The performance of quantum computing readout chains is largely determined by their initial amplifier stage, demanding innovations in sensitivity and efficiency. Researchers have now developed a radio frequency parametric amplifier based on modulating the quantum capacitance of an ultrahigh mobility two-dimensional electron gas, offering a potential alternative to existing superconducting and semiconductor designs. These amplifiers use the fluctuation-dissipation theorem, focusing on superconductivity to achieve minimal noise levels. This new approach addresses limitations of current amplifiers, including restricted frequency operation and difficulty functioning in magnetic fields, while potentially bridging the gap between superconducting and semiconductor technologies.

Quantum Capacitance Amplification for Weak RF Signals

A variable quantum capacitance, achieved over a 10 millivolt range, forms the core of a new radio frequency parametric amplifier designed to boost weak signals critical for applications like quantum computing and radio astronomy. This capacitance, modulated by controlling electron density within a two-dimensional electron gas formed in a gallium arsenide/aluminum gallium arsenide heterostructure, acts as the bottom plate of a capacitor with a niobium titanium nitride gate layer as the top plate.

The resulting device, termed a Quantum Capacitance Parametric Amplifier or QCPA, demonstrates gain through an increase in reflected signal power when activated, compared to an idle state with a direct current gate bias. The amplifier’s effectiveness stems from its ability to use a linear dependence between the active capacitance and applied voltage, facilitating the mixing of pump, idler and source signals to achieve amplification.

This approach differs from existing superconducting amplifiers, which rely on superconducting quantum interference devices, bistable junctions, or other parametric methods, each facing limitations in frequency operation, input power handling, or susceptibility to magnetic fields. The QCPA’s design focuses on minimizing dissipation by using superconductivity, guided by the fluctuation-dissipation theorem which suggests that nondissipative devices offer the lowest noise levels. Beyond the specific materials used, GaAs/AlGaAs and NbTiN, the principle of modulating quantum capacitance offers potential for broader implementation.

Silicon MOS structures, silicon-germanium heterostructures, van der Waals heterostructures, and graphene all represent potential materials for building similar devices. The QCPA’s design is particularly well-suited for integration with existing qubit platforms that already use the dispersive response of radio frequency resonators for readout, potentially enabling in situ amplification directly within those systems. Because the first-stage amplifier in a quantum computing readout chain largely dominates the performance of the entire readout subsystem, even modest improvements in this area can yield disproportionate gains in overall platform performance.

GaAs/AlGaAs Heterostructure Enables QCPA Operation

Using a heterostructure grown with molecular beam epitaxy, the design of the quantum capacitance parametric amplifier (QCPA) enables a low-loss quantum capacitance important for amplifying weak radio frequency signals. This approach differs from kinetic inductance-based superconducting amplifiers, which require significantly larger areas, and avoids the increased noise and power dissipation inherent in semiconductor amplifiers like those using high electron mobility transistors. The QCPA’s variable quantum capacitance arises from a two-dimensional electron gas (2DEG) formed 91 nanometers beneath the surface of the GaAs/AlGaAs heterostructure, functioning as one plate of a capacitor.

A 200-nanometer layer of niobium titanium nitride is the opposing gate, completing the capacitive element, while a dc block capacitance in series with a 22 nanohenry inductance prevents signal shorting. At the QCPA’s operating frequency, this configuration slightly reduces the inductance to 21.3 nanohenry, maintaining a low impedance path above 100 MHz.

The inductive branch participates at a rate of 51.367%, contributing to a quality factor for the GaAs/AlGaAs nonlinear device, which represents the dominant loss mechanism within the QCPA circuit. Measurements demonstrate that increasing the cryostat temperature from 30 millikelvin to 4 Kelvin reduces maximum gain for a given pump power. But this reduction can be offset by increasing the pump power itself.

While higher pump power increases dissipation, the cryostat’s cooling capacity also increases at higher temperatures, offering a pathway to sustained performance. “The gain can be recovered, however, by increasing the pump power at elevated temperatures,” the researchers report, highlighting a key advantage for practical quantum computing applications.

Modulation of 2DEG Density Generates Parametric Gain

Modulating the density of a two-dimensional electron gas generates parametric gain through oscillating quantum capacitance, a principle recently demonstrated in a radio frequency amplifier designed for quantum computing readout chains. Unlike previous parametric gain demonstrations relying on quantum dots and electron tunneling, this amplifier uses ballistic transport within 2D heterostructures to achieve a significantly larger modulated quantum capacitance relative to the total capacitance.

Measurements reveal the amplifier’s gain varies predictably with frequency, aligning with theoretical models of parametric operation. This performance is achieved through a circuit design incorporating a coupling capacitor and choke inductor forming a bias tee on a printed circuit board, effectively creating a parallel tank parametric amplifier.

The team introduced a factor into their expression to account for a slight discrepancy between theoretical predictions and experimental data, refining the model to better fit observed results. Further analysis reveals that the amplifier’s gain in the degenerate case, where the frequencies of the idler and source tones converge, can exceed the maximum center-frequency gain of a non-degenerate amplifier for the same circuit. This occurs as the negative conductance increases with pump amplitude, eventually offsetting tank losses and inducing an oscillatory mode within the amplifier. “It is worth noting that the gain in Eq.

QCPA Performance: Gain, Bandwidth, and Noise Temperature

The amplifier’s gain scales linearly with frequency, described by the equation (2) where represents the maximum nondegenerate gain frequency and defines the bandwidth. Detailed calculations supporting this gain expression are available in the accompanying Appendix. Analyzing the circuit’s loss budget is key, directly influencing both the design process and the amplifier’s ultimate performance; the quality factor of components at the resonance frequency is a key consideration in this analysis.

A cryogenic switch was integrated into the experimental setup to normalize the amplifier’s noise response against an open circuit, allowing for precise measurement of the integrated noise power at the readout port. Determining the system’s noise temperature involved a Y-factor method, revealing a value of with the QCPA operating at a specific gain level.

Correcting for circuit losses, researchers estimate the intrinsic noise temperature of the QCPA to be, a figure obtained through careful calibration and spectral analysis using a Keysight N9030B spectrum analyzer. This detailed measurement process allowed the team to investigate how attenuation affects the overall system noise temperature, a factor linked to the characteristic noise temperature of lossy components and their physical temperature. The output noise temperature of the entire system is expressed in equation (B2). The total system gain is defined as leading to an equation (B3) for the system noise temperature.

While a minor correction was observed due to, a more significant effect was the multiplication of the QCPA’s noise temperature by losses in the preceding circuit, increasing the system noise temperature by a factor of 2.52. The derivation of the QCPA gain expression, detailed in Appendix C builds upon previous work documented in Ref., considering the parallel tank circuit and its impact on performance.

QCPA Design: NbTiN Gate and Circuit Components

Analysis transforms the QCPA into a parallel tank circuit, allowing for detailed gain assessment and revealing a linear gain-bandwidth relationship. The device requires pump power amplitudes of approximately 10 millivolts applied to the gate, a necessity that guides the overall system architecture. Measurements of the reflection coefficient as a function of frequency conducted at low source power demonstrate a shift in resonance frequency as the gate voltage becomes more negative, indicating a tunable capacitance determined from the resonance frequency using a simplified tank circuit model.

The variable capacitance of the active device exhibits a change over a 10 millivolt voltage range, a substantial modulation essential for three-wave mixing. To maximize the linearity of the capacitance-voltage curve, the gate layout incorporates an extensive perimeter, enhancing the mixing of the pump with both the idler and source signals, and thus, their amplification.

The QCPA circuit itself is fixed to a printed circuit board using silver paste, bonding the device to the circuit and forming the amplifier tank, with the ground plane of the active device connected to the PCB’s ground plane. The tank inductance is provided by an air-core spring inductor in series with a capacitance to ground.

QCPA Integration Improves Quantum Dot Readout SNR

Including the contribution from the idler signal doubles this noise temperature to, while subtracting the idler results in a lower value of 1. 3 K. This detailed analysis provides a baseline for comparison with measurements obtained by directly reading out a quantum dot device, offering a cross-validation of the amplifier’s performance characteristics. Integrating the QCPA as the first-stage low-noise amplifier (LNA) in a double quantum dot readout experiment demonstrably improves signal-to-noise ratio (SNR).

Data collected with the QCPA turned off and on show a clear difference in charge state resolution, with the amplifier enhancing the visibility of distinct quantum states. Specifically, statistical distributions of the readout signals for labeled charge states exhibit greater separation when the QCPA is active, indicating a more reliable and accurate measurement. The experiment used a radio frequency quantum point contact (rf-QPC) to perform the readout, matching its resonance frequency to the QCPA’s gain peak.

The use of the QCPA improves the SNR of charge-state readout by approximately 9 dB, a substantial gain considering the amplifier’s negligible dissipation when switched off. Researchers found the SNR obtained in the QCPA OFF state was comparable to that of an open-circuit rf standard, confirming minimal interference from the device itself.

“Using the QCPA as a first-stage amplifier improves the SNR by approximately 9 dB,” the team reports, highlighting the amplifier’s impact on readout fidelity. A small discrepancy in noise temperature between the QCPA and the Y-factor measurement setup is attributed to differences in thermalization between the quantum dot and the measurement apparatus, a point for future refinement.

Comparison of QCPA to Josephson and HEMT Amplifiers

The newly developed quantum capacitance parametric amplifier (QCPA) demonstrates a noise temperature comparable to high electron mobility transistor (HEMT) amplifiers, achieving approximately 2 K in initial testing, but with fundamentally different operating characteristics. Unlike HEMTs, which are limited by self-heating in the milliwatt range, the QCPA operates at millikelvin temperatures with microwatt power dissipation, suggesting potential for even lower noise levels through improved thermalization and reduction of ohmic losses within its components.

This difference in power consumption and thermal behavior represents a key advantage for integration into sensitive quantum readout systems. A detailed comparison with other cryogenic amplifiers, including Josephson junction and varactor parametric amplifiers, reveals the QCPA’s strengths and weaknesses across several key specifications, as summarized in a table accompanying the research. The QCPA achieves a gain of 20-30 dB and operates across a broad frequency range of 100s of MHz, though its bandwidth is limited to 1-2 MHz.

The table also highlights the QCPA’s high linearity and compatibility with magnetic fields, features not consistently found in all competing technologies. The QCPA’s performance was further validated through integration with a quantum dot device at 20 mK, where it demonstrably improved the signal-to-noise ratio (SNR) by approximately 9 dB when pump power was applied. Researchers note that resistive losses, largely temperature-independent below 4 K, may contribute to a reduction in gain at lower temperatures, potentially due to decreased transconductance.

Ballistic Transport Regime Reduces Dissipation in QCPA

The ability to minimize dissipation is central to the performance of quantum capacitance parametric amplifiers, or QCPAs, as carrier mean free paths exceeding 100 microns are now routinely achieved in 2D heterostructures operating in the ballistic transport regime. This suppression of dissipation allows the QCPA to function as a dual to superconducting parametric amplifiers, offering a distinct advantage over traditional semiconductor approaches reliant on cryo-cooled transistors. This capability is particularly significant for integration with spin qubits, as it expands the operational range beyond the extremely low temperatures typically required for superconducting devices.

👉 More information
🗞 rf quantum capacitance parametric amplifier
✍️ A. El Kass et al.
🧠 DOI: http://link.aps.org/doi/10.1103/3146-fgdw

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