photon loss out of the resonator. The non-linearity provides several different regimes for operating this device. I focused on the parametric regime, in which the non-linear element was being modulated (pumped) at or near twice the resonant frequency. This pumping can lead to amplification and frequency conversion of an incoming signal. It can also give rise to instabilities and self-oscillations "parametric oscillations" - that is, the generation of an intense electric field in the resonator (the creation of photons). Parametric oscillations set in when the pumping strength exceeds a threshold value, and also depends on the pump-frequency detuning from twice the resonance and on the static flux through the SQUID. I characterized the devices over a wide parameter range by doing homodyne detection of the reflected signal or of the emitted field oscillations. In particular, I investigated the damping and two leading nonlinearities, dominating in different operating regimes, which influence the dynamics of the parametric resonator. First, I extracted the Duffing nonlinearity by studying the line width of the resonator as a function of the input signal (without pumping the SQUID). Second, with high pump amplitude, I extracted the pump-induced nonlinearity by determining the threshold parameters (pump amplitude and detuning) for the onset of parametric oscillations; this nonlinearity leads to the generation of higher-order pump terms that complicate the system dynamics, but can be mitigated now that they have been understood. My results validate a recent theoretical model for the classical, non-linear dynamics of parametric resonance, and helps determine workable design parameters. Finally, I helped develop a linearized model −-− the "pumpistor" - describing this device in terms of a flux-controlled impedance. This will be useful when designing more complex circuits. One goal of this work is to demonstrate single-shot measurements on superconducting qubits (quantum bits of information). We will use the parametric resonator as a threshold discriminator, associating the qubit's two energy eigenstates with the parametric oscillations either turning on or not. This would be a very useful device in the quantum engineer's toolbox when designing systems for quantum information processing and communication.
We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.