Microwave-multiplexed qubit controller using adiabatic superconductor logic

Cryogenic qubit controllers (QCs) are the key to build large-scale superconducting quantum processors. However, developing scalable QCs is challenging because the cooling power of a dilution refrigerator is too small (~10 $\mu$W at ~10 mK) to operate conventional logic families, such as complementary metal-oxide-semiconductor logic and superconducting single-flux-quantum logic, near qubits. Here we report on a scalable QC using an ultra-low-power superconductor logic family, namely adiabatic quantum-flux-parametron (AQFP) logic. The AQFP-based QC, referred to as the AQFP-multiplexed QC (AQFP-mux QC), produces multi-tone microwave signals for qubit control with an extremely small power dissipation of 81.8 pW per qubit. Furthermore, the AQFP-mux QC adopts microwave multiplexing to reduce the number of coaxial cables for operating the entire system. As a proof of concept, we demonstrate an AQFP-mux QC chip that produces microwave signals at two output ports through microwave multiplexing and demultiplexing. Experimental results show an output power of approximately $-$80 dBm and on/off ratio of ~40 dB at each output port. Basic mixing operation is also demonstrated by observing sideband signals.


INTRODUCTION
A significant engineering effort is required to develop practical, fault-tolerant quantum processors (QPs).Quantum computing has the potential to surpass classical computing in some applications [1][2][3][4] ; however, quantum error correction requires numerous physical qubits [5][6][7][8] .This is a great engineering challenge for superconducting QPs because superconducting qubits are cooled to ~10 mK inside a dilution refrigerator to suppress thermal noise and should be controlled in a hardware-efficient way 9 .Currently, superconducting QPs 10,11 (including hundreds of qubits at the most 12 ) use the brute-force scheme to control qubits, in which microwave pulses generated by room-temperature electronics are applied to each qubit via coaxial cables between 300-K and 10-mK stages.This control scheme is not scalable because the number of available coaxial cables is limited by the cooling power and physical space of the dilution refrigerator 13 .
One of the most promising control schemes is the implementation of cryogenic qubit controllers (QCs) in dilution refrigerators.Recently, two types of QCs have been developed extensively, cryogenic complementary metaloxide-semiconductor (cryo-CMOS) logic-based [14][15][16] and superconducting single-flux-quantum (SFQ) logic-based [17][18][19] QCs.Although both QCs successfully controlled superconducting qubits, they need to be placed at relatively warm stages (i.e., the 3-K stage); therefore, they still have scalability limitations associated with coaxial cables between the 3-K and 10-mK stages.This is because the cooling power of the 10-mK stage is too small (~10 μW) to operate cryo-CMOS and SFQ circuits, whereas a very simple SFQ QC can operate at the 10-mK stage 17 .Typically, the power dissipation of cryo-CMOS and SFQ QCs is 1-100 mW per qubit 16 and 1-100 μW per qubit 18,19 , respectively.Therefore, to build large-scale superconducting QPs, it is crucial to develop ultra-low-power QCs that can operate together with qubits at the 10-mK stage.
In this study, we propose a scalable QC using adiabatic superconductor logic, namely adiabatic quantum-fluxparametron (AQFP) logic 20,21 .AQFP circuits are based on the quantum flux parametron 22,23 and can operate with an extremely small power dissipation of ~7 pW per Josephson junction 24 owing to adiabatic switching [25][26][27] .For instance, a very-large-scale AQFP circuit having 10 6 Josephson junctions can operate with a power dissipation of only ~7 μW, which is still less than the cooling power of the 10-mK stage.Furthermore, inspired by microwave-multiplexed superconducting sensor arrays 28,29 , the proposed QC adopts AQFP-based microwave multiplexing to reduce the number of coaxial cables for driving the QC.These features ensure very high scalability in terms of both power dissipation and cable count, indicating the possibility of implementation with qubits at the 10-mK stage.The proposed QC is termed the AQFP-multiplexed QC (AQFP-mux QC).
In the following sections, we describe the details of the AQFP-mux QC using numerical simulations and demonstrate an AQFP-mux QC chip at 4.2 K as a proof of concept.Specifically, we show that the AQFP-mux QC can produce multi-tone microwave signals for controlling qubits with an ultra-low power dissipation of 81.8 pW per qubit and can be driven by using a single coaxial cable, independently of the qubit count.For clear terminology, we distinguish AQFP logic from SFQ logic, since typical SFQ logic families (such as rapid SFQ logic 30 ) use SFQ pulses to encode data, whereas AQFP logic uses the polarity of current for data encoding.

AQFP-multiplexed qubit controller
Fig. 1a illustrates a conceptual diagram of the AQFP-mux QC, where both the AQFP-mux QC and qubit chips are implemented at the 10-mK stage inside a dilution refrigerator.A multi-tone microwave generated by room-temperature electronics is applied to the AQFP-mux QC chip via a single coaxial cable connecting the 300-K and 10-mK stages.The AQFP-mux QC demultiplexes the microwave tones and applies microwave pulses with different frequencies to the qubits, where the qubit frequencies should match the microwave tones.The number of coaxial cables in the entire system does not increase with the qubit count owing to microwave multiplexing, which is a clear advantage over previously proposed qubit controllers [14][15][16][17][18][19] .The AQFP-mux QC comprises both analog and digital parts.The analog component demultiplexes the input microwave tones, mixes each microwave tone with a baseband signal to produce microwave pulse trains, and switches each microwave pulse on and off.The digital component sends digital signals to the analog component to control the switching of each microwave pulse in accordance with the given quantum algorithm.Because the main component of the AQFP-mux QC is the analog part, we will describe only the analog part in this study and discuss the digital part in future work.
The core of the AQFP-mux QC is the AQFP mixer shown in Fig. 1b Fig. 1c shows the numerical simulation of the AQFP mixer by JoSIM 31 , where Ilo is a 5-GHz sinusoidal current, Ibb is a triangular current as an example of BB signals, and the dashed lines represent zero for each waveform.The figure clearly shows that the AQFP mixer generates a 5-GHz microwave pulse (Vout) by mixing Ilo and Ibb, and switches on/off Vout by Iin (the polarities of Iin and Ifix represent their logical values).The envelope of Vout is not identical to the shape of Ibb because of the nonlinear relationship between Ibb and the output currents (Iouta and Ioutb), that is, the AQFP mixer operates as a nonlinear mixer.Precise pulse shaping for Vout is possible by considering the nonlinear relationship, as shown later.
Fig. 1d shows a detailed diagram of the AQFP-mux QC.Multiple AQFP mixers are excited by a single LO current (Ilo) including multiple microwave tones, using a superconducting resonator array as a microwave demultiplexer.Assuming that Ilo includes three different microwave tones (f1, f2, and f3) that correspond to the qubit frequencies, AQFP mixers 1, 2, and 3 are coupled to Ilo through resonators with resonance frequencies of f1, f2, and f3, respectively.Furthermore, all AQFP mixers are coupled to the common BB current Ibb.Consequently, each AQFP mixer generates microwave pulses with a different frequency by mixing Ibb and the LO signal in the resonator coupled to the mixer.For instance, AQFP mixer 1 generates microwave pulses Vout1 with a frequency of f1 by mixing Ibb and the LO current in the f1 resonator (Ir1).Importantly, the number of control lines (Ilo and Ibb) does not increase with the qubit count because all AQFP mixers share Ilo and Ibb lines.Note that the level of Ilo for each tone is determined such that magnetic flux with an amplitude of 0.5Φ0 is applied to each AQFP in the mixers (see the Methods section for more details).
Fig. 1e shows the numerical simulation of the AQFP-mux QC by JoSIM, where Ilo includes two microwave tones (f1 = 4.5 GHz and f2 = 5 GHz).Iin1 and Iin2 are the input currents applied to AQFP mixers 1 and 2, respectively, to switch the outputs on and off.The figure shows that the two AQFP mixers generate microwave pulses (Vout1 and Vout2) with different frequencies (f1 and f2), and that each output is individually turned on/off by Iin1 or Iin2.This result indicates that the AQFP-mux QC can apply microwave pulses to arbitrary qubits in accordance with the given quantum algorithm.

Performance estimation
We estimated the performance (output power and power dissipation) of the AQFP mixer through numerical simulations using JSIM_n 32 .The performance of the AQFP mixer changes with the load line design (Fig. 1b).In this study, the impedance of the load line was designed to be a small value of 2 Ω to extract relatively large output power from the mixer; accordingly, the matching resistor Rs and input impedance of the BPF were designed to be 2 Ω.The BPF was also designed to convert impedance from 2 Ω (input) to 50 Ω (output) to drive general 50-Ω loads.Details of the BPF design can be found in the Methods section.In both the numerical simulation and experiments, the AQFP mixer was evaluated with a 50-Ω load at the output port.
The output power (when Ibb was at the maximum) was estimated to be 21.9 pW (= −76.6 dBm) for 5-GHz operation, which is assumed to be large enough for typical qubit control.If necessary, the output power can be further increased by adding more AQFPs to the load line of the AQFP mixer.Two types of power dissipation were estimated for the 5-GHz operation, namely standby power Psby (when Ibb was off) and maximum power Pmax (when Ibb was at the maximum).Psby and Pmax were estimated to be 2.82 pW (2.29 pW for AQFPs and 0.533 pW for Rs) and 81.8 pW (22.3 pW for AQFPs and 59.5 pW for Rs), respectively.Hence, the power dissipation of the AQFP-mux QC is 81.8 pW per qubit at the most, excluding the digital processing circuits.This power dissipation is orders of magnitude lower than cryo-CMOS and SFQ QCs.Note that the power dissipation of the AQFP-mux QC was estimated using circuit parameters at 4.2 K since the circuit parameters do not vary much between 4.2 K and 10 mK.For instance, the change in the critical current of an Nb-based Josephson junction (critical temperature: ~9 K) is estimated to be less than 10% between 4.2 K and 10 mK 33,34 .Also, this parameter change can be compensated by slightly changing the layout design of each junction when customizing the AQFP-mux QC for 10-mK operation.
In addition, we discuss the frequency efficiency of the microwave multiplexing.Assuming the use of Nb resonators 35 with a quality factor Q of ~10 4 and a resonance frequency f0 of ~5 GHz, the minimum frequency spacing between adjacent microwave tones is approximately given by f0/Q = 500 kHz.Therefore, a single LO line can transmit ~4,000 microwave tones, assuming a bandwidth of 2 GHz.This is much more frequency-efficient than the frequency multiplexing used in the cryo-CMOS QC 15 , which can multiplex 32 signals over a control line.This is because continuous microwaves are multiplexed in the AQFP-mux QC, whereas microwave pulses are multiplexed in the cryo-CMOS QC (i.e., wide frequency spacing is required).
We roughly compare the scalability of the AQFP-mux QC with that of other QCs from the viewpoints of power dissipation and the number of coaxial cables.According to the literature 15 , the power dissipation of a cryo-CMOS QC is 12 mW per qubit.The cryo-CMOS QC is placed at the 3-K stage, and each signal line can multiplex 32 qubits by frequency multiplexing; thus, the number of the coaxial cables between 10-mK and higher-temperature (i.e., 3-K) stages is Ncable ~ Nqubit/32 (Nqubit: number of qubits), where the cables for two-qubit gates and readout are omitted for simplicity.The power dissipation of SFQ QCs is 1.6 μW per qubit and 51.7 μW per qubit for the pulse-based control 18 and microwave-based control 19 , respectively.The SFQ QCs are assumed to be placed at 3-K stages and currently do not implement frequency-multiplexing, i.e., Ncable ~ Nqubit.The power dissipation of the AQFP-mux QC is 81.8 pW per qubit, and each LO line can multiplex ~4,000 qubits owing to microwave multiplexing, i.e., Ncable ~ Nqubit/4000.The above comparison indicates that the AQFP-mux QC has the potential to control the qubits in a large-scale QP with much less power dissipation and cable count than other QCs.It should also be noted that, at this moment, the cryo-CMOS QC has much richer circuit functions than the SFQ and AQFP-mux QCs; thus, more systematic, fair comparison will be required in future work.

Experimental demonstration
As a proof of concept, we fabricated an AQFP-mux QC chip and demonstrated its operation at 4.2 K in liquid helium using a wideband cryoprobe 36 .As mentioned above, the changes in the circuit parameters between 4.2 K and 10 mK are small and do not make a difference on the operating principle of the AQFP-mux QC; thus, we conducted proofof-concept experiments at 4.2 K. Fig. 2a shows a micrograph of the AQFP-mux QC chip, which multiplexes two AQFP mixers (1 and 2) using two resonators with resonance frequencies of f1 and f2.Both the mixers were excited by a single Ilo including two microwave tones (f1 and f2) and a common Ibb.The outputs of the mixers (Vout1 and Vout2) were controlled by the input currents (Iin1 and Iin2) and were observed using a signal analyzer.We analyzed the insertion loss of the LO line using a vector network analyzer to determine the resonance frequencies and found f1 = 4.3392 GHz and f2 = 4.8171 GHz.
First, we demonstrated the switching operation of the AQFP-mux QC.A DC current inducing 0.5Φ0 on each AQFP in the mixers was applied to Ibb, and Vout1 and Vout2 were observed for different sets of the logical values of Iin1 and Iin2 (a1 and a2).Fig. 2b shows the measurement results of Vout1 at f1 and Vout2 at f2 for (a1, a2) ∈ {(0, 0), (0, 1), (1, 0), (1, 1)}.This figure indicates that Vout1 and Vout2 can be individually controlled by Iin1 and Iin2, respectively, as shown in the waveforms in Fig. 1e.For instance, Vout1 is switched on for (1, 0) and (1, 1), and off for (0, 0) and (0, 1).The output power of Vout1 and Vout2 when switched on is −82.1 dBm and −81.8 dBm, respectively.These power values may be smaller than the estimated value (−76.6 dBm) because of cryoprobe losses and parameter mismatches between the design values and fabricated chip.The on/off ratios of Vout1 and Vout2 are 42.7 dB and 39.0 dB, respectively, which are comparable with those of previously reported cryogenic microwave switches [37][38][39][40] .We also evaluated the leakage power between the output channels, that is, Vout1 at f2 and Vout2 at f1, as shown in Fig. 2c.The leakage power to Vout1 and Vout2 is at the most −117.1 dBm and −121.1 dBm, respectively.The on/off ratios and leakage power may have been determined by various factors, such as crosstalk between Ilo and the output channels inside the cryoprobe, parameter imbalance in the AQFPs, and interaction between the AQFP mixers.Further studies are required to improve the on/off ratios and reduce the leakage power.
We then demonstrated the basic mixing operation of the AQFP-mux QC by observing sideband signals generated from LO and baseband signals.A square pulse with a repetition frequency fbb of 1 MHz was applied to Ibb (the low and high levels induced 0Φ0 and 0.5Φ0, respectively, on each AQFP), and Vout1 and Vout2 were observed at the LO and sideband frequencies for (a1, a2) = (1, 1).We randomly selected a repetition frequency of 1 MHz since any frequencies below the LO frequency can be used for sideband observation.Fig. 2d shows Vout2 at f2 and f2 ± fbb, which demonstrates that the Ibb signal is upconverted by f2, i.e., AQFP mixer 2 modulates Vout2 by mixing Ibb and the f2 tone in Ilo.We observed similar modulation characteristics for Vout1.It should be noted that the duration time of qubit- control pulses is tens of nanoseconds 41 , so we plan to perform much faster modulation in future experiments to enhance the feasibility of AQFP-based qubit control.

Power calibration
In addition to the individual switching of each output, QCs must implement the individual power calibration of each output because the output power of each mixer and the coupling strength between each pair of output channels and qubits can vary from device to device and chip to chip.The AQFP-mux QC can perform individual power calibrations by adjusting each microwave tone in Ilo.Fig. 3a shows the simulated waveforms for the AQFP-mux QC when the power of the f2 tone was reduced by 3 dB compared with the normal excitation condition (Fig. 1e).A comparison of Figs.1e and 3a shows that the amplitude and duration of the microwave pulses at Vout2 decrease with decreasing f2 tone power in Ilo (the duration decreases because a larger Ibb value is required to excite the AQFPs), whereas those at Vout1 do not change, that is, the power of Vout2 can be individually adjusted without changing that of Vout1.
We experimentally demonstrated individual power calibration using an AQFP-mux QC chip.Fig. 3b shows the power of Vout1 and Vout2 as a function of the f2 tone power in Ilo, where an f2 tone of −56 dBm is the normal excitation condition and a DC current inducing 0.5Φ0 on each AQFP was applied to Ibb.The figure shows that the power of Vout2 can be individually adjusted by the f2 tone power over a wide range while keeping the power of Vout1 almost constant.We observed similar individual power calibrations for Vout1.

Pulse shaping
It is important to apply microwave pulses with an appropriate envelope to each qubit to avoid unintentional qubit excitation 41 , such as leakage to a higher energy level.As mentioned above, the AQFP mixer operates as a nonlinear mixer; therefore, special care should be taken for Ibb to achieve Vout with the desired envelope.Precise pulse shaping is possible by designing the evolution of Ibb considering the nonlinear relationship between Vout and Ibb.Fig. 4a shows the simulation results for the amplitude of Vout as a function of the magnetic flux Φbb applied to each AQFP in the mixer by Ibb.The amplitude of Vout is determined by Φbb one-to-one, so the time evolution of Ibb for achieving a desired envelop is uniquely determined from Fig. 4a.Figs.4b and 4c show the simulated waveforms that achieved Vout with triangular and Gaussian envelopes, respectively, as examples of pulse shaping.The envelope of Vout was first determined, and the evolution of Ibb was designed by converting Vout at each time step to the corresponding Ibb value, based on Fig. 4a.These results suggest that the AQFP mixers in the AQFP-mux QC can produce microwave pulses with appropriate envelopes by carefully designing the evolution of Ibb.

DISCUSSION
We discuss the challenges of integration with qubits.In the AQFP-mux QC, the qubit frequencies are assumed to be equal to the resonance frequencies of the resonator array operating as a microwave demultiplexer, even with process variation.Therefore, a frequency-matching mechanism must be incorporated.It is not possible to use superconducting quantum interference device (SQUID)-based tunable resonators 42 for frequency matching because a relatively large current must flow through a resonator to drive an AQFP mixer.Therefore, integration with frequency-tunable qubits such as flux qubits 43 and split transmons 44 is preferable.To calibrate each output power individually, it is also assumed that all qubit frequencies are different from each other.This constraint must be considered when designing the qubit frequencies.
Furthermore, circuit design challenges should be considered.A QC must control the phases of the produced microwave pulses to form a universal quantum gate set 41 .For instance, the "Clifford + T" set 45 includes a T gate, which rotates the qubit state by 45 degrees about the Z-axis; in this case, a QC needs to control microwave phases by 45 degrees, assuming the use of virtual Z gates 46 .Currently, the AQFP mixers in the AQFP-mux QC can control the microwave phases by only 180 degrees [in Fig. 1c, the phase of Vout changes by 180 degrees by inverting the polarities of Iin and Ifix].Thus, the analog part of the AQFP-mux QC requires improvement to achieve a better phase resolution.Moreover, the digital part should be carefully designed so that the entire architecture exhibits high scalability.One of the most straightforward designs for the digital part is an address decoder 37 that selects which AQFP mixers to turn on following externally applied digital signals.Regardless of the architecture adopted, it is crucial to densely combine analog and digital parts using high-density circuit technology, such as a multi-junction-layer process 47 and multi-chip module 48 .It will be also necessary to investigate how to integrate the AQFP-mux QC with memory circuits that store pulse sequence information and qubit readout circuits.
In conclusion, we proposed the AQFP-mux QC as a scalable QC for large-scale superconducting QPs.The AQFP mixers in the AQFP-mux QC produce microwave pulse trains for controlling qubits by exploiting the nonlinearity of AQFPs, and switch each microwave pulse on/off by controlling the output polarities of the AQFPs.The AQFPmux QC operates with an ultra-low power dissipation of 81.8 pW per qubit at the most, except for the digital processing circuits, and can be driven by a frequencymultiplexed microwave using a single coaxial cable.These features suggest the high scalability of the AQFP-mux QC in terms of both power dissipation and cable count.As a proofof-concept, we demonstrated the operation of an AQFP-mux QC chip at 4.2 K, which multiplexed two AQFP mixers using a two-tone microwave.The experimental results indicated an output power of approximately −80 dBm and an on/off ratio of approximately 40 dB at each output port.The basic mixing operation was also demonstrated by observing LO and sideband signals.These results indicate the feasibility of energy-efficient, scalable qubit control using AQFP logic.Our next step is to demonstrate the AQFP-mux QC chip at 10 mK (where fast modulation toward qubit control should be performed) as a preliminary test for integration with qubits.

METHODS
AQFP design.The AQFPs in the AQFP mixer were designed using 50-μA Josephson junctions and inductances based on previously developed AQFP cell libraries.The physical layout was designed by estimating each inductance using InductEx 49 .BPF design.The BPF in the AQFP mixer comprises a low-pass filter (LPF), impedance transformer, and DC blocking capacitor (3 pF) in series.The LPF is a five-pole Chebyshev LPF with an impedance of 2 Ω, passband ripple of 0.2 dB, and cutoff frequency of 1.3fop, where fop is the operating frequency.The impedance transformer is a two-section Chebyshev quarter-wave transformer 50 , which converts an input impedance of 2 Ω to an output impedance of 50 Ω with a bandwidth of 0.4fop.In the AQFP-mux QC chip, the BPFs in AQFP mixers 1 and 2 were designed for fop = 4.5 GHz and 5 GHz, respectively.Resonator design.The resonators used for microwave demultiplexing are lumped-element LC resonators.Each resonator was designed using the resonator model shown in Supplementary Fig. 1a, where R represents the equivalent resistance of the source and load impedances for the LO line (i.e., R = 50 Ω + 50 Ω= 100 Ω), and Lr and Cr are the resonator inductance and capacitance, respectively.The resonator is magnetically coupled to the LO line through a transformer composed of L1 and L2 with mutual inductance M = k(L1L2) 0.5 .The resistance of the resonator was assumed negligible, that is, the loaded quality factor was equal to the external quality factor.Supplementary Fig. 1b is the equivalent circuit after converting the LO line using M as an impedance inverter, where R′ = (ωM) 2 R/[R 2 + (ωL1) 2 ], L1′ = −(ωM) 2 L1/[R 2 + (ωL1) 2 ], and ω is an angular frequency.From this circuit diagram, the resonance angular frequency is given by ω0 = 1/(LtotCr) 0.5 , where Ltot = Lr + L1′ + L2, and the quality factor is given by Q = ω0Ltot/R′ = {[R 2 + (ω0L1) 2 ]Lr + [R 2 + (1 − k 2 )(ω0L1) 2 ]L2}/ω0M 2 R. Because of the power equivalence between the two circuit diagrams (RIlo 2 /2 = R′Ir 2 /2), the current ratio is given by Ir/Ilo = [R 2 + (ω0L1) 2 ] 0.5 /ω0M, where Ilo is the amplitude of the current through the LO line and Ir is that through the resonator.Assuming R 2 >> (ω0L1) 2 , ω0 ≈ 1/[(Lr + L2)Cr] 0.5 , Q ≈ (Lr + L2)R/ω0M 2 , and Ir/Ilo ≈ R/ω0M.Resonators 1 and 2 in the AQFP-mux QC chip were designed for ω0/2π = 4.5 GHz and ω0/2π = 5.0 GHz, respectively, with a Q of ~200.The power of each microwave tone was determined using the current ratios (Ir/Ilo = 88 and Ir/Ilo = 79 for resonators 1 and 2, respectively).
Power calculation.The entire power dissipation Ptot of the AQFP mixer plus output load (50 Ω) was calculated by integrating the current through and voltage across the LO line over time 51 , and the output power Pout was calculated by integrating the current through and voltage across the output load over time.The power dissipation of the AQFP mixer was then calculated by Paqfp = Ptot − Pout.
Circuit fabrication.The AQFP-mux QC chip was fabricated using a 10-kA/cm 2 four-Nb-layer process provided by AIST, namely the high-speed standard process 52 .
Measurement.The LO signal (Ilo), which included two microwave tones (f1 and f2), was generated by combining microwaves from a two-channel signal generator (Anritsu, MG3710A) using a power combiner.The BB signal (Ibb) was generated using an arbitrary waveform generator (Keysight, M3202A).The digital inputs (Iin1 and Iin2) were generated using a multichannel source measurement unit (Keysight, M9614A).The outputs of the AQFP-mux QC chip (Vout1 and Vout2) were directly observed without amplification using a signal analyzer (Anritsu, MS2830A).

Fig. 1 |
Fig. 1 | AQFP-multiplexed qubit controller (AQFP-mux QC).a. Conceptual diagram.The AQFP-mux QC chip produces microwave pulses for controlling qubits from a single multi-tone microwave input at the 10-mK stage, thereby solving the scalability limitation due to coaxial cables between 300-K and 10-mK stages.b.AQFP mixer.The output voltage Vout is generated by mixing the local-oscillator (LO) current Ilo and baseband current Ibb using the nonlinearity of AQFPs A and B. c. Numerical simulation of the AQFP mixer.A microwave pulse is generated at Vout by mixing Ilo (5-GHz sinusoidal current) and Ibb (triangular current as an example), and Vout is switched on/off by the digital input currents Iin and Ifix.d.Detailed diagram of the AQFP-mux QC.Multiple AQFP mixers are driven by a single multi-tone LO current Ilo using a superconducting resonator array operating as a microwave demultiplexer.The number of control lines (Ilo and Ibb) does not increase with the qubit count thanks to microwave multiplexing.e. Numerical simulation of the AQFP-mux QC, where Ilo includes two microwave tones (4.5 GHz and 5 GHz).4.5-GHz and 5-GHz microwave pulses are generated at different output ports (Vout1 and Vout2) and individually switched on/off by the input currents Iin1 and Iin2, respectively.

Fig. 2 |
Fig. 2 | Experimental demonstration.a. Micrograph of an AQFP-mux QC chip, multiplexing two AQFP mixers (1 and 2) via two resonators with resonance frequencies of f1 = 4.3392 GHz and f2 = 4.8171 GHz.The mixers were excited by a single LO current Ilo including f1 and f2 tones.The output voltages from the mixers (Vout1 and Vout2) were observed by a signal analyzer.b.Switching operation for Vout1 at f1 and Vout2 at f2, with the baseband current Ibb fixed to induce 0.5Φ0 on each AQFP.Vout1 and Vout2 are individually switched on/off by Iin1 and Iin2, respectively, the logical values of which are represented by (a1, a2).The output power of Vout1 and Vout2 when switched on is −82.1 dBm and −81.8 dBm, respectively.The on/off ratios of Vout1 and Vout2 are 42.7 dB and 39.0 dB, respectively.c.Leakage power between output channels, i.e., Vout1 at f2 and Vout2 at f1.The leakage power to Vout1 and Vout2 is at the most, −117.1 dBm and −121.1 dBm, respectively.d.Mixing operation for Vout2, with a 1-MHz square current applied to Ibb.Peak power appears at the LO and sideband frequencies (i.e., f2 and f2 ± 1 MHz), demonstrating modulation by AQFP mixer 2.

Fig. 3 |
Fig. 3 | Power calibration.a. Numerical simulation of the AQFPmux QC when the power of the f2 tone (5 GHz) in the LO current Ilo is reduced by 3 dB, compared to the numerical simulation shown in Fig. 1e.The amplitude and duration of the microwave pulses at Vout2 decrease with decreasing f2 tone power.b.Measurement results of each output power vs the f2 tone power in Ilo.The power of Vout2 can be individually adjusted by the f2 tone power, without changing that of Vout1.

Fig. 4 |
Fig. 4 | Pulse shaping.a. Numerical simulation for Vout vs magnetic flux applied to each AQFP (Φbb) by the baseband current Ibb.b.Triangular microwave pulse.c.Gaussian microwave pulse.Microwave pulses with desired envelopes can be achieved by designing the evolution of Ibb based on the nonlinear relation shown in Fig. 4a.
, which produces a microwave pulse train by mixing the local oscillator (LO) and baseband (BB) signals and switches each microwave pulse on/off following the digital inputs.The AQFP mixer comprises paired AQFPs (A and B) coupled to two excitation currents, Ilo and Ibb.Ilo and Ibb apply LO and BB magnetic fluxes with an amplitude of 0.5Φ0 each, to each AQFP, where Φ0 is the flux quantum.Paired AQFPs are excited when both Ilo and Ibb are at high levels, consequently generating mixed signals of Ilo and Ibb as output currents (Iouta and Ioutb).Iouta and Ioutb apply magnetic fluxes (Φa and Φb) to the load line, the time derivative of which generates electromotive force and appears as the output microwave Vout through a bandpass filter (BPF).The switching of Vout is controlled by digital input currents Iin and Ifix (i.e., Vout is switched on/off by the logical states of the paired AQFPs).Vout is turned on when Iin and Ifix have the same logical values, because Φa and Φb have the same polarity.In contrast, Vout is turned off when Iin and Ifix have different logical values, because Φa and Φb cancel out each other.Hereafter, Ifix is fixed to logic 1; therefore, the switching of Vout is controlled by Iin.