DC-powered broadband quantum-limited microwave amplifier

TL;DR

This work introduces a DC-powered, broadband quantum-limited microwave amplifier based on an impedance-engineered Inelastic Cooper-pair Tunneling Amplifier (ICTA). By biasing a voltage-driven SQUID and transforming its input impedance, the device delivers about $13$ dB of gain across a $3.5$ GHz bandwidth with added noise below $0.2$ photons, eliminating the need for pump tones. Semiclassical simulations accurately predict gain and saturation, guiding design adjustments and enabling scalable, multi-channel quantum-limited amplification for superconducting qubit readout. The approach promises significantly reduced hardware complexity while maintaining quantum-limited performance, making it attractive for large-scale quantum processors.

Abstract

Fast, high-fidelity, single-shot readout of superconducting qubits in quantum processors demands quantum-limited amplifiers to preserve the optimal signal-to-noise ratio. Typically, quantum-limited amplification is achieved with parametric down-conversion of a strong pump tone, which imposes significant hardware overhead and severely limits scalability. Here, we demonstrate the first DC-powered broadband amplifier operating within 0.2 photons of the quantum limit. Our impedance-engineered Inelastic Cooper-pair Tunneling Amplifier (ICTA)-a voltage-biased SQUID in which Cooper pairs tunnel inelastically by emitting signal-idler photon pairs-operates in reflection, delivering 13 dB of average gain across a 3.5 GHz bandwidth in a single stage. Semiclassical simulations accurately predict the gain and saturation power, enabling further design improvements. By eliminating the pump-tone infrastructure, the broadband ICTA promises to dramatically reduce the hardware complexity of quantum-limited amplification in superconducting quantum processors.

Figures (6)

• Figure 1: Impedance-Transformed ICTA.(a) Left: Single-resonator ICTA, featuring a lumped-element LC resonator (orange) in series with a SQUID loop (yellow). A DC source (turquoise) biases the SQUID through the inductor of the $LC$ resonator, while a large capacitor (magenta) shunts the resonator to ground at RF frequencies. An on-chip flux bias line (purple) enables tuning of the SQUID’s critical current. Right: An impedance transformed negative resistance amplifier (NRA) based on a second-order resonator-network. (b) Circuit diagram of an impedance-engineered ICTA combining single-Resonator ICTA with a second order network employing a lumped-element series $LC$ resonator paired with a $\lambda/4$ coplanar waveguide (CPW) resonator to transform the ICTA's input impedance for broadband amplification. (c) Circuit impedance seen by the Josephson junctions of the SQUID for the optimized design parameters. (d) Zoomed-in grayscale optical microscope image of the device, excluding the $\lambda/4$ CPW resonator of the impedance inverter. All elements are color-coded as in the circuit diagram, light gray denotes two niobium layers (ground plane), darker gray denotes a silicon nitride layer atop a single niobium base, and black denotes the absence of niobium layers.
• Figure 2: Semiclassical simulations of impedance transformed ICTA(a) Gain characteristics as a function of signal frequency, $f_{\text{s}}$, and voltage bias, $f_{\text{dc}}$, at $I_{\text{c}} =200nA$. High gain (blue) is achieved in a parallelogram-shaped region where the circuit impedance seen by the SQUID (see Fig. \ref{['fig:fig1']}(c)) is high at both signal frequency $f_\text{s}$ and idler frequency $f_\text{i} = f_\text{dc} - f_\text{s}$. The sharp lines are due to the AC Josephson effect (slope 1) and degenerate parametric amplification (slope 2). (b) Simulated gain and input-referred 1dB compression point of the ICTA biased at ($f_{\text{dc}} = 12GHz$, $I_{\text{c}} = 280nA$), as a function of signal frequency.
• Figure 3: Simulations and experimental performance of the ICTA.(a) Simulated gain of the impedance-transformed ICTA, including realistic impedance mismatches in the cables connecting the amplifier and circulator (cable length: $330mm$ @ $1/\sqrt{2}$ relative phase velocity, $55Ω$ impedance). (b) Simulated gain for a $100mm$ cable at $I_{\text{c}} = 280nA$, near the design $f_{\text{dc}} = 12GHz$, used to identify voltage bias points that minimize gain ripples. The dashed light brown line at $12.6GHz$ marks an optimal bias where standing waves in signal and idler modes cancel, yielding minimal ripple. Red patches indicate regions where the simulation did not converge. (c) Experimental 2D gain map at relatively low $I_{\text{c}}$ ($\Phi_\text{ext} = 0.34\Phi_0$) with $\sim 330mm$ of transmission line between circulator and amplifier. The data shows good qualitative agreement with the simulation in (a). (d) Experimental gain color plot with a $\sim 100mm$ transmission line at higher $I_{\text{c}}$ ($\Phi_\text{ext} = 0.32\Phi_0$) in qualitative agreement with the simulation in (b). (e) Amplifier performance at $f_{\text{dc}} = 12.25GHz$ (dashed line in (d)): gain (left axis) and added noise above the standard quantum limit (right axis) for the same $I_{\text{c}}$ as in panel (d) ($\Phi_\text{ext} = 0.32\Phi_0$, solid, dark) and higher $I_{\text{c}}$ ($\Phi_\text{ext} = 0.29\Phi_0$, dashed, light). (f) Input-referred 1dB compression point versus frequency at same conditions as dark lines in panel (e) ($\Phi_\text{ext} = 0.32\Phi_0$). The dashed green line and greyed region near $6.125GHz$ represent the degenerate bias point, where injection locking leads to high uncertainty of saturation power.
• Figure S1: Wiring Diagram. Schematic of the cryogenic microwave measurement setup for the impedance-transformed ICTA in the 4--8 GHz band. The input line (red) is heavily attenuated at multiple temperature stages and routed to the device via a cryogenic circulator and a six-port switch. The output chain (blue) includes two isolators, a bandpass filter, a 4 K HEMT amplifier, and room-temperature amplification before single-heterodyne downconversion. Two 50Ω terminations anchored to the mixing chamber and still plate (light green) enable Y-factor noise calibration at the switch reference plane. DC/flux bias lines are heavily filtered at the base temperature.
• Figure S2: Spontaneous photon emission at the Josephson frequency.(a) Power spectral density (PSD) as a function of flux-tuned critical current $I_\text{c}$ (x-axis, in units of $\Phi_0$) and emission frequency (y-axis, in GHz), measured at a fixed junction bias voltage corresponding to $f_\text{dc} = 12.261GHz$. Strong emission occurs exactly at $f_\text{dc}$ when the amplifier is biased for high gain. (b) Photon emission power integrated from $\SIrange{11.5}{12.5}{\giga\hertz}$, for five different Josephson frequencies plotted versus $I_\text{c}$. Left axis: power referred to the switch output (dBm); right axis: equivalent photon rate (photons/s). The optimal operating point, marked by the yellow star, corresponds to $\Phi_\text{ext} \approx 0.32\,\Phi_0$