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

Creating directional quantum-limited amplification using multiple parametric drives

Tzu-Chiao Chien

Published Sep 16, 2020• 0 citations
OpenAlex

Abstract

One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.

Related papers

Harnessing Unconventional and Multiple Parametric Couplings for Superconducting Quantum Information

Olivia Lanes

Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation power, lack of directionality, and narrow bandwidth. The primary aim of this thesis is to attack these problems by using multiparametric drives. We will discuss an assortment of multiparametric pumping schemes, and in particular, present an amplifying scheme that is created by applying imbalanced, simultaneous, strong gain and conversion pump tones in a Josephson Parametric Converter. This mode of amplification features broadband gain in transmission that is 10X the bandwidth of a typical, single-pumped JPC amplifier and is matched in reflection up to -15 dB, making it only one scattering parameter away from the ideal quantum-limited amplifier. Since this amplifier is matched in reflection, we also explore the possibility of being able to chain these amplifiers to enhance the saturation power and work towards a fully directional amplifier. In addition, we discuss superconducting, thin-film van der Waals materials for use in superconducting circuits. We began by studying the nature of the contact made between 3D bulk aluminum and these 2D flakes, and discovered we could create truly superconducting contact at their interface. Next, we created a superconducting SQUID from two of these atypical junctions, and studied its quantum interference pattern. We were able to measure critical currents of 10-100's of $\mu$A, and also found that the effective area of both the junctions and the superconducting loop itself is much larger than their physical size due to the geometry of the flake. In addition, we studied the kinetic inductance of these flakes by placing them in NbTiN superconducting resonators, and found that the kinetic inductance we were measuring is around 2 orders of magnitude higher than what was predicted by theory. The thesis paves the way for using nontraditional elements and pumping schemes in superconducting circuits to create a new generation of devices for use in superconducting quantum information processes. In the future, hopefully, these fabrication techniques and experimental discoveries will bring the field closer to a fault tolerant, universal quantum computer.

•Sep 16, 2020•0 citations

Amplification paramétrique en résonance et à ondes progressives proche de la limite quantique

Luca Planat

A requirement for quantum information experiments using superconducting quantum circuits is the readout of extremely weak microwave signals. Quantum limited amplifiers are essential for such task and this is precisely why they occupy an always-growing importance in such experiments, particularly for superconducting quantum bits readout.In this thesis, we present two quantum limited amplifiers architectures: the first one is based on a resonator while the second one leverages a traveling-wave construction. These amplifiers both take advantage of tunable Josephson junctions (squid). It is the ideal component for quantum limited parametric amplification: it is both nonlinear and dissipationless (given its superconducting nature). This thesis demonstrates the operation of these Josephson quantum limited amplifiers and how they go beyond the state-of-the-art thanks to original design choices.An important limitation of resonant Josephson parametric amplifiers is their poor dynamic range. We identified the Kerr nonlinearity as the main cause, and we successfully managed to tailor it using Josephson junction arrays. We also developed a model in good agreement with the experimental data, therefore validating our initial assumption that the Kerr nonlinearity and saturation are linked. However, most of the resonant Josephson parametric amplifiers suffer from a fundamental issue, arising from their architecture. It is the conservation of the gain bandwidth product, therefore limiting their bandwidth. Traveling-wave architectures are well suited to overcome this limitation. However, two new issues must be dealt with: impedance matching and phase matching. To tackle the former, we developed an original and simple fabrication process in order to obtain a 50ohm matched 2000 squid array. As for the phase, we matched it by periodically modulating the impedance of the squid transmission line in order to open a photonic band gap. Therefore, we locally distort the dispersion relation. This step does not add any complexity to the initial fabrication process. Moreover, we developed a model in good agreement with experimental data while considering the nonlinear behavior of the photonic gap in a Josephson metamaterial. In addition to demonstrating high performance amplifiers poised for numerous quantum technological applications, this thesis opens the door to more fundamental quantum optics experiments taking advantage of these highly nonlinear transmission lines.With the resonant amplifiers, we measured a 1dB compression point around -117dBm and 45MHz bandwidth (at 20 db gain). With the traveling-wave amplifiers, we measured 18dB gain on a 2.25GHz bandwidth, a 1dB compression point reaching -103dBm and near quantum-limited noise performances.

•Jun 22, 2020•0 citations

A Traveling Wave Parametric Amplifier Isolator

Arpit Ranadive, Bekim Fazliji, Gwenael Le Gal +8 more

Superconducting traveling-wave parametric amplifiers have emerged as highly promising devices for near-quantum-limited broadband amplification of microwave signals and are essential for high quantum-efficiency microwave readout lines. Built-in isolation, as well as gain, would address their primary limitation: lack of true directionality due to potential backward travel of electromagnetic radiation to their input port. Here, we demonstrate a Josephson-junction-based traveling-wave parametric amplifier isolator. It utilizes third-order nonlinearity for amplification and second-order nonlinearity for frequency upconversion of backward propagating modes to provide reverse isolation. These parametric processes, enhanced by a novel phase matching mechanism, exhibit gain of up to 20~dB and reverse isolation of up to 30~dB over a static 3~dB bandwidth greater than 500~MHz, while keeping near-quantum limited added noise. This demonstration of a broadband truly directional amplifier ultimately paves the way towards broadband quantum-limited microwave amplification lines without bulky magnetic isolators and with inhibited back-action.

arXiv:2406.19752•Jun 28, 2024•2 citations

Quantum Measurement and Bath Engineering for Superconducting Qubits via Multiple Parametric Couplings

Xi Cao

Quantum computers have huge potential applications, but do not currently exist. It has already been proven that a quantum computer would outperform the best classical supercomputers in certain problems, some of which have vital connections with our daily lives. For example, quantum computers efficiently solve the prime number factoring problem, which in turn is the foundation of the RSA algorithm behind most online transactions. There is a great deal of current effort to implement quantum computers, and we have seen good progress in platforms including superconducting circuits, ion traps, and photons in cavity QED systems and spins in semiconductors. These machines include up to roughly 50 quantum bits at present, but they are not very useful as quantum errors quickly decohere the computer's state and prevent computation. These errors can be mitigated via quantum error correction at the cost of additional size and complexity. Progress in the field towards error corrected, large-scale quantum machines requires us to require new tools for controlling, coupling, and reading out qubits. In this thesis, I will focus on such explorations in superconducting circuits. In this thesis, we seek to expand the already flexible toolkit of quantum circuits by exploring the uses of parametric couplings based on third-order nonlinearities. This type of nonlinearities has only been used in quantum-limited amplifiers before, here we try to further explore their applications by creating new methods for controlling and measuring qubits that based on it. In the first experiment, we address the problem of implementing a highly efficient quantum non-demolition qubit readout. With the use of two-mode squeezed (TMS) light and combined with phase-preserving parametric amplifiers into an interferometer for dispersive qubit readout, we demonstrate a measurement scheme with a 44$\%$ improvement in power signal-to-noise ratio. We also investigate the back-action of the measurement scheme. In the second experiment, we create an effective chemical potential for photons with parametric system-bath coupling. In particular, we use a lossy Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) as both the bath and coupler. The bath engineering is realized by combining the multiple parametric drives and the dissipation together.

•May 3, 2021•0 citations

Optimizing Josephson-ring-modulator-based Josephson parametric amplifiers via full Hamiltonian control

Chenxu Liu, Tzu-Chiao Chien, Michael Hatridge +1 more

Josephson parametric amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate near the quantum limit, their gain saturates for very small (few-photon) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the fourth-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enables amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson ring modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by $\ensuremath{\approx}15\phantom{\rule{0.16em}{0ex}}\mathrm{dB}$. Finally, we argue that our methods and qualitative results are applicable to a broad range of cavity-based JPAs.

arXiv:1911.11176•Physical Review A•Apr 21, 2020•22 citations

Graphene-based superconducting quantum circuits : the Josephson parametric amplifier

Guilliam Butseraen

With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.

•Nov 8, 2022•0 citations
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation power, lack of directionality, and narrow bandwidth. The primary aim of this thesis is to attack these problems by using multiparametric drives. We will discuss an assortment of multiparametric pumping schemes, and in particular, present an amplifying scheme that is created by applying imbalanced, simultaneous, strong gain and conversion pump tones in a Josephson Parametric Converter. This mode of amplification features broadband gain in transmission that is 10X the bandwidth of a typical, single-pumped JPC amplifier and is matched in reflection up to -15 dB, making it only one scattering parameter away from the ideal quantum-limited amplifier. Since this amplifier is matched in reflection, we also explore the possibility of being able to chain these amplifiers to enhance the saturation power and work towards a fully directional amplifier. In addition, we discuss superconducting, thin-film van der Waals materials for use in superconducting circuits. We began by studying the nature of the contact made between 3D bulk aluminum and these 2D flakes, and discovered we could create truly superconducting contact at their interface. Next, we created a superconducting SQUID from two of these atypical junctions, and studied its quantum interference pattern. We were able to measure critical currents of 10-100's of μ\muμA, and also found that the effective area of both the junctions and the superconducting loop itself is much larger than their physical size due to the geometry of the flake. In addition, we studied the kinetic inductance of these flakes by placing them in NbTiN superconducting resonators, and found that the kinetic inductance we were measuring is around 2 orders of magnitude higher than what was predicted by theory. The thesis paves the way for using nontraditional elements and pumping schemes in superconducting circuits to create a new generation of devices for use in superconducting quantum information processes. In the future, hopefully, these fabrication techniques and experimental discoveries will bring the field closer to a fault tolerant, universal quantum computer.
A requirement for quantum information experiments using superconducting quantum circuits is the readout of extremely weak microwave signals. Quantum limited amplifiers are essential for such task and this is precisely why they occupy an always-growing importance in such experiments, particularly for superconducting quantum bits readout.In this thesis, we present two quantum limited amplifiers architectures: the first one is based on a resonator while the second one leverages a traveling-wave construction. These amplifiers both take advantage of tunable Josephson junctions (squid). It is the ideal component for quantum limited parametric amplification: it is both nonlinear and dissipationless (given its superconducting nature). This thesis demonstrates the operation of these Josephson quantum limited amplifiers and how they go beyond the state-of-the-art thanks to original design choices.An important limitation of resonant Josephson parametric amplifiers is their poor dynamic range. We identified the Kerr nonlinearity as the main cause, and we successfully managed to tailor it using Josephson junction arrays. We also developed a model in good agreement with the experimental data, therefore validating our initial assumption that the Kerr nonlinearity and saturation are linked. However, most of the resonant Josephson parametric amplifiers suffer from a fundamental issue, arising from their architecture. It is the conservation of the gain bandwidth product, therefore limiting their bandwidth. Traveling-wave architectures are well suited to overcome this limitation. However, two new issues must be dealt with: impedance matching and phase matching. To tackle the former, we developed an original and simple fabrication process in order to obtain a 50ohm matched 2000 squid array. As for the phase, we matched it by periodically modulating the impedance of the squid transmission line in order to open a photonic band gap. Therefore, we locally distort the dispersion relation. This step does not add any complexity to the initial fabrication process. Moreover, we developed a model in good agreement with experimental data while considering the nonlinear behavior of the photonic gap in a Josephson metamaterial. In addition to demonstrating high performance amplifiers poised for numerous quantum technological applications, this thesis opens the door to more fundamental quantum optics experiments taking advantage of these highly nonlinear transmission lines.With the resonant amplifiers, we measured a 1dB compression point around -117dBm and 45MHz bandwidth (at 20 db gain). With the traveling-wave amplifiers, we measured 18dB gain on a 2.25GHz bandwidth, a 1dB compression point reaching -103dBm and near quantum-limited noise performances.
Superconducting traveling-wave parametric amplifiers have emerged as highly promising devices for near-quantum-limited broadband amplification of microwave signals and are essential for high quantum-efficiency microwave readout lines. Built-in isolation, as well as gain, would address their primary limitation: lack of true directionality due to potential backward travel of electromagnetic radiation to their input port. Here, we demonstrate a Josephson-junction-based traveling-wave parametric amplifier isolator. It utilizes third-order nonlinearity for amplification and second-order nonlinearity for frequency upconversion of backward propagating modes to provide reverse isolation. These parametric processes, enhanced by a novel phase matching mechanism, exhibit gain of up to 20~dB and reverse isolation of up to 30~dB over a static 3~dB bandwidth greater than 500~MHz, while keeping near-quantum limited added noise. This demonstration of a broadband truly directional amplifier ultimately paves the way towards broadband quantum-limited microwave amplification lines without bulky magnetic isolators and with inhibited back-action.
Quantum computers have huge potential applications, but do not currently exist. It has already been proven that a quantum computer would outperform the best classical supercomputers in certain problems, some of which have vital connections with our daily lives. For example, quantum computers efficiently solve the prime number factoring problem, which in turn is the foundation of the RSA algorithm behind most online transactions. There is a great deal of current effort to implement quantum computers, and we have seen good progress in platforms including superconducting circuits, ion traps, and photons in cavity QED systems and spins in semiconductors. These machines include up to roughly 50 quantum bits at present, but they are not very useful as quantum errors quickly decohere the computer's state and prevent computation. These errors can be mitigated via quantum error correction at the cost of additional size and complexity. Progress in the field towards error corrected, large-scale quantum machines requires us to require new tools for controlling, coupling, and reading out qubits. In this thesis, I will focus on such explorations in superconducting circuits. In this thesis, we seek to expand the already flexible toolkit of quantum circuits by exploring the uses of parametric couplings based on third-order nonlinearities. This type of nonlinearities has only been used in quantum-limited amplifiers before, here we try to further explore their applications by creating new methods for controlling and measuring qubits that based on it. In the first experiment, we address the problem of implementing a highly efficient quantum non-demolition qubit readout. With the use of two-mode squeezed (TMS) light and combined with phase-preserving parametric amplifiers into an interferometer for dispersive qubit readout, we demonstrate a measurement scheme with a 44%\%% improvement in power signal-to-noise ratio. We also investigate the back-action of the measurement scheme. In the second experiment, we create an effective chemical potential for photons with parametric system-bath coupling. In particular, we use a lossy Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL) as both the bath and coupler. The bath engineering is realized by combining the multiple parametric drives and the dissipation together.
Josephson parametric amplifiers (JPA) are nonlinear devices that are used for quantum sensing and qubit readout in the microwave regime. While JPAs regularly operate near the quantum limit, their gain saturates for very small (few-photon) input power. In a previous work, we showed that the saturation power of JPAs is not limited by pump depletion, but instead by the fourth-order nonlinearity of Josephson junctions, the nonlinear circuit elements that enables amplification in JPAs. Here, we present a systematic study of the nonlinearities in JPAs, show which nonlinearities limit the saturation power, and present a strategy for optimizing the circuit parameters for achieving the best possible JPA. For concreteness, we focus on JPAs that are constructed around a Josephson ring modulator (JRM). We show that by tuning the external and shunt inductors, we should be able to take the best experimentally available JPAs and improve their saturation power by $\ensuremath{\approx}15\phantom{\rule{0.16em}{0ex}}\mathrm{dB}$. Finally, we argue that our methods and qualitative results are applicable to a broad range of cavity-based JPAs.
With a large portfolio of elemental quantum components, superconducting quantum circuits have contributed to dramatic advances in microwave quantum optics. Of these elements, quantum-limited parametric amplifiers have proven to be essential for low noise readout of quantum systems whose energy range is intrinsically low (tens of µeV). They are also used to generate non classical states of light that can be a resource for quantum enhanced detection. Superconducting parametric amplifiers, like quantum bits, typically utilize a Josephson junction as a source of magnetically tunable and dissipation-free nonlinearity. The magnetic control is not an industry standard for devices and starts already to be an issue in large scale circuits. In recent years, efforts have been made to introduce semiconductor weak links as electrically tunable nonlinear elements, with demonstrations of microwave resonators and quantum bits using semiconductor nanowires, a two dimensional electron gas, carbon nanotubes and graphene. However, given the challenge of balancing nonlinearity, dissipation, participation, and energy scale, parametric amplifiers have not yet been implemented with a semiconductor weak link. The work presented in this PhD thesis demonstrates the design, fabrication and performances of a parametric amplifier leveraging a graphene Josephson junction.The graphene is encapsulated in between hBN flakes in order to improve its quality. Using such high quality junctions, we demonstrate amplification with 20 dB gain which is the milestone for overcoming noise of the classical amplifiers in the rest of the amplification chain. The Josephson parametric amplifier being based on a resonant structure (around 6 GHz) suffers from the gain bandwidth product limiting the amplification to a few MegaHertz frequency range. The use of a side gate to electrically tune the graphene gives control of the Josephson junction inductance and thus the resonant frequency of the amplifier. We demonstrate a near 1 GHz tunability of the amplification frequency with the use of a side gate which is as good as the tunability offered by using a magnetic flux on a SQUID for similar amplifier designs. Moreover, graphene has shown to exhibit nonlinear loss under a strong microwave irradiation arising because of dynamics in the Andreev states. Dissipation is known to add intrinsic noise on quantum amplifiers and could be a problem for quantum limited parametric amplification. We demonstrate that despite the presence of nonlinear loss, graphene based Josephson parametric amplifiers can reach near quantum limited amplification. A two photon loss model was used to describe the behaviour of the device but we show that a more complex model is required in order to take into account the nonlinear dissipation and the non-sinusoidal current phase relation. We also studied the dynamic range and showed that the graphene based Josephson parametric amplifier can reach a 1 dB compression point of -123 dBm which is as good as single tunnel junctions based parametric amplifiers. Our results expand the toolset for electrically tunable superconducting quantum circuits and offer new opportunities for the development of quantum technologies such as quantum computing, quantum sensing and fundamental science.