I. INTRODUCTION

Quantum computing has emerged as one of the most promising fields in modern science and technology, offering the potential to solve complex problems that are intractable for classical computers ^[1,2]. Central to this revolutionary technology are qubits, the basic units of quantum information. Superconducting qubits, in particular, have gained significant attention due to their scalability and compatibility with existing semiconductor fabrication technologies ^[3]. However, accurate and efficient read-out of qubit states remains a critical challenge in the development of practical quantum computing systems.

In the read-out process of superconducting qubits, the ability to precisely measure the quantum state without disturbing the system is crucial. This task often relies on high-performance radio frequency (RF) circuits, including mixers, to down-convert the qubit's microwave signals for processing. The mixer, as a fundamental RF component, plays a vital role in converting signals from one frequency to another, which is necessary for both signal detection and processing in quantum computing systems.

The performance of the mixer directly influences the fidelity of qubit read-out. To address the stringent requirements for quantum computing applications, mixers must offer wide bandwidth, low noise, and high linearity, all while minimizing power consumption ^[4]. In this work, we propose a 1.8mW low-power mixer with a 4-8GHz RF bandwidth, specifically designed for superconducting qubit read-out. By incorporating bleeding transistors, the proposed mixer enhances linearity and reduces noise, making it suitable for the high precision needed in quantum measurements ^[5].

This paper is organized as follows: Section 2 introduces the current bleeding technique, which is a key aspect of the proposed mixer design. Section 3 presents the detailed design of the proposed mixer, including the use of bleeding transistors. Section 4 provides simulation results, demonstrating the performance of the mixer in terms of bandwidth, power efficiency, and noise figure. Finally, Section~5 discusses the implications of this work for large-scale quantum computing systems and future research directions.

II. CURRENT-BLEEDING TECHNIQUE FEATURE

The current bleeding technique can be explained more easily using a single-balanced mixer and conventional double-balanced mixer topology shown in Fig. 1. When RF devices operate in the saturation region, the conversion gain (CG) and IIP3 can be approximated using the following equitons

In these formulas, $R_L$ represents the load resistance, while $I_{RF}$ is the drain current of the RF transistors. The constant ${\mu }_n$ represents the electron mobility of the transistor, $C_{ox}$ is the gate oxide capacitance, and $W$ and $L$ represent the width and length of the transistor.

According to Eqs. (1) and (2), both IIP3 and the conversion gain are proportional to the square root of the bias current. Thus, increasing the bias current is a straightforward way to improve linearity and gain. However, in practice, increasing the bias current results in a higher voltage drop across the load resistance ($R_L$), which could disrupt the proper functioning of the switching transistors. Specifically, when the supply voltage ($V_{DD}$) is fixed, increasing the bias current requires reducing the load resistance to maintain the bias conditions of the switching devices, which in turn reduces the conversion gain. Therefore, to enhance both linearity and gain, it is more effective to increase $I_{RF}$ without changing the drain-source current of the switching transistors.

The proposed current-bleeding technique can address the aforementioned issue. In Fig. 1(a), a bleeding current source ($I_{BLD}$) is added to the core of a single-balanced mixer. Without $I_{BLD}$, the total bias current is given by

By introducing $I_{BLD}$, the bias current can be increased without changing $I_{D1}$ or $I_{D2}$

The presented approach improves both linearity and conversion gain simultaneously

Fig. 1. (a)Single balanced mixer with current-bleeding source (b) Conventional double-balanced mixer.

III. MIXER CIRCUIT DESIGN

Fig. 2 shows the schematic of proposed mixer, and Table 1 presents device dimension. The design of a mixer for superconducting qubit read-out requires careful consideration of power efficiency, linearity, and noise performance. Therefore, this section focuses on the implementation of bleeding transistors and cross-couple techniques to improve linearity and noise characteristics based on the conventional double-balanced mixer presented in Fig. 1(b).

The proposed mixer follows a double-balanced architecture, which is commonly used in RF applications due to its superior rejection for low local oscillator (LO) leakage ^[6]. The core components of the mixer include a pair of switching transistors that modulate the RF input signal with the LO signal. The output is taken after the down-conversion, where the difference between the RF and LO frequencies is obtained.

The cross-coupled current bleeding technique effectively enhances the CG and noise performance compared to conventional current bleeding mixers. This technique employs cross-coupled PMOS switches to regulate the current of the switching transistors, activating at the LO zero-crossing to supply DC current. As a result, it maintains the transconductance ($g_m$) of the active switching transistors while reducing both thermal noise and flicker noise ($1/f$). Furthermore, the positive feedback effect of the cross-coupled structure enhances stability while further increasing conversion gain. Consequently, while maintaining the same level of noise contribution from the input source resistance as in conventional double-balanced mixer, this technique significantly minimizes the noise impact from the switching, bleeding, and load stages. Therefore, the cross-coupled current bleeding technique is highly suitable for high-gain, low-noise mixer designs ^[7].

In the design, complementary metal oxide semiconductor (CMOS) technology is utilized, taking advantage of its low power consumption and scalability. The input stage consists of a transconductance amplifier that converts the RF voltage into a current, which is then mixed with the LO signal by the switching pair. The LO signal drives the mixer transistors, ensuring high conversion gain while minimizing signal distortion.

A critical challenge in the design of mixers for quantum computing applications is achieving high linearity without sacrificing power efficiency. Nonlinearities in the mixer can introduce the intermodulation distortion, which affects the fidelity of qubit read-out. To address this issue, we introduce bleeding transistors into the mixer architecture. These transistors serve to maintain a constant current through the switching pair, reducing the variation in the LO current during operation. As a result, the linearity of the mixer is significantly improved.

The bleeding transistors are biased in such a way that they allow a small, steady current to flow through the switching transistors even when the LO signal is not actively switching ^[8]. This reduces the impact of LO signal fluctuations, thereby improving the overall linearity of the mixer. Additionally, the introduction of bleeding transistors helps to mitigate flicker noise, which is particularly important in quantum applications where noise minimization is crucial.

The proposed mixer is designed for minimized power consumption, which is a key requirement for scalable quantum computing systems ^[9]. By operating at only 1.8~mW, the mixer consumes significantly less power compared to conventional designs, as shown in the performance comparison in Table 2. This low power consumption is achieved by optimizing the biasing of the transistors and carefully selecting the operating points of both the RF input stage and the LO switching pair.

Table 1. Device dimension.

Table 2. Comparison of mixer with proposed mixer.

In terms of noise performance, the use of bleeding transistors contributes to a lower overall noise figure by reducing flicker noise and thermal noise contributions. The wide bandwidth of 4-8GHz ensures that the mixer can accommodate a broad range of qubit read-out frequencies, making it highly versatile for various quantum computing applications.

Fig. 2. Schematic of proposed mixer.

IV. SIMULATION RESULTS

In this section, we present the post-layout simulation results of the proposed mixer designed for superconducting qubit read-out. The performance of the mixer is evaluated based on key metrics such as conversion gain, noise figure, linearity, and power consumption. Simulation data are analyzed to demonstrate the effectiveness of the bleeding transistors and the overall design.

In RF applications, a higher conversion gain is preferred to ensure sufficient signal levels for further processing. The simulation results, as shown in Fig. 3, demonstrate that the mixer achieves a gain of 16.8 dB at 6 GHz, 10 dB at 4 GHz, and 12 dB at 8 GHz. Fig. 3(a) illustrates the conversion gain across the 4-8 GHz, while Fig. 3(b) shows the conversion gain behavior with varying temperatures, confirming that the mixer operates effectively even in low-temperature environments. The use of bleeding transistors contributes to the stability of the conversion gain, especially at higher frequencies, where traditional designs often experience degradation.

At 6 GHz, the noise figure reaches approximately 8.6 dB. The bleeding transistors play a significant role in reducing flicker noise, contributing to the overall low noise performance. Fig. 4 shows the noise figure of the mixer, where Fig. 4(a) illustrates the noise figure across different frequencies, and Fig. 4(b) presents the noise figure as a function of temperature. In typical superconducting qubit readout systems, achieving a noise figure (NF) below 1 dB at temperatures under 4 K is crucial. The readout chain generally begins with a Josephson parametric amplifier (JPA) providing approximately 20 dB of gain. Following this, a High Electron Mobility Transistor (HEMT) amplifies the signal by an additional 20-30 dB before it reaches the CMOS-based read-out circuit. The first stage of this circuit incorporates a low-noise amplifier (LNA). According to Friis equation, if the mixer's NF remains below 30 dB, its impact on the overall system NF is minimal, contributing less than 0.1 dB. As a result, the NF of the mixer is not at the sufficient level in the design.

Linearity is a critical parameter for maintaining the integrity of the qubit signal ^[10] proposed design achieves a 1 dB compression point (P1dB) of -11.7 dBm and an IIP3 of -1.2 dBm in simulations, which are considered high for a low-power mixer. Fig. 5 shows the P1dB and IIP3 of the mixer. The bleeding transistors help maintain high linearity by stabilizing the current through the switching pair, as discussed in Section 2.

The circuit to read the qubits existing at 10 mK is typically located at an ultra-low temperature of 4 K. The cooling capacity limit at the 4 K stage in a dilution refrigerator is 1-1.5 W. The capacity of the system to read about 8 qubits should be less than 20 mW/qubit. Therefore, it is essential to reduce the power consumption of the system, and the proposed mixer consumes only 1.8 mW. This is a significant improvement over existing designs that typically consume higher power at similar performance levels ^[11]. Table 3 shows the power consumption as a function of temperature, and Fig. 6 shows the layout of the proposed mixer.

Table 4 provides a comparison of the proposed mixer with other state-of-the-art designs. As shown, the proposed mixer offers competitive performance in terms of conversion gain, noise figure, and linearity while consuming significantly less power. The incorporation of bleeding transistors distinguishes this design by enhancing both linearity and noise performance, making it well-suited for quantum computing applications.

Fig. 3. Conversion gain of the proposed mixer: (a) conversion gain vs. frequency, and (b) conversion gain vs. temperature.

Fig. 6. Layout of proposed mixer.

Fig. 4. Noise figure of the mixer: (a) noise figure vs. frequency, and (b) noise figure vs. temperature.

Fig. 5. P1dB of the mixer: (a) P1dB & IIP3 vs. frequency, and (b) P1dB vs. temperature.

V. CONCLUSIONS

In this paper, we presented the design and implementation of a 1.8 mW low-power mixer with a 4-8 GHz bandwidth, specifically developed for superconducting qubit read-out. By integrating bleeding transistors into the mixer architecture, the proposed de-sign achieves significant improvements in linearity and noise performance, both of which are critical for the precise detection of quantum states. The mixer's low power consumption, wide bandwidth, and robust linearity make it a promising candidate for use in large-scale quantum computing systems where energy efficiency and performance are paramount.

Simulation results demonstrate that the mixer achieves a conversion gain of approximately 16.7 dB with a low noise figure of 8.6 dB, maintaining competitive performance in comparison to state-of-the-art designs. The implementation of bleeding transistors reduces flicker noise and enhances linearity, yielding an P1dB of up to -11.7 dBm. Moreover, the mixer operates with minimal power consumption, meeting the stringent requirements of quantum computing applications.