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IEEE Microwave and Wireless Technology Letters

A Cryo-CMOS Parametric Frequency Divider With −189.1 dBm/Hz Output Noise Floor at 4.2 K for High-Fidelity All-Parametric Quantum Reflectometer

Yujie Geng, Haichuan Lin, Bo Wang, Cheng Wang

Published Oct 26, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1109/lmwt.2023.3325730

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Digest of technical papers/Digest of technical papers - IEEE International Solid-State Circuits Conference•Feb 18, 2024•19 citations
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 is2×2\times 2×of the prior art at 300 K.
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.
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.
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.
Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of 4 × 32 qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz.
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.