Frequency Up-Conversion Schemes for Controlling Superconducting Qubits

2025-04-22 0 0 1.64MB 9 页 10玖币

侵权投诉

Johannes Herrmann,

1, 2, ∗

Christoph Hellings,

Stefania Lazar,

Fabian Pf¨aﬄi,

Florian Haupt,

Tobias Thiele,

Dante Colao Zanuz,

Graham J. Norris,

Flavio Heer,

Christopher Eichler,

and Andreas Wallraﬀ

1, 3

Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland

Zurich Instruments AG, CH-8005 Zurich, Switzerland

Quantum Center, ETH Zurich, CH-8093 Zurich, Switzerland

(Dated: October 7, 2022)

High-ﬁdelity control of superconducting qubits requires the generation of microwave-frequency

pulses precisely tailored on nanosecond timescales. These pulses are most commonly synthesized

by up-converting and superimposing two narrow-band intermediate-frequency signals referred to

as the in-phase (I) and quadrature (Q) components. While the calibration of their DC-oﬀsets,

relative amplitude and phase allows one to cancel unwanted sideband and carrier leakage, this IQ

mixing approach suﬀers from the presence of additional spurious frequency components. Here, we

experimentally study an alternative approach based on double frequency conversion, which overcomes

this challenge and circumvents the need for IQ-calibration. We ﬁnd a spurious-free dynamic range of

more than 70 dB and compare the quality of pulse generation against a state-of-the-art IQ mixing

scheme by performing repeated single-qubit randomized benchmarking on a superconducting qubit.

I. INTRODUCTION

Superconducting qubits have emerged as one of the

most promising platforms for building error-corrected

quantum computers [

–

], which have the potential to

solve problems beyond the reach of classical computers [

Large-scale quantum computing crucially relies on clas-

sical electronics hardware to orchestrate the control and

measurement signals. Of particular importance are de-

vices for generating nanosecond-long microwave pulses,

which are used for control [

], measurement [

–

], and

entangling operations [

] of superconducting qubits

and which also play an important role for operating semi-

conductor spin qubits [13, 14] and trapped ions [15, 16].

Microwave pulse generation typically employs a radio

frequency mixer to up-convert pulses generated by an

arbitrary waveform generator (AWG) at an intermediate

megahertz frequency to the typical gigahertz transition

frequency range of the superconducting qubit [

]. Com-

pared to the direct digital synthesis (DDS) of control

pulses [

], frequency up-conversion allows for using

AWGs with lower sampling rate, which relaxes resource re-

quirements and thereby eases the scale-up to large channel

numbers [20].

Conventional frequency up-conversion schemes utilize

an IQ mixer, which up-converts an in-phase and a quadra-

ture component to destructively interfere unwanted side-

band and carrier leakages, which can ultimately limit the

achievable single-qubit gate ﬁdelity. However, realistic IQ

mixers require extensive calibration of the IQ components

to achieve optimal performance, and the up-converted

output spectrum exhibits additional spurious frequency

components, which cannot be canceled by the interference

mechanism.

∗johannes.herrmann@phys.ethz.ch

Here, we control a superconducting qubit with an alter-

native microwave pulse generation scheme, which makes

use of two frequency conversion stages and uses analog

ﬁlters to remove the unwanted sideband and carrier leak-

ages from the up-converted control pulse. We compare

the signal quality of this double frequency conversion

scheme to a conventional IQ mixing scheme, and ﬁnd the

output of the double-conversion stage to exhibit smaller

spurious frequency components and to be less aﬀected by

variations in the ambient temperature. We also ﬁnd a

slight improvement in the single-qubit gate ﬁdelity when

using the double frequency conversion scheme to generate

the control pulses. For our study, we use a high-density

IQ converter (HDIQ) and a super-high-frequency signal

generator (SHFSG) to investigate the two schemes.

II. FREQUENCY UP-CONVERSION

High-ﬁdelity single-qubit control is achieved with reso-

nant microwave pulses of the general form

Vd(t) = ˜vI(t) cos(ωt +φ) + ˜vQ(t) sin(ωt +φ),(1)

where

is the transition frequency of the qubit,

global phase, and

˜vI

(

) and

˜vQ

(

) are two independent

pulse envelope functions. A common choice for

˜vI

(

)

and

˜vQ

(

) is the Gaussian DRAG pulse parametrization,

which allows to avoid leakage into non-computational

states [6, 7, 21].

To generate the control pulse at frequency

by up-

conversion, we multiply an intermediate frequency signal

generated by an AWG with a local oscillator continuously

running at frequency

ωLO

in the gigahertz range. The IF

signal consists of the two independent pulse envelope func-

tions

˜vI

(

) and

˜vQ

(

) deﬁned in software and modulated

digitally at frequency

ωIF

, see Appendix A for details. We

multiply the IF signal with the LO using a radio frequency

mixer resulting in an output spectrum

(

) featuring two

arXiv:2210.02513v1 [quant-ph] 5 Oct 2022

FIG. 1. Frequency up-conversion schemes. (a) Diagram and schematic output spectrum S(ω) of a radio frequency mixer

used for up-conversion, where both sidebands at frequencies

ωLO ±ωIF

are equally present. The frequency of the LO carrier is

indicated with a dashed arrow. (b) Sketch of an IQ mixer, for which the outputs of two parallel up-conversion paths, with an

LO signal shared through a 90

◦

-hybrid splitter, are superimposed in a microwave combiner. The IF signals for the IQ mixer are

generated by two independent digital-to-analog converters (DAC). (c) Sketch of a double frequency conversion scheme with two

separate mixing stages fed by two diﬀerent LO signals. The analog ﬁltering after each stage is indicated by a dashed box in the

respective spectrum Si(f).

sidebands centered around the frequencies

ωLO ±ωIF

, see

Fig. 1(a). Throughout the paper, we use the convention

of driving the qubit with the upper sideband at frequency

ωLO

ωIF

and consider the frequency component

ωLO −ωIF

the undesired image of the control pulse, which,

when present in the spectrum of the qubit drive pulse,

induces a gate error.

III. IQ MIXING SCHEME

An established method to eliminate the image compo-

nent is IQ mixing [

], as shown in Fig. 1(b). Here, two

parallel up-conversion paths, for two IF signal waveforms

(

) and

(

), are equipped with radio frequency (RF)

mixers which share a local oscillator signal through a

hybrid splitter which adds a 90

◦

-phase shift to the sig-

nal driving the Q port mixer. The signals from the two

parallel mixing paths are superimposed in a microwave

combiner, where ideally one of the two up-converted side-

bands is canceled out by destructive interference, see

Appendix A. The spectra in Fig. 1(b) illustrate this mech-

anism for the case in which both

(

) and

(

) have

a real-valued Fourier transform. In this particular case,

the destructive interference in the microwave combiner

is visible from the opposite signs of the lower-sideband

signals at frequency

ωLO −ωIF

, see the spectra

and

after the respective RF mixers in Fig. 1(b). To generate

the control pulse described by Eq.

(1)

with an IQ mixer,

we follow the procedure described in Appendix A and

compute in software two IF signals

(

) and

(

), which,

when up-converted using an ideal IQ mixer, result in an

image-free spectrum.

Under realistic conditions, however, the implementa-

tion of an IQ mixer is subject to imperfections, such as

amplitude and phase imbalances between the two parallel

mixing paths [

]. These imperfections result in an

up-converted spectrum that exhibits unwanted sideband

and carrier leakage, which we compensate for by calibrat-

ing the relative phase, amplitude and DC oﬀsets of the

IF signals, as described in the following.

First, the LO carrier signal leaks through each of the

two RF mixers with amplitude

and phase

θI

θQ

respectively, such that the LO signal at the output of the

IQ mixer is [23]

yLO(t) = LIcos(ωLOt+θI) + LQsin(ωLOt+θQ).(2)

In many basic applications, this eﬀect is not compensated

for, but an additional DC bias at the IQ mixer input

can help to decrease the amplitude of

yLO

(

). For this

purpose, we apply DC voltages

and

to the IF-ports

of the IQ mixer, which create additional signals of the

form

VIcos

(

ωLOt

) +

VQsin

(

ωLOt

) at the output. These

signals interfere destructively with

yLO

(

) to result in a

total amplitude

YLO =|VI+LIeiθI−iVQ−iLQeiθQ|(3)

of carrier leakage at the output of the mixer.

YLO

minimized for one speciﬁc combination of DC compensa-

tion voltages. To ﬁnd this combination experimentally,

we measure the amplitude

YLO

with an FPGA-based ac-

quisition system, see Appendix B, while varying the DC

oﬀsets

and

with coarse resolution, see Fig. 2(a).

We ﬁt Eq.

(3)

to the measured data to obtain optimal

compensation parameters, which are not limited to the

resolution between the discrete values of the underlying

measurement data and further enhance the calibration

accuracy, see Fig. 2(b).

Second, imbalances in the relative amplitude and phase

between the two parallel mixing paths modeled by the

scaling factor

˜α·

i˜

can result in an imperfect destructive

interference of the image component at frequency

ωIM

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

FrequencyUp-ConversionSchemesforControllingSuperconductingQubitsJohannesHerrmann,1,2,ChristophHellings,1StefaniaLazar,1FabianPfai,2FlorianHaupt,2TobiasThiele,2DanteColaoZanuz,1GrahamJ.Norris,1FlavioHeer,2ChristopherEichler,1andAndreasWallra1,31DepartmentofPhysics,ETHZurich,CH-8093Zurich,Switzerl...

展开>> 收起<<

Frequency Up-Conversion Schemes for Controlling Superconducting Qubits.pdf

共9页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Frequency Up-Conversion Schemes for Controlling Superconducting Qubits

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: