A Method for Measuring the Amplitude-Frequency Response of Sub-Microwave Signals in an Extreme Temperature Variation System

Abstract

The present invention discloses a method for measuring the amplitude-frequency response of a submicrowave signal in an extreme temperature-varying system, specifically relating to the field of quantum precision measurement technology. The method comprises the following steps: Step 1: calibrating the intrinsic frequency-longitudinal field DC intensity of a quantum bit; Step 2: selecting a suitable longitudinal field DC bias point; Step 3: determining the gate parameters at the longitudinal field DC bias point; Step 4: measuring the frequency shift introduced by the modulated longitudinal field using a Ramsey waveform; Step 5: varying the frequency of the alternating longitudinal field signal and repeating Step 4 to obtain an amplitude-frequency response characteristic curve. All signal transmission and measurement in the present invention are performed at room temperature, meeting the operating temperature range of general arbitrary waveform generators and microwave sources, making it easy to implement.

Description

Technical Field

[0001] The present invention relates to the field of quantum precision measurement technology, and in particular to a method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-variable system. Background Art

[0002] Quantum computing, one of the most emerging technologies of our time, holds strong promise for applications in fields as diverse as information technology, biomedicine, atmospheric science, and finance. We have entered the Noise Intermediate-Scale Quantum (NISQ) era, and superconducting qubits, one of the most promising platforms for quantum computing, offer advantages in gate operation time, scalability, and integration capabilities.

[0003] Longitudinal field control technology is a key technology for manipulating superconducting quantum bits. For frequency-adjustable superconducting quantum bits, a DC longitudinal field signal can be used to adjust their eigenfrequency; coupled bits can often be connected using an adjustable coupler, and by adjusting the longitudinal field strength on the adjustable coupler, the coupling strength between bits can be adjusted. Furthermore, by modulating the longitudinal field signal, quantum two-bit gate operations such as iSWAP gates and CZ gates can be efficiently implemented. Since the longitudinal field modulation signal will cause the bit's eigenfrequency to shift, and this shift is closely related to the amplitude of the longitudinal field modulation signal, based on this, the longitudinal field modulation of superconducting quantum bits also has potential applications in the field of quantum precision measurement.

[0004] Superconducting qubits are driven using microwave signals, with microwave control signals emitted from an external room-temperature environment. Because superconducting qubit samples are typically stored in extremely low-temperature environments, the microwave signal undergoes extreme temperature fluctuations before driving the qubit. This causes waveform deformation and introduces nonlinear effects, resulting in varying amplitude-frequency responses for microwave signals of different frequencies. Because samples for low-temperature experiments are often placed inside dilution refrigerators, it is difficult to directly measure the amplitude-frequency response characteristics of submicrowave signals at extremely low temperatures using room-temperature measurement and control systems.

[0005] The lack of an amplitude-frequency response characteristic curve makes it difficult to determine the appropriate power required to drive the sample using a longitudinal field, which is not conducive to achieving high-precision quantum gate operations. Based on the above considerations, it is very important to develop a new method to measure the amplitude-frequency response curve of sub-microwave signals in extreme temperature environments. Summary of the Invention

[0006] To this end, the present invention provides a method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system to solve the problems raised in the background technology.

[0007] To achieve the above object, the present invention provides the following technical solution: a method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system, comprising the following steps:

[0008] Step 1: Calibrate the eigenfrequency of the quantum bit and the DC intensity of the longitudinal field;

[0009] Step 2: Select the appropriate longitudinal field DC bias point;

[0010] Step 3: Determine the gate parameters under the longitudinal field DC bias point;

[0011] Step 4: Use Ramsey waveform to measure the frequency shift introduced by the modulated longitudinal field;

[0012] Step 5: Change the frequency of the alternating longitudinal field signal and repeat step 4 to obtain the amplitude-frequency response characteristic curve.

[0013] Preferably, step 1 comprises the following steps: applying DC longitudinal field signals of different intensities to a single quantum bit, and measuring the energy spectrum of the bit under the DC longitudinal field signals of different intensities, thereby calibrating the relationship between the longitudinal field intensity and the eigenfrequency of the double-junction quantum bit; theoretically, the relationship between the eigenfrequency and the magnetic flux of the sample satisfies formula (1):

[0014]

[0015] Where ω represents the eigenfrequency of the bit, E J represents the Josephson energy, E C represents the charge energy, Φ ext Represents the external magnetic flux, that is, the longitudinal field amplitude here, Φ0 represents the magnetic flux quantum; using the energy spectrum information under different intensities of DC longitudinal field, the above function is fitted to ensure that the eigenfrequency of the bit under each longitudinal field amplitude and the first and second order derivatives of the bit eigenfrequency with respect to the longitudinal field intensity are obtained. and

[0016] Preferably, step 2, specifically the following steps: in order to make the frequency offset introduced by the longitudinal field modulation more obvious, in principle, a suitable DC bias point needs to be selected before the longitudinal field signal is parameter modulated; considering that the signal form of the longitudinal field modulation satisfies Φ(t)=Φ dc +Φ ac cos(ω z t), where Φ dc >>Φ ac , Φ is the modulated longitudinal field signal, Φ dc is the intensity of the DC part of the longitudinal field, Φ ac is the intensity of the longitudinal field AC part, ω z is the oscillation frequency of the longitudinal field signal; the longitudinal field signal is added to the quantum bit, considering the small amount Φ ac cos(ωz t) Expand and then perform time averaging. The bit eigenfrequency should satisfy:

[0017]

[0018] Place the longitudinal field DC bias point at Large enough for any location.

[0019] Preferably, step three comprises the following steps: first calibrating the eigenfrequency of the bit at the longitudinal field DC bias point; based on the selected longitudinal field DC bias point, driving the bit at the corresponding eigenfrequency according to the energy spectrum information to make it perform Rabi oscillation, and calibrating the bit The driving time corresponding to the gate is then used to accurately calibrate the eigenfrequency of the bit at this time using the detuned Ramsey waveform.

[0020] Preferably, step 4, specifically the following steps: Consider a Ramsey waveform, the system keeps adding the selected DC longitudinal field bias during the entire measurement sequence, first input a calibrated in step 3 into the system gate, then add an alternating vertical field signal to the system, and then add a calibrated The gate is opened, and finally the detection signal is input to read the measurement result. The duration of the alternating longitudinal field signal is continuously changed. Based on the principle of Ramsey waveform measurement, it is observed that there is an oscillation relationship between the bit population and the duration of the alternating longitudinal field signal. The oscillation frequency is the frequency offset introduced by the longitudinal field modulation signal. Formula (2) has pointed out that the size of this offset is only related to the intensity of the alternating longitudinal field signal felt by the bit. Therefore, the frequency offset can be used to infer the intensity of the alternating longitudinal field signal felt by the bit at this time, that is:

[0021]

[0022] Preferably, step five specifically comprises the following steps: maintaining the intensity of the longitudinal field modulation signal input at room temperature unchanged, changing the frequency of the alternating longitudinal field signal, repeating step four, obtaining a series of relationships between the longitudinal field signal frequency and the frequency offset, and based on the analysis of formula (3), obtaining the relationship between the alternating longitudinal field signal frequency and the alternating longitudinal field signal intensity felt by the quantum bit, that is, obtaining the required amplitude-frequency response relationship.

[0023] The present invention has the following advantages:

[0024] 1. The present invention realizes the measurement of amplitude-frequency curve response in extreme temperature-varying environments based on the response of superconducting quantum bits to longitudinal fields. During the entire operation, all signal transmission and measurement are carried out at room temperature, which meets the operating temperature range of general arbitrary waveform generators and microwave sources and is easy to implement.

[0025] 2. The present invention is implemented using a single frequency-adjustable superconducting quantum bit, which does not have high requirements on the sample itself. Moreover, since it does not involve multiple bits, the requirements for phase calibration are not high, and the operation is relatively simple.

[0026] 3. The longitudinal field signal does not need to go through the IQ mixing process, the spurious frequency is small, and the single-frequency characteristics of the signal are obvious, ensuring the accuracy of the amplitude-frequency response curve measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A flow chart of the method for measuring the amplitude-frequency response of sub-microwave signals in an extreme temperature-varying system provided by the present invention;

[0028] Figure 2 The present invention provides Figure 1 The waveform timing involved in step four.

[0029] Figure 3 This is an example diagram of Ramsey oscillation measured on an Oxford Triton 400 refrigerator using the method provided by the present invention.

[0030] Figure 4 This is an example diagram of Ramsey oscillation measured on an Oxford Triton 400 refrigerator using the method provided by the present invention.

[0031] Figure 5 The figure shows the amplitude-frequency response results measured on an Oxford Triton 400 refrigerator using the method provided by the present invention.

[0032] Figure 6 This is an example diagram of Ramsey oscillation measured on an Oxford Triton 500 refrigerator using the method provided by the present invention.

[0033] Figure 7 The figure shows the amplitude-frequency response results measured on an Oxford Triton 500 refrigerator using the method provided by the present invention. DETAILED DESCRIPTION

[0034] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0035] Example

[0036] In this embodiment, the microwave source used to drive the quantum bit is the R&SSGS100ASGMA radio frequency source, and its operating temperature range is 291.15K-306.15K. The arbitrary waveform generator used for the mixing signal and longitudinal field driving signal of the IQ mixing is the Keysight M3202APXIe arbitrary waveform generator, and the operating temperature range of the arbitrary waveform generator is 273.15K-313.15K. The bit driving signal and the longitudinal field signal are generated at room temperature and reach the sample through the microwave line. The quantum bit sample is inside the Oxford Triton 400 dilution refrigerator, and the temperature near the sample is on the order of 10mK. The digital acquisition card uses the Alazar Tech ATS9870, and its operating temperature range is 273.15K-328.15K. The measurement goal of this embodiment is to measure the amplitude-frequency response introduced by the extreme temperature change of the sub-microwave signal starting from room temperature and entering the vicinity of the quantum bit sample through the microwave line. Since the digital acquisition card cannot work directly in an ultra-low temperature environment, it is impossible to directly measure the amplitude-frequency response characteristics in an ultra-low temperature environment. By utilizing the method of the present invention, the amplitude-frequency response characteristics of the sample position can be effectively measured.

[0037] Refer to the instruction manual Figure 1-2 , a method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to this embodiment includes the following steps:

[0038] Step 1: Calibrate the eigenfrequency of the quantum bit against the DC longitudinal field strength. The specific steps are as follows: by adding DC longitudinal field signals of different strengths to a single quantum bit, the energy spectrum of the bit under the DC longitudinal field signals of different strengths is measured respectively, thereby calibrating the relationship between the longitudinal field strength and the eigenfrequency of the double-junction quantum bit; theoretically, the relationship between the eigenfrequency of the sample and the magnetic flux satisfies the formula (1)

[0039]

[0040] Where ω represents the eigenfrequency of the bit, E J represents the Josephson energy, E C represents the charge energy, Φ ext Represents the external magnetic flux, that is, the longitudinal field amplitude here, Φ0 represents the magnetic flux quantum; using the energy spectrum information under different intensities of DC longitudinal field, the above function is fitted to ensure that the eigenfrequency of the bit under each longitudinal field amplitude and the first and second order derivatives of the bit eigenfrequency with respect to the longitudinal field intensity are obtained. and

[0041] Step 2: Select a suitable DC bias point for the longitudinal field. The specific steps are as follows: In order to make the frequency offset introduced by the longitudinal field modulation more obvious, in principle, a suitable DC bias point needs to be selected before the longitudinal field signal is modulated. Considering that the signal form of the longitudinal field modulation satisfies Φ(t)=Φdc +Φ ac cos(ω z t), where Φ dc >>Φ ac , Φ is the modulated longitudinal field signal, Φ dc is the intensity of the DC part of the longitudinal field, Φ ac is the intensity of the longitudinal field AC part, ω z is the oscillation frequency of the longitudinal field signal; the longitudinal field signal is added to the quantum bit, considering the small amount Φ ac cos(ω z t) Expand and then perform time averaging. The bit eigenfrequency should satisfy:

[0042]

[0043] Place the longitudinal field DC bias point at Large enough for any location.

[0044] Step 3: Determine the gate parameters under the longitudinal field DC bias point. The specific steps are as follows: first, calibrate the eigenfrequency of the bit at the longitudinal field DC bias point; based on the selected longitudinal field DC bias point, drive the bit with the corresponding eigenfrequency according to the energy spectrum information to make it do Rabi oscillation, and calibrate the bit. The driving time corresponding to the gate is then used to accurately calibrate the eigenfrequency of the bit at this time using the detuned Ramsey waveform.

[0045] Step 4: Use Ramsey waveform to measure the frequency shift introduced by the modulated longitudinal field. The specific steps are as follows: Consider a Ramsey waveform. The system keeps adding the selected DC longitudinal field bias during the entire measurement sequence. First, a frequency offset calibrated in step 3 is input into the system. gate, then add an alternating vertical field signal to the system, and then add a calibrated The gate is opened, and finally the detection signal is input to read the measurement result. The duration of the alternating longitudinal field signal is continuously changed. Based on the principle of Ramsey waveform measurement, it is observed that there is an oscillation relationship between the bit population and the duration of the alternating longitudinal field signal. The oscillation frequency is the frequency offset introduced by the longitudinal field modulation signal. Formula (2) has pointed out that the size of this offset is only related to the intensity of the alternating longitudinal field signal felt by the bit. Therefore, the frequency offset can be used to infer the intensity of the alternating longitudinal field signal felt by the bit at this time, that is:

[0046]

[0047] Specific visible Figure 3 As shown, Figure 3 The measurement results obtained using Ramsey waveform at longitudinal field frequencies of 50 MHz and 350 MHz are shown respectively. Figure 4As shown in Figure 1, taking a longitudinal field frequency of 100 MHz as an example, the oscillation measured using the Ramsey waveform can be fitted to determine the bit eigenfrequency shift introduced by the longitudinal field. The fitted bit eigenfrequency shift here is 17.61 MHz, meaning the bit eigenfrequency offset is 17.61 MHz. By back-calculating based on formula (3), the intensity of the alternating longitudinal field signal felt by the bit can be obtained.

[0048] Step 5: Change the frequency of the alternating longitudinal field signal and repeat step 4 to obtain the amplitude-frequency response characteristic curve. The specific steps are: keep the intensity of the longitudinal field modulation signal input at room temperature unchanged, change the frequency of the alternating longitudinal field signal, repeat step 4, and obtain a series of relationships between the longitudinal field signal frequency and the bit frequency offset. Figure 5 An example of measurement results is shown, showing the relationship between the bit's eigenfrequency shift induced by the longitudinal field and the longitudinal field frequency. Under the influence of alternating longitudinal fields of the same intensity but different frequencies, the bit's eigenfrequency shift varies. Based on the analysis of formula (3), the relationship between the alternating longitudinal field signal frequency and the alternating longitudinal field signal intensity felt by the quantum bit is obtained, thus obtaining the required amplitude-frequency response relationship.

[0049] The above scheme is general and can be implemented in different refrigerator systems. In another set of tests, the quantum bit sample was inside the Oxford Triton500 dilution refrigerator, and the temperature near the sample was on the order of 10mK. The digital acquisition card used was AlazarTech ATS9371, whose operating temperature range was 273.15K-328.15K. The other equipment was consistent with the previous case. Similarly, based on the mentioned step 4, the corresponding Ramsey waveform measurement results can be obtained. For example Figure 6 As shown in the figure, in the Triton500 dilution refrigerator, when the vertical field frequency is 350MHz, the fitted bit eigenfrequency shift is 13.05MHz, and the bit frequency eigenfrequency offset is 13.05MHz. Based on the step 5 mentioned above, the relationship between different vertical field signal frequencies and bit eigenfrequency offsets can be obtained, that is, Figure 7 As shown. Based on the reverse calculation of formula (3), the intensity of the alternating longitudinal field signal felt by the bit can be obtained. Based on the above discussion, it can be seen that this solution has good adaptability in various dilution refrigerators and digital acquisition cards.

[0050] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system, characterized by: The following steps are involved: Step 1: Calibrate the eigenfrequency of the quantum bit to the longitudinal field DC intensity, fitting the eigenfrequency of the bit at each longitudinal field amplitude and the first-order and second-order derivatives of the bit eigenfrequency with respect to the longitudinal field intensity, providing parameters for the subsequent calculation of the longitudinal field DC bias point and the alternating longitudinal field signal intensity; Step 2: Selecting a suitable longitudinal field DC bias point based on the second-order derivative obtained in step 1 to obtain the relationship between the eigenfrequency offset introduced by the longitudinal field modulation and the second-order derivative of the longitudinal field intensity; Step 3: Determine the gate parameters under the longitudinal field DC bias point based on the longitudinal field DC bias point obtained in step 2, including calibrating the bit The driving time and eigenfrequency corresponding to the gate provide parameters for calculating the strength of the alternating longitudinal field signal; Step 4: Use the bits from step 3 The Ramsey waveform is constructed by measuring the population oscillation under the action of the alternating longitudinal field to obtain the frequency offset introduced by the modulated longitudinal field. Based on the relationship between the intrinsic frequency offset introduced by the longitudinal field modulation in step 2 and the second-order derivative of the longitudinal field intensity, the intensity of the alternating longitudinal field signal is inferred. Step 5: Change the frequency of the alternating longitudinal field signal and repeat step 4 to obtain the amplitude-frequency response characteristic curve.

2. The method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to claim 1, characterized in that: Step 1, specifically: by adding DC longitudinal field signals of different intensities to a single quantum bit, the energy spectrum of the bit under the DC longitudinal field signals of different intensities is measured respectively, thereby calibrating the relationship between the longitudinal field intensity and the eigenfrequency of the double-junction quantum bit; the relationship between the eigenfrequency and the magnetic flux of the sample satisfies the formula (1) Where ω represents the eigenfrequency of the bit, E J represents the Josephson energy, E C represents the charge energy, Φ ext Represents the external magnetic flux, that is, the longitudinal field amplitude here, and Φ0 represents the magnetic flux quantum; using the energy spectrum information under different intensities of DC longitudinal field, formula (1) is fitted to ensure that the eigenfrequency of the bit under each longitudinal field amplitude and the first and second order derivatives of the bit eigenfrequency with respect to the longitudinal field intensity are obtained. and 3. The method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to claim 2, characterized in that: Step 2, specifically: in order to make the frequency offset introduced by the longitudinal field modulation more obvious, in principle, a suitable DC bias point needs to be selected before the longitudinal field signal is modulated; the signal form of the longitudinal field modulation satisfies Φ(t)=Φ dc +Φ ac cos(ω z t), where Φ dc >>Φ ac , Φ is the modulated longitudinal field signal, Φ dc is the intensity of the DC part of the longitudinal field, Φ ac is the intensity of the longitudinal field AC part, ω z is the oscillation frequency of the longitudinal field signal; the longitudinal field signal is added to the quantum bit, considering the small amount Φ ac cos(ω z t) Expand and then perform time averaging. The bit eigenfrequency should satisfy: Place the longitudinal field DC bias point at Large enough for any location.

4. The method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to claim 3, characterized in that: Step 3, specifically the following steps: first calibrate the eigenfrequency of the bit at the longitudinal field DC bias point; based on the selected longitudinal field DC bias point, according to the energy spectrum information, drive the bit at the corresponding eigenfrequency to make it do Rabi oscillation, and calibrate the bit The driving time corresponding to the gate is then used to accurately calibrate the eigenfrequency of the bit at this time using the detuned Ramsey waveform.

5. The method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to claim 4, characterized in that: Step 4: Consider a Ramsey waveform. The system keeps adding the selected DC longitudinal field bias during the entire measurement sequence. First, a calibrated value in step 3 is input into the system. gate, then add an alternating vertical field signal to the system, and then add a calibrated The gate is opened, and finally the detection signal is input to read the measurement result. The duration of the alternating longitudinal field signal is continuously changed. Based on the principle of Ramsey waveform measurement, it is observed that there is an oscillation relationship between the bit population and the duration of the alternating longitudinal field signal. The oscillation frequency is the frequency offset introduced by the longitudinal field modulation signal. Formula (2) has pointed out that the size of this offset is only related to the intensity of the alternating longitudinal field signal felt by the bit. Therefore, the frequency offset is used to infer the intensity of the alternating longitudinal field signal felt by the bit at this time, that is:

6. The method for measuring the amplitude-frequency response of a sub-microwave signal in an extreme temperature-varying system according to claim 5, characterized in that: Step five, the specific steps are: keep the input longitudinal field modulation signal intensity at room temperature unchanged, change the frequency of the alternating longitudinal field signal, repeat step four, and obtain a series of relationships between the longitudinal field signal frequency and the frequency offset. Based on the analysis of formula (3), the relationship between the alternating longitudinal field signal frequency and the alternating longitudinal field signal intensity felt by the quantum bit is obtained, that is, the required amplitude-frequency response relationship is obtained.

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