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IEEE Journal of Solid-State Circuits

Cryo-CMOS Dual-Qubit Homodyne Reflectometer Array With Degenerate Parametric Amplification

Yujie Geng, Haichuan Lin, Bo Wang, Cheng Wang

Published Jul 30, 2024• 6 citations
Publisher

Abstract

In quantum computers, the quantum state discrimination of the physical quantum bits (Qubits) occupies ~80% of the quantum error correction (QEC) cycle. The RF reflectometry or dispersive readout determines the Qubit state by monitoring the RF reflection of the attached high-Q resonant tank. Compared to their dc counterparts, the RF reflectometers enjoy a high signal-to-noise ratio (SNR), low drifting, and fast speed. As a result, a high-fidelity, single-shot, scalable reflectometer array based on cryogenic CMOS (Cryo-CMOS) ICs is in demand for the future large-scale Qubit array ($10^{3} {\sim } 10^{6}$Qubits). However, the classic Cryo-CMOS heterodyne reflectometers, consisting of MOSFET-based LNA, mixer, and baseband blocks, suffer from high noise temperature and dc power. To address these issues, the Cryo-CMOS parametric circuitry based on varactors is explored. In this article, a dual-Qubit homodyne reflectometer array with 2 RX channels and 1 TX channel is demonstrated. In the RX, the degenerate parametric amplifier (DPA) enjoys a Q-enhanced,$\lambda _{\mathrm { RF}}/2$differential-mode (DM) resonator for the high-gain parametric amplification. The common mode (CM) RF input of DPA interacts with the DM resonator by a nonreciprocal, dynamic mode coupling (DMC). It eliminates the necessity of a circulator and the potential oscillation of DPA. The scalability challenge of the DPA’s noise temperature$T_{\mathrm { noise}}$versus the environment temperature$T_{\mathrm { env}}$is also investigated. In the TX, a current-mode logic (CML) divider with interstate locking and a vector modulator (VM) is implemented to achieve fast modulation for the spur and noise rejection. Measured at 4.2 K, the implemented 65 nm Cryo-CMOS chip presents a$4.5{\sim }7$GHz bandwidth, 52 dB peak RF gain, and 78 K noise temperature, and generates a 10 MHz TX pulse train with -22 dBm RF power and 30 dB tunability. It consumes a total dc power of 33 mW.

DOI
10.1109/jssc.2024.3430079

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In quantum computers, the quantum state discrimination of the physical quantum bits (Qubits) occupies ~80% of the quantum error correction (QEC) cycle. The RF reflectometry or dispersive readout determines the Qubit state by monitoring the RF reflection of the attached high-Q resonant tank. Compared to their dc counterparts, the RF reflectometers enjoy a high signal-to-noise ratio (SNR), low drifting, and fast speed. As a result, a high-fidelity, single-shot, scalable reflectometer array based on cryogenic CMOS (Cryo-CMOS) ICs is in demand for the future large-scale Qubit array (103∼10610^{3} {\sim } 10^{6}103∼106Qubits). However, the classic Cryo-CMOS heterodyne reflectometers, consisting of MOSFET-based LNA, mixer, and baseband blocks, suffer from high noise temperature and dc power. To address these issues, the Cryo-CMOS parametric circuitry based on varactors is explored. In this article, a dual-Qubit homodyne reflectometer array with 2 RX channels and 1 TX channel is demonstrated. In the RX, the degenerate parametric amplifier (DPA) enjoys a Q-enhanced,λRF/2\lambda _{\mathrm { RF}}/2λRF​/2differential-mode (DM) resonator for the high-gain parametric amplification. The common mode (CM) RF input of DPA interacts with the DM resonator by a nonreciprocal, dynamic mode coupling (DMC). It eliminates the necessity of a circulator and the potential oscillation of DPA. The scalability challenge of the DPA’s noise temperatureTnoiseT_{\mathrm { noise}}Tnoise​versus the environment temperatureTenvT_{\mathrm { env}}Tenv​is also investigated. In the TX, a current-mode logic (CML) divider with interstate locking and a vector modulator (VM) is implemented to achieve fast modulation for the spur and noise rejection. Measured at 4.2 K, the implemented 65 nm Cryo-CMOS chip presents a4.5∼74.5{\sim }74.5∼7GHz bandwidth, 52 dB peak RF gain, and 78 K noise temperature, and generates a 10 MHz TX pulse train with -22 dBm RF power and 30 dB tunability. It consumes a total dc power of 33 mW.
Error-corrected quantum computing does not only require large-scale (106–109) physical Qubit arrays but also relies on high-fidelity, scalable quantum-to-classic interface electronics. Quantum control and readout systems based on cryogenic CMOS integrated circuits mitigate the error of Qubit manipulation, reduce the cabling complexity, and facilitate the quantum feedback, which pave the way towards practical quantum error correction (QEC) and logic quantum gates. RF reflectometry is widely adopted for qubit states readout. Reflectometry conducts Qubit states discrimination (collapsed to “0” or “1”) by detecting the resonant frequency through RF reflection of a high-Q LC tank associated with the sensor Qubit (Fig. 1). The quantum states are encoded in either the amplitude or the phase of the reflected RF signal. Compared with its DC counterpart, the reflectometry achieves unprecedented charge sensitivity, reduces the integration time, and avoids long-term drifting. However, conventional heterodyne reflectometer schemes [1][4][5] adopt sophisticated up/down mixers, ADC, DAC, and PLL for the Qubit excitation and down-mixing, respectively. They suffer from poor TX-RX isolation, inter-modulation, and high DC power, which deteriorate the scalability and readout fidelity. To address these challenges, a highly scalable dual-Qubit homodyne reflectometer array is proposed in this paper. It drives the LC tank by a single PLL and detects the reflection by a high-gain degenerate parametric amplifier (DPA). Along with fast modulation and lock-in detection, it mitigates the interference, complex cabling, and high DC power of conventional heterodyne reflectometers.
Main-stream quantum computers employ dispersive reflectometry for quantum-bit (Qubit) state discrimination. An all-parametric quantum reflectometer (APQR) scheme has been proposed for high-fidelity, scalable Qubit array readout in this letter. For the RF excitation of APQR, a 10.7–16.9 GHz 65-nm cryogenic CMOS (Cryo-CMOS) parametric frequency divider (PFD) is demonstrated here. It adopts a pair of parallelly connected nonlinear artificial transmission lines (NLATLs), a wideband varactor-based dynamic coupler, and a transformer-based CM filter (TCMF). Due to the minimized device self-heating without dc power consumption and the intrinsic common-mode (CM) to differential-mode (DM) isolation, the PFD presents a measured output thermal noise floor of −189.1 dBm/Hz at 4.2 K. This is only 3.3 dB higher than 4.2-K blackbody radiation. At 4.2 K, the PFD also exhibits an ultralow phase noise of −128.8 dBc/Hz at 1 MHz at 6.75 GHz, which is 2.6 dB lower than a conventional Cryo-CMOS CML divider. It presents a 44.9% relative bandwidth at 4.2 K, which is$2\times $of the prior art at 300 K.
Continuous rounds of quantum error correction (QEC) are essential to achieve fault-tolerant quantum computers (QCs). In each QEC cycle, thousands of ancilla quantum bits (qubits) must be read out faster than the qubits’ decoherence time (≫T2∗∼120μs(\gg \mathrm{T}_{2} * \sim 120 \mu \mathrm{s}(≫T2​∗∼120μs for spin qubits). To address this urgent need, several CMOS receivers operating at cryogenic temperatures (cryo-CMOS RXs) have recently been introduced for gate-based [1] and RF reflectometry [2] readout of spin qubits, as well as transmons’ dispersive readout [3]. However, they have a few shortcomings. First, due to the temperature-independent shot noise of transistors in nanometer CMOS technology [4], their measured noise temperature (TN)(\mathrm{T}_{{\mathrm {N}}})(TN​) is limited to 40K, thus degrading qubit readout fidelity. Second, due to their large TN, prior art showed either only the electrical performance of their chips by applying a relatively large (i.e., -85dBm [2]) modulated signal directly to the RX input [2, 3] or offered limited qubit measurements by exploiting a HEMT amplifier prior to the RX [1]. Those issues hinder future monolithic integration between solid-state qubits and readout electronics. This work advances the prior art by (1) introducing a wideband passive amplification circuit at the RX front-end to minimize the shot noise contribution of the active devices, lowering prior art TNby ∼2.7x\sim 2.7\mathrm{x}∼2.7x; (2) demonstrating the RX performance in an RF-reflectometry qubit readout scheme without using off-the-shelf LNA prior to the RX.
A scalable spin-qubit quantum processor requires fast, high-fidelity readout circuits operating at cryogenic temperatures (CTs). This work analyzes the radio frequency (RF) reflectometry readout mechanism to establish the link between conductance modulation, single-electron transistor (SET) matching network design, reflected signal power, and receiver (RX) noise temperature. Based on this analysis, a cryogenic RX architecture employing a passive switched-capacitor front-end is proposed. The front-end performs RF amplification and downconversion using transistors as switches, avoiding active RF amplification and mitigating shot-noise limitations. The RX is implemented in 40-nm CMOS and operates from 100 MHz to 2.2 GHz. Measurements demonstrate a minimum noise temperature of approximately 15 K at 4.2 K. When integrated with a quantum device, the RX achieves a signal-to-noise ratio (SNR) of 9.8 dB for a 10-µs integration time and enables 99.9% charge-state readout fidelity without external cryogenic amplifiers. This work represents the first demonstration of such fidelity using a cryo-CMOS RX and constitutes an important step toward scalable integration of qubit readout electronics.
This article presents a cryogenic CMOS receiver operating across 4.7–7.9 GHz for frequency-division multiplexing (FDM) quantum state readout. The designed receiver employs a double quadrature (DQ) architecture and a hybrid poly-phase filter (PPF) is proposed to achieve an impressive image rejection ratio (IRR) to meet the 99.99% higher fidelity requirements in quantum error correction (QEC). In addition, gain tuning at different stages of the low noise amplifier (LNA) facilitates a broadband gain and flatness, while the subsequent receiver chains of a broadband mixer and an improved four-input intermediate frequency amplifier (IF-AMP) provide further gain compensation. Fabricated with a standard 55-nm CMOS technology, the LNA achieves a measured power gain of 27.4 dB, with a −3-dB bandwidth (BW) of 5.2 GHz at 6 K. The measured cryogenic noise figure (NF) ranges from 0.79 to 1 dB consuming merely 5.5 mW from a 1.2-V supply. Overall receiver measurements demonstrate a peak gain of 48.2 dB, a −5-dB flatness of 3.2 GHz, and an IRR that exceeds 40 dB at 6 K. These results demonstrate the receiver’s capacity for high-fidelity qubits’ state readout.
Cryogenic CMOS control and readout circuits tightly interfaced with the qubits have emerged as a promising solution for future quantum computers with tens-of-thousands to millions of qubits [1] –[5]. A lownoise cryo-CMOS receiver at 3−4 K3-4 \mathrm{~K}3−4 K integrated tightly with the lowcryogenic quantum processor can relax or even potentially eliminated the need for the HEMT LNA, and keep the whole control loop at cryogenic temperature, hence avoiding any high-speed interconnects to room temperature (Fig. 1). Additionally, wide bandwidths in the receiver enables qubit-multiplexing, where qubits can be frequency multiplexed with a spacing of 10MHz−40MHz10 \mathrm{MHz}-40 \mathrm{MHz}10MHz−40MHz, allowing anywhere from 10’s-100’s of qubits to be packed in to a single readout line with gigahertz-scale bandwidths. A second critical metric is power consumption, since the cooling power available in a typical dilution refrigerator is limited to a few watts at 3−4 K3-4 \mathrm{~K}3−4 K. Therefore, the control and readout circuits should be designed with low power consumption, projected to be <1 mW\lt 1 \mathrm{~mW}<1 mW per qubit (Fig. 1). While there has been initial progress in the design of cryo-CMOS readout systems, a leap forward is required in their overall power consumption to be viable for future quantum systems. In this work, we showcase the design and implementation of the first sub-mWper-qubit cryo-CMOS RX - a wideband, I/Q-downconversion, 4 K4 \mathrm{~K}4 K receiver for qubit readout that achieves >1.9GHz>1.9 \mathrm{GHz}>1.9GHz of IF bandwidth with >50 dB>50 \mathrm{~dB}>50 dB conversion gain and 0.7 dB0.7 \mathrm{~dB}0.7 dB NF while consuming only 17 mW17 \mathrm{~mW}17 mW of power consumption, thanks to various design techniques including near-threshold operation and low-1/f-noise passive mixers, representing 3−5×3-5 \times3−5× lower power consumption than prior works [2]–[3] while achieving similar noise, BW and gain performance. In addition, we demonstrate a real-time qubit read-out measurement by integrating our cryogenic-CMOS receiver with a transmon qubit.