Resistance measurement method and device of superconducting quantum interferometer and application of resistance measurement method and device

Abstract

The invention discloses a resistance measurement method and device of a superconducting quantum interferometer and application of the resistance measurement method and device, and belongs to the technical field of quantum chip measurement. The superconducting quantum interferometer comprises a first Josephson junction and a second Josephson junction which are connected in parallel, the first resistance of the first Josephson junction is different from the second resistance of the second Josephson junction, and the resistance measurement method of the superconducting quantum interferometer comprises the steps that the equivalent resistance and the asymmetry degree of the superconducting quantum interferometer are obtained; and determining a first resistance and a second resistance based on the asymmetry degree and the equivalent resistance. According to the method, the resistance values of the two Josephson junctions connected in parallel in the superconducting quantum interferometer can be efficiently and accurately calculated based on the obtained asymmetry degree and equivalent resistance of the superconducting quantum interferometer.

Description

Technical Field

[0001] This invention belongs to the field of quantum chip measurement technology, specifically a method, device, and application for measuring the resistance of a superconducting quantum interference device. Background Technology

[0002] The key structure on a superconducting quantum chip is the superconducting quantum bit, and the key structure of a superconducting quantum bit is the Josephson junction. Currently, the structure of a superconducting quantum bit mainly consists of a superconducting quantum interference device (SQI) composed of two Josephson junctions connected in parallel, and a capacitor connected in parallel with the SQI. Since the resistance of the Josephson junction is a core parameter of the superconducting quantum bit, accurate measurement of the resistance of the Josephson junction is of great significance.

[0003] Currently, the normal-state resistance of a Josephson junction is obtained by applying a signal exceeding the critical current at a refrigerator temperature of 10 mK, and then obtaining the non-superconducting resistance of the Josephson junction based on the IV curve. However, during the measurement process, applying the current signal causes the refrigerator to heat up, and the measurement can only continue after the refrigerator cools down, which affects efficiency.

[0004] Therefore, how to efficiently obtain the normal resistance value of the Josephson junction is an urgent problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus and application for measuring the resistance of a superconducting quantum interference device (QFID) to overcome the shortcomings of the prior art. It can efficiently measure the resistance of a QFID.

[0006] The solution presented in this application example is implemented through the following steps.

[0007] In a first aspect, an example of this application proposes a method for measuring the resistance of a superconducting quantum interference device (SQUID), the SQUID comprising a first Josephson junction and a second Josephson junction connected in parallel, wherein a first resistance of the first Josephson junction and a second resistance of the second Josephson junction are different, the method comprising:

[0008] Obtain the equivalent resistance and asymmetry of the superconducting quantum interference device;

[0009] The first resistor and the second resistor are determined based on the asymmetry and the equivalent resistance.

[0010] In one embodiment of this application, determining the first resistance and the second resistance based on the asymmetry and the equivalent resistance includes:

[0011] The first resistance and the second resistance are determined based on the first correspondence between the asymmetry and the first resistance and the second resistance, and the second correspondence between the equivalent resistance and the first resistance and the second resistance; wherein the asymmetry is inversely proportional to the sum of the first resistance and the second resistance, and directly proportional to the difference between the second resistance and the first resistance.

[0012] In one embodiment of this application, obtaining the equivalent resistance of the superconducting quantum interference device includes:

[0013] Obtain the first step frequency corresponding to the transition from the v0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device;

[0014] The self-capacitance parameter of the superconducting quantum interference device is determined based on the difference between the first step frequency and the second step frequency.

[0015] The equivalent resistance is determined based on the square of the first step frequency and the self-capacitance parameter.

[0016] In one embodiment of this application, obtaining the asymmetry of the superconducting quantum interference device includes:

[0017] Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device;

[0018] The anharmonic parameters of the superconducting quantum interference device are determined based on the difference between the first step frequency and the second step frequency.

[0019] Obtain the upper degeneracy point frequency and the lower degeneracy point frequency of the superconducting quantum interference device;

[0020] The asymmetry is determined based on the sum of the anharmonic parameter and the upper degenerate point frequency, and the sum of the anharmonic parameter and the lower degenerate point frequency.

[0021] In one embodiment of this application, determining the asymmetry based on the sum of the anharmonic parameter and the upper degenerate point frequency, and the sum of the anharmonic parameter and the lower degenerate point frequency, includes:

[0022] The sum of the anharmonic parameter and the upper degenerate point frequency is taken as the first sum, and the sum of the anharmonic parameter and the lower degenerate point frequency is taken as the second sum.

[0023] The asymmetry is obtained by squared the quotient of the first sum and the second sum.

[0024] In one embodiment of this application, obtaining the upper degeneracy point frequency and the lower degeneracy point frequency of the superconducting quantum interference device includes:

[0025] By applying a Z signal only to the superconducting quantum interference device, a target curve of the cavity frequency of the readout cavity coupled to the superconducting quantum interference device as a function of the voltage of the Z signal is obtained;

[0026] Based on the target curve, the voltage corresponding to the peak in the target curve is taken as the first voltage, and the voltage corresponding to the trough in the target curve is taken as the second voltage;

[0027] A Z signal with the first voltage is applied to the superconducting quantum interference device (QFID), and the voltage of the XY signal applied to the QFID is changed to obtain the frequency corresponding to the first transition of the QFID, which is used as the upper degeneracy point frequency.

[0028] A Z signal with the second voltage is applied to the superconducting quantum interference device (SQI), and the voltage of the XY signal applied to the SQI is changed to obtain the frequency corresponding to the first transition of the SQI, which is taken as the lower degeneracy point frequency.

[0029] In one embodiment of this application, determining the anharmonic parameters of the superconducting quantum interference device based on the difference between the first step frequency and the second step frequency includes:

[0030] Half of the difference between the first step frequency and the second step frequency is taken as the value of the anharmonic parameter.

[0031] In one embodiment of this application, obtaining the asymmetry of the superconducting quantum interference device includes:

[0032] Obtain the voltage value, upper degeneracy point frequency, and anharmonic parameters corresponding to the remanence of the superconducting quantum interference device;

[0033] Multiple Z signals satisfying a preset voltage range are applied to the superconducting quantum interference device (SQI), and the first transition frequency of the SQI from the |0> state to the |1> state corresponding to the voltage value of each Z signal is obtained, thereby generating a target spectrum curve.

[0034] The asymmetry of the superconducting quantum interference device is determined based on the target fitting formula and the target spectrum curve.

[0035] Secondly, examples of this application provide a resistance measurement device for a superconducting quantum interference device (QFID), the QFID comprising a first Josephson junction and a second Josephson junction connected in parallel, wherein a first resistance of the first Josephson junction and a second resistance of the second Josephson junction are different, and the device comprises:

[0036] The acquisition module is used to acquire the equivalent resistance and asymmetry of the superconducting quantum interference device;

[0037] A resistance determination module is used to determine the first resistance and the second resistance based on the asymmetry and the equivalent resistance.

[0038] In one embodiment of this application, the resistance determination module is specifically used for:

[0039] The first resistance and the second resistance are determined based on the first correspondence between the asymmetry and the first resistance and the second resistance, and the second correspondence between the equivalent resistance and the first resistance and the second resistance; wherein the asymmetry is inversely proportional to the sum of the first resistance and the second resistance, and directly proportional to the difference between the second resistance and the first resistance.

[0040] In one embodiment of this application, the acquisition module is specifically used for:

[0041] Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device;

[0042] The self-capacitance parameter of the superconducting quantum interference device is determined based on the difference between the first step frequency and the second step frequency.

[0043] The equivalent resistance is determined based on the square of the first step frequency and the self-capacitance parameter.

[0044] In one embodiment of this application, the acquisition module is specifically used for:

[0045] Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device;

[0046] The anharmonic parameters of the superconducting quantum interference device are determined based on the difference between the first step frequency and the second step frequency.

[0047] Obtain the upper degeneracy point frequency and the lower degeneracy point frequency of the superconducting quantum interference device;

[0048] The asymmetry is determined based on the sum of the anharmonic parameter and the upper degenerate point frequency, and the sum of the anharmonic parameter and the lower degenerate point frequency.

[0049] In one embodiment of this application, the acquisition module is specifically used for:

[0050] The sum of the anharmonic parameter and the upper degenerate point frequency is taken as the first sum, and the sum of the anharmonic parameter and the lower degenerate point frequency is taken as the second sum.

[0051] The asymmetry is obtained by squared the quotient of the first sum and the second sum.

[0052] In one embodiment of this application, the acquisition module is specifically used for:

[0053] By applying a Z signal only to the superconducting quantum interference device, a target curve of the cavity frequency of the readout cavity coupled to the superconducting quantum interference device as a function of the voltage of the Z signal is obtained;

[0054] Based on the target curve, the voltage corresponding to the peak in the target curve is taken as the first voltage, and the voltage corresponding to the trough in the target curve is taken as the second voltage;

[0055] A Z signal with the first voltage is applied to the superconducting quantum interference device (QFID), and the voltage of the XY signal applied to the QFID is changed to obtain the frequency corresponding to the first transition of the QFID, which is used as the upper degeneracy point frequency.

[0056] A Z signal with the second voltage is applied to the superconducting quantum interference device (SQI), and the voltage of the XY signal applied to the SQI is changed to obtain the frequency corresponding to the first transition of the SQI, which is taken as the lower degeneracy point frequency.

[0057] In one embodiment of this application, the acquisition module is specifically used for:

[0058] Obtain the voltage value, upper degeneracy point frequency, and anharmonic parameters corresponding to the remanence of the superconducting quantum interference device;

[0059] Multiple Z signals satisfying a preset voltage range are applied to the superconducting quantum interference device (SQI), and the first transition frequency of the SQI from the |0> state to the |1> state corresponding to the voltage value of each Z signal is obtained, thereby generating a target spectrum curve.

[0060] The asymmetry of the superconducting quantum interference device is determined based on the target fitting formula and the target spectrum curve.

[0061] Thirdly, examples of this application present an application of the resistance measurement method of the superconducting quantum interference device described in the first aspect above in the manufacture or measurement of a quantum chip, the quantum chip comprising superconducting qubits, the superconducting qubits comprising the superconducting quantum interference device.

[0062] In the resistance measurement method of the superconducting quantum interference device described in the foregoing example of this application, the resistance values ​​of the two Josephson junctions connected in parallel in the superconducting quantum interference device are calculated based on the obtained asymmetry and equivalent resistance of the superconducting quantum interference device. This method can efficiently and accurately perform Josephson junction resistance measurement. Attached Figure Description

[0063] To illustrate this more clearly, the accompanying drawings used in the description will be briefly introduced below.

[0064] Figure 1 This is a flowchart of a resistance measurement method using a superconducting quantum interference device, as shown in one example of this application.

[0065] Figure 2 This is a flowchart of a resistance measurement method for a superconducting quantum interference device, as shown in another example of this application;

[0066] Figure 3 This is a flowchart of a resistance measurement method for a superconducting quantum interference device, as shown in another example of this application;

[0067] Figure 4 This is a flowchart of a resistance measurement method for a superconducting quantum interference device, as shown in another example of this application;

[0068] Figure 5 This is a structural block diagram of the resistance measurement device of a superconducting quantum interference device in one example of this application. Detailed Implementation

[0069] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of this application. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0070] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "left", "right", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0071] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0072] Two Josephson junctions connected in parallel form a superconducting quantum interference device (SQUID), which can be equivalently viewed as a Josephson junction. The asymmetry parameter 'd' of the SQUID is related to the Josephson energy of the parallel Josephson junction. When d ≠ 0, the Josephson energies of the two Josephson junctions are not equal, and this is called an asymmetric SQUID. Asymmetric SQUIDs are mainly used to control the adjustable frequency range of qubits, bringing the frequency interval between the upper and lower degeneracy points of the qubits closer together, making the frequency change with magnetic flux more gradual. This is beneficial for optimizing the phase decoherence time of the qubits. The final engineering manifestation of a Josephson junction is its resistance value. When the resistances of the parallel Josephson junctions in the SQUID are not equal, d ≠ 0, confirming that the SQUID is an asymmetric SQUID.

[0073] Currently, the normal-state resistance of a Josephson junction is obtained by applying a signal exceeding the critical current at a refrigerator temperature of 10 mK, and then using the IV curve to obtain the resistance of the Josephson junction in its non-superconducting state. However, during the measurement process, the applied electrical signal must always be greater than the critical current. Applying this current signal causes the refrigerator to heat up, and the measurement can only continue after the refrigerator cools down. Therefore, in the current technology for measuring the normal-state resistance of a Josephson junction, both electrical signal modulation and refrigerator temperature control are required simultaneously, which obviously affects the efficiency of the normal-state resistance measurement.

[0074] Based on this, such as Figure 1 As shown, an embodiment of the present invention provides a method for measuring the resistance of a superconducting quantum interference device, the method comprising:

[0075] S110, to obtain the equivalent resistance and asymmetry of the superconducting quantum interference device;

[0076] S120, based on the asymmetry and equivalent resistance, determine the first resistor and the second resistor.

[0077] The superconducting quantum interference device (SQUID) includes a first Josephson junction and a second Josephson junction connected in parallel. The first resistance of the first Josephson junction and the second resistance of the second Josephson junction are different. The technical solution of this application is applicable to superconducting quantum interference devices with unequal resistances of the two parallel Josephson junctions. The equivalent resistance of the superconducting quantum interference device is the equivalent resistance corresponding to the resistances of the two unequal parallel Josephson junctions.

[0078] It should be noted that the parameters obtained in this application are the equivalent resistance and asymmetry of a superconducting quantum interference device operating in a low-temperature environment, and all of them are obtained non-destructively, but the specific method of obtaining the equivalent resistance and asymmetry is not limited.

[0079] In one embodiment of this application, the asymmetry parameter can be determined based on the Josephson energy corresponding to the first Josephson node and the second Josephson node.

[0080] Specifically,

[0081]

[0082] Where γ is the ratio of the Josephson energies of the two Josephson junctions in the superconducting quantum interference device, and E j1 For the Josephson energy of the first Josephson knot, E j2 Josephson energy for the second Josephson knot.

[0083]

[0084] Where d is the asymmetric parameter of the superconducting quantum interference device.

[0085] In one embodiment of this application, the frequency ω corresponding to the transition from the |0> state to the |1> state by the superconducting quantum interference device can be used. 01 The equivalent resistance is determined by the self-capacitance parameters of the superconducting quantum interference device.

[0086] Specifically,

[0087] ω 01 =k*C -0.5 *R -0.5

[0088] Where R is the equivalent resistance; C is the self-capacitance parameter; ω 01 The frequency corresponding to the transition of the superconducting quantum interference device from the |0> state to the |1> state.

[0089] Specifically, the equivalent resistance and asymmetry satisfy the following relationships with the first and second resistances:

[0090]

[0091] Where R is the equivalent resistance; R1 is the first resistance; R2 is the second resistance; and d is the degree of asymmetry.

[0092] Based on the above formula, the resistance values ​​of the two Josephson junctions connected in parallel in the superconducting quantum interference device can be determined according to the obtained asymmetry and equivalent resistance.

[0093] The technical solution disclosed in this application determines the resistance values ​​of two parallel Josephson junctions by obtaining the asymmetry and equivalent resistance of the superconducting quantum interference device (SQFID). Compared with the prior art, this application determines the parallel resistance values ​​based on the performance parameters of the SQFID, which can improve the accuracy and efficiency of the normal resistance measurement of the SQFID.

[0094] In one embodiment of this application, step S120, which determines the first resistor and the second resistor based on asymmetry and equivalent resistance, includes:

[0095] The first and second resistances are determined based on the first correspondence between the asymmetry and the first and second resistances, and the second correspondence between the equivalent resistance and the first and second resistances; wherein the asymmetry is inversely proportional to the sum of the first and second resistances, and directly proportional to the difference between the second and first resistances.

[0096] because

[0097]

[0098] I c *R≈230

[0099] Among them, E j The Josephson energy of a (single) Josephson junction; Φ0 is the magnetic flux quantum; I c R is the critical current corresponding to the Josephson junction; R is the resistance of the Josephson junction.

[0100] and

[0101]

[0102] Therefore, by combining the above three formulas, we can obtain:

[0103]

[0104] This yields the first correspondence, where the asymmetry is inversely proportional to the sum of the first and second resistances, and directly proportional to the difference between the second and first resistances.

[0105] The second correspondence is:

[0106]

[0107] Where R is the equivalent resistance; R1 is the first resistance; R2 is the second resistance; and d is the asymmetry. The second correspondence is the relationship between conventional parallel resistance and equivalent resistance.

[0108] like Figure 2As shown, in one embodiment of this application, step S110, obtaining the equivalent resistance of the superconducting quantum interference device, includes:

[0109] Step S210: Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device.

[0110] Specifically, the Z signal input to the superconducting quantum interference device (SQFID) is fixed, while the XY signals input to the SQFID are changed. The Rabi oscillation curve is obtained from the readout output port of the readout cavity coupled to the SQFID. Since the amplitude of the Rabi oscillation curve is highest when the XY signal frequency resonates with the SQFID frequency, the voltage corresponding to the first resonance between the XY signal and the SQFID, i.e., the first target voltage value, can be determined based on the Rabi oscillation curve. Based on the SQFID frequency corresponding to the first target voltage value, the first step frequency ω corresponding to the transition from the |0> state to the |1> state of the SQFID is determined. 01 .

[0111] After determining the first step frequency corresponding to the transition of the superconducting quantum interference device (SQI) from state |0> to state |1>, the voltage of the XY signal is increased, and Rabi oscillation curves are acquired. Based on the obtained Rabi oscillation curves, the voltage corresponding to the second resonance between the XY signal and the SQI is determined, i.e., the second target voltage value. Based on the SQI frequency corresponding to the second target voltage value, the second step frequency ω corresponding to the transition of the SQI from state |1> to state |2> is determined. 12 .

[0112] Step S220: Determine the self-capacitance parameters of the superconducting quantum interference device based on the difference between the first step frequency and the second step frequency.

[0113] Specifically, the relationship between the self-capacitance parameter and the anharmonicity of the superconducting quantum interference device is as follows:

[0114]

[0115] Where C is the self-capacitance parameter of the superconducting quantum interference device, h is Planck's constant, e is the elementary charge number, and η is the anharmonic parameter of the superconducting quantum interference device.

[0116] The anharmonic parameters of a superconducting quantum interference device (SQI) are related to the first and second step frequencies as follows:

[0117]

[0118] Where η is the anharmonic parameter of the superconducting quantum interference device, ω 01 ω is the first step frequency corresponding to the transition of the superconducting quantum interference device from the |0> state to the |1> state.12 This is the second step frequency corresponding to the transition of the superconducting quantum interference device from the |1> state to the |2> state.

[0119] In summary, the self-capacitance parameter of the superconducting quantum interference device satisfies the following relationship with the first and second step frequencies:

[0120]

[0121] Based on this, the self-capacitance parameters of the superconducting quantum interference device can be determined by combining the difference between the first and second step frequencies with Planck's constant and the elementary charge number.

[0122] Step S230: Determine the equivalent resistance based on the square of the first step frequency and the self-capacitance parameter.

[0123] Specifically, the frequency corresponding to the transition from the |0> state to the |1> state in a superconducting quantum interference device (SQI) has the following theoretical relationship with the resistance of the SQI:

[0124] ω 01 =k*C -0.5 *R -0.5

[0125] Where k is a constant coefficient, ω 01 denoted as the first step frequency of the superconducting quantum interference device (SQFID), C is the self-capacitance parameter of the SQFID, and R is the equivalent resistance of the SQFID.

[0126] The above formula can be transformed to obtain:

[0127]

[0128] Based on this, the equivalent resistance of the superconducting quantum interference device (SQFID) can be determined by the square of the first step frequency and the self-capacitance parameter of the SQFID.

[0129] Furthermore, by transforming the formula, we can obtain:

[0130]

[0131] Based on this, the first step frequency ω corresponding to the transition from the |0> state to the |1> state in a superconducting quantum interference device can be used as a reference. 01 The second step frequency ω corresponding to the transition from state |1> to state |2> in a superconducting quantum interference device. 12 The equivalent resistance of the superconducting quantum interference device was determined.

[0132] In obtaining the equivalent resistance of the superconducting quantum interference device (SQFID) described above, the frequencies corresponding to the first and second transitions of the SQFID are determined by acquiring the Rabi oscillation curve. Then, based on the correspondence between the frequencies of the first and second transitions and the equivalent resistance, the equivalent resistance is determined. This measurement method only requires obtaining the frequencies of the first and second transitions from the Rabi oscillation curve to determine the equivalent resistance. Since the SQFID operates in a cryogenic environment, this method can accurately determine the equivalent resistance of the SQFID in cryogenic environments.

[0133] like Figure 3 As shown, in one embodiment of this application, step S110, obtaining the asymmetry of the superconducting quantum interference device, includes:

[0134] Step S310: Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state of the superconducting quantum interference device.

[0135] Specifically, the Z signal input to the superconducting quantum interference device (SQFID) is fixed, while the XY signals input to the SQFID are changed. The Rabi oscillation curve is obtained from the readout output port of the readout cavity coupled to the Josephson junction. Since the amplitude of the Rabi oscillation curve is highest when the XY signal frequency resonates with the SQFID frequency, the voltage corresponding to the first resonance between the XY signal and the SQFID, i.e., the first target voltage value, can be determined based on the Rabi oscillation curve. Based on the SQFID frequency corresponding to the first target voltage value, the first step frequency ω corresponding to the transition from the |0> state to the |1> state of the SQFID is determined. 01 .

[0136] After determining the first step frequency corresponding to the transition of the superconducting quantum interference device (SQI) from state |0> to state |1>, the voltage of the XY signal is increased, and Rabi oscillation curves are acquired. Based on the obtained Rabi oscillation curves, the voltage corresponding to the second resonance between the XY signal and the SQI is determined, i.e., the second target voltage value. Based on the SQI frequency corresponding to the second target voltage value, the second step frequency ω corresponding to the transition of the SQI from state |1> to state |2> is determined. 12 .

[0137] Step S320: Determine the anharmonic parameters of the superconducting quantum interference device based on the difference between the first step frequency and the second step frequency.

[0138] The anharmonicity of a superconducting quantum interference device (SQI) is related to the first and second step frequencies as follows:

[0139]

[0140] Where η is the anharmonic parameter of the superconducting quantum interference device, ω 01 ω is the first step frequency corresponding to the transition of the superconducting quantum interference device from the |0> state to the |1> state. 12 This is the second step frequency corresponding to the transition of the superconducting quantum interference device from the |1> state to the |2> state.

[0141] Furthermore, the anharmonic parameters of the superconducting quantum interference device can be determined based on the difference between the first and second step frequencies.

[0142] Step S330: Obtain the upper degeneracy point frequency and lower degeneracy point frequency of the superconducting quantum interference device.

[0143] In this system, a superconducting quantum interference device and capacitive coupling constitute a quantum bit. The upper degeneracy point frequency refers to the highest bit frequency of the quantum bit, and the lower degeneracy point refers to the lowest bit frequency of the quantum bit.

[0144] Step S340: Determine the degree of asymmetry based on the sum of the anharmonic parameter and the upper degenerate point frequency, and the sum of the anharmonic parameter and the lower degenerate point frequency.

[0145] Specifically,

[0146]

[0147] Where, ω 01min ω is the lower degeneracy point frequency of the superconducting quantum interference device. 01max Let η be the upper degeneracy point frequency of the superconducting quantum interference device, η be the anharmonic parameter, and d be the asymmetry.

[0148] Further derivation yields:

[0149]

[0150] Based on this, the asymmetry of the superconducting quantum interference device (SQI) is determined according to the frequencies of the upper and lower degeneracy points of the SQI, the frequencies corresponding to the transition from the |0> state to the |1> state, and the frequencies corresponding to the transition from the |1> state to the |2> state.

[0151] In one embodiment of this application, step S340, which determines the asymmetry based on the sum of the anharmonic parameter and the upper degenerate frequency, and the sum of the anharmonic parameter and the lower degenerate frequency, includes:

[0152] The sum of the anharmonic parameter and the upper degenerate point frequency is taken as the first sum, and the sum of the anharmonic parameter and the lower degenerate point frequency is taken as the second sum.

[0153] The degree of asymmetry is obtained by squared the quotient of the first and second sums.

[0154] Specifically,

[0155]

[0156] Where, ω 01 E represents the bit frequency of a quantum bit. C E is the energy of electric charge. J1 For the Josephson energy of the first Josephson knot, E J2 For the Josephson knot of the second Josephson knot,

[0157] E J1 +E J2 =E J For the total Josephson energy of the superconducting quantum interference device, Φ ext Let Φ be the external magnetic flux of the loop, Φ0 be the magnetic flux quantum, and d be the asymmetry.

[0158] The qubits of an asymmetric superconducting quantum interference device have two operating points, the highest and the lowest, namely ω. 01max Upper degeneracy point frequency, ω 01min The lower degenerate point frequency, according to the above formula, can be obtained as follows:

[0159]

[0160] Transforming the two formulas above, we get:

[0161]

[0162] Where, Φ max The external magnetic flux of the loop corresponding to the upper degenerate point frequency, Φ min Let be the external magnetic flux of the loop corresponding to the lower degenerate point frequency, and □ be the reduced Planck constant.

[0163] Based on the trigonometric function theorem, the above formula can be transformed to obtain:

[0164]

[0165] Theoretically, Φ max =0, And E J1 +E J2 =E J Therefore, from the above formula, we can obtain:

[0166]

[0167] because,

[0168]

[0169] Where C represents the self-capacitance parameter of the superconducting quantum interference device, and I c It is the critical current of the Josephson junction.

[0170] It can be deduced that:

[0171]

[0172] Based on this, the asymmetry of the superconducting quantum interference device (SQI) can be determined by the sum of the upper degenerate point frequency and the anharmonic parameter, as well as the sum of the lower degenerate point frequency and the anharmonic parameter.

[0173] like Figure 4 As shown, in one embodiment of this application, step S330, obtaining the upper degeneracy point frequency and lower degeneracy point frequency of the superconducting quantum interference device, includes:

[0174] Step S410: Apply the Z signal only to the superconducting quantum interference device (SQI) to obtain the target curve of the cavity frequency of the readout cavity coupled to the SQI as a function of the voltage of the Z signal.

[0175] Specifically, only the voltage-changing Z signal is applied to the superconducting quantum interference device (SQI), without applying the XY signal. The output signal is obtained from the readout output port of the readout cavity coupled to the SQI, and thus the target curve of the cavity frequency of the readout cavity as a function of the voltage of the Z signal is obtained.

[0176] Step S420: Based on the target curve, the voltage corresponding to the peak in the target curve is taken as the first voltage, and the voltage corresponding to the trough in the target curve is taken as the second voltage.

[0177] Specifically, when the quantum bit and the readout cavity are in the region of strong coupling and large detuning parameters, i.e. dispersion shift occurs, the Z signal can modulate the cavity frequency. A modulation spectrum curve of the cavity frequency changing with the Z signal voltage can be fitted, indicating that the frequency of the quantum bit is adjustable and there is a bit frequency modulation spectrum. The voltage value corresponding to the highest cavity frequency point and the voltage value corresponding to the lowest cavity frequency point can be obtained from the modulation spectrum curve image.

[0178] Step S430: Apply a Z signal with a first voltage to the superconducting quantum interference device (SQI), change the voltage of the XY signal applied to the SQI, and obtain the frequency corresponding to the first transition of the SQI, which is taken as the upper degeneracy point frequency.

[0179] Specifically, the Z signal input to the superconducting quantum interference device (SQI) is fixed as the voltage value corresponding to the highest cavity frequency. The power of the XY signals input to the SQI is varied, and the Rabi oscillation curve is obtained from the readout output port of the readout cavity coupled to the Josephson junction. Since the amplitude of the Rabi oscillation curve is highest when the XY signal frequency resonates with the SQI frequency, the voltage corresponding to the first resonance between the XY signal and the SQI, i.e., the first voltage value, can be determined based on the Rabi oscillation curve. Based on the SQI frequency corresponding to the first voltage value, the frequency ω corresponding to the transition from the |0> state to the |1> state is determined. 01max , as the frequency of the upper degeneracy point.

[0180] Step S440: Apply a Z signal with a second voltage to the superconducting quantum interference device (SQI), change the voltage of the XY signal applied to the SQI, and obtain the frequency corresponding to the first transition of the SQI, which is taken as the lower degeneracy point frequency.

[0181] Specifically, the Z signal input to the superconducting quantum interference device (SQFID) is fixed as the voltage value corresponding to the lowest cavity frequency. The power of the XY signal input to the SQFID is varied, and the Rabi oscillation curve is obtained from the readout output port of the readout cavity coupled to the Josephson junction. Since the amplitude of the Rabi oscillation curve is highest when the XY signal frequency resonates with the SQFID frequency, the voltage corresponding to the first resonance between the XY signal and the SQFID, i.e., the first voltage value, can be determined based on the Rabi oscillation curve. Based on the SQFID frequency corresponding to the first voltage value, the frequency ω corresponding to the transition from the |0> state to the |1> state is determined. 01min , as the lower degeneracy point frequency.

[0182] In the aforementioned technical solution for obtaining the upper and lower degeneracy frequencies of a superconducting quantum interference device (SQFID), the voltage of the Z-signal is changed to determine the Z-signal voltage corresponding to the highest and lowest cavity frequencies of the readout cavity coupled to the SQFID. Then, the Z-signal voltages are fixed to the values ​​corresponding to the highest and lowest cavity frequencies, respectively. By changing the power of the XY signals input to the SQFID, the upper and lower degeneracy frequencies corresponding to the first transition of the SQFID are determined. Based on this, only the Z-signal and XY signals need to be changed during the entire process of obtaining the upper and lower degeneracy points; no other test signals are required, improving measurement accuracy and reducing the risk of interference during the measurement process.

[0183] In one embodiment of this application, step S320, which determines the anharmonic parameters of the superconducting quantum interference device based on the difference between the first step frequency and the second step frequency, includes:

[0184] Half of the difference between the first and second step frequencies is taken as the value of the anharmonic parameter.

[0185] The anharmonicity of a superconducting quantum interference device (SQI) is related to the first and second step frequencies as follows:

[0186]

[0187] Where η is the anharmonic parameter of the superconducting quantum interference device, ω 01 ω is the first step frequency corresponding to the transition of the superconducting quantum interference device from the |0> state to the |1> state. 12 This is the second step frequency corresponding to the transition of the superconducting quantum interference device from the |1> state to the |2> state.

[0188] In one embodiment of this application, step S110, obtaining the asymmetry of the superconducting quantum interference device, includes:

[0189] Obtain the voltage value, upper degeneracy point frequency, and anharmonic parameters corresponding to the remanence of the superconducting quantum interference device.

[0190] Specifically, obtaining the voltage value corresponding to the remanence of the superconducting quantum interference device includes:

[0191] A voltage-changing Z signal is applied to the superconducting quantum interference device (SQFID) without applying XY signals. The output signal is obtained from the readout output port of the readout cavity coupled to the SQFID, and the target curve of the cavity frequency of the readout cavity as a function of the voltage of the Z signal is obtained. The voltage of the Z signal corresponding to the highest cavity frequency is obtained from this curve, which is the voltage value corresponding to the remanence.

[0192] The specific methods for obtaining the upper degenerate point frequency and anharmonic parameters have been described above and will not be repeated here.

[0193] Multiple Z signals satisfying a preset voltage range are applied to the superconducting quantum interference device (SQI), and the first transition frequency of the SQI from the |0> state to the |1> state corresponding to the voltage value of each Z signal is obtained, generating the target spectrum curve.

[0194] The highest value of the preset voltage range is greater than or equal to the first voltage, and the lowest value of the preset voltage range is less than or equal to the second voltage. The first voltage is the Z signal voltage corresponding to the highest value of the cavity frequency in the target curve of the cavity frequency changing with the Z signal voltage, and the second voltage is the Z signal voltage corresponding to the lowest value of the cavity frequency in the target curve of the cavity frequency changing with the Z signal voltage.

[0195] Specifically, multiple Z signals with different voltage values ​​within a preset voltage range are applied to the superconducting quantum interference device (SQI), and the step frequency of the SQI transitioning from the |0> state to the |1> state under each Z signal is measured to generate the target spectrum curve.

[0196] The asymmetry of the superconducting quantum interference device is determined based on the target fitting formula and the target spectrum curve.

[0197] Specifically, the target fitting formula includes:

[0198] Φ = π × M × (x - offset)

[0199]

[0200] Where Φ is the external magnetic flux of the loop, M is the mutual inductance coefficient, x is the voltage value applied to the Z-line signal, offset is the voltage value corresponding to the remanence, and ω 01 ω is the first step frequency ω corresponding to the transition of a superconducting quantum interference device from the |0> state to the |1> state. 01 ω 01max Let η be the upper degeneracy point of the superconducting quantum interference device, and η be the anharmonic parameter.

[0201] Furthermore, based on the target fitting formula and the obtained target spectrum curve information, the asymmetry in the superconducting quantum interference device (SQI) can be accurately determined. Using this method, the normal resistance of the SQI in a low-temperature environment can be accurately obtained.

[0202] It should be noted that this application provides at least one feasible method for obtaining equivalent resistance and asymmetry, but is not limited to the above-described embodiments. The method for non-destructive measurement of equivalent resistance and asymmetry can be selected according to actual needs.

[0203] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0204] Based on the same inventive concept, this application also provides a resistance measuring device for a superconducting quantum interference device (SQU) for implementing the resistance measuring method of the superconducting quantum interference device described above. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the resistance measuring device for a superconducting quantum interference device provided below can be found in the limitations of the resistance measuring method for the superconducting quantum interference device described above, and will not be repeated here.

[0205] like Figure 5 As shown in the figure, an embodiment of the present invention proposes a resistance measurement device 500 for a superconducting quantum interference device. The superconducting quantum interference device includes a first Josephson junction and a second Josephson junction connected in parallel. The first resistance of the first Josephson junction and the second resistance of the second Josephson junction are different. The device includes:

[0206] Acquisition module 510 is used to acquire the equivalent resistance and asymmetry of the superconducting quantum interference device;

[0207] The resistance determination module 520 is used to determine the first resistance and the second resistance based on the asymmetry and the equivalent resistance.

[0208] In one embodiment of this application, the resistance determination module 520 is specifically used for:

[0209] The first and second resistances are determined based on the first correspondence between the asymmetry and the first and second resistances, and the second correspondence between the equivalent resistance and the first and second resistances; wherein the asymmetry is inversely proportional to the sum of the first and second resistances, and directly proportional to the difference between the second and first resistances.

[0210] In one embodiment of this application, the acquisition module 510 is specifically used for:

[0211] Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state in the superconducting quantum interference device;

[0212] The self-capacitance parameters of the superconducting quantum interference device are determined based on the difference between the first and second step frequencies.

[0213] The equivalent resistance is determined based on the square of the first step frequency and the self-capacitance parameter.

[0214] In one embodiment of this application, the acquisition module 510 is specifically used for:

[0215] Obtain the first step frequency corresponding to the transition from the |0> state to the |1> state and the second step frequency corresponding to the transition from the |1> state to the |2> state in the superconducting quantum interference device;

[0216] The anharmonic parameters of the superconducting quantum interference device are determined based on the difference between the first and second step frequencies.

[0217] Obtain the upper degeneracy point frequency and lower degeneracy point frequency of the superconducting quantum interference device;

[0218] The degree of asymmetry is determined based on the sum of the anharmonic parameter and the upper degenerate frequency, and the sum of the anharmonic parameter and the lower degenerate frequency.

[0219] In one embodiment of this application, the acquisition module 510 is specifically used for:

[0220] The sum of the anharmonic parameter and the upper degenerate point frequency is taken as the first sum, and the sum of the anharmonic parameter and the lower degenerate point frequency is taken as the second sum.

[0221] The degree of asymmetry is obtained by squared the quotient of the first and second sums.

[0222] In one embodiment of this application, the acquisition module 510 is specifically used for:

[0223] By applying a Z signal only to a superconducting quantum interference device (SQI), a target curve of the cavity frequency of the readout cavity coupled to the SQI as a function of the voltage of the Z signal is obtained.

[0224] Based on the target curve, the voltage corresponding to the peak in the target curve is taken as the first voltage, and the voltage corresponding to the trough in the target curve is taken as the second voltage.

[0225] A Z signal with a first voltage is applied to the superconducting quantum interference device (SQI). The voltages of the XY signals applied to the SQI are changed to obtain the frequency corresponding to the first transition of the SQI, which is taken as the upper degeneracy point frequency.

[0226] A Z signal with a second voltage is applied to the superconducting quantum interference device (SQI). The voltages of the XY signals applied to the SQI are changed to obtain the frequency corresponding to the first transition of the SQI, which is taken as the lower degeneracy point frequency.

[0227] In one embodiment of this application, the acquisition module 510 is specifically used for:

[0228] Obtain the voltage value, upper degeneracy point frequency, and anharmonic parameters corresponding to the remanence of the superconducting quantum interference device;

[0229] Multiple Z signals satisfying a preset voltage range are applied to a superconducting quantum interference device (SQI), and the first transition frequency of the SQI from the |0> state to the |1> state corresponding to the voltage value of each Z signal is obtained, thereby generating the target spectrum curve.

[0230] The asymmetry of the superconducting quantum interference device is determined based on the target fitting formula and the target spectrum curve.

[0231] Based on the same inventive concept, the present invention also provides the application of the resistance measurement method of the superconducting quantum interference device of any of the foregoing embodiments in the manufacture or measurement of quantum chips, wherein the quantum chip includes superconducting qubits and the superconducting qubits include a superconducting quantum interference device.

[0232] In the manufacturing or measurement of quantum chips, it is crucial to test the performance of superconducting qubits. As a key component of superconducting qubits, the resistance and other parameters of the superconducting quantum interference device (SQI) directly affect the performance of the superconducting qubits. The resistance measurement method of the superconducting quantum interference device in any of the aforementioned embodiments can accurately measure the resistance of the two Josephson junctions connected in parallel in the superconducting quantum interference device, which helps to accurately characterize the performance of the qubits.

[0233] In the description of this specification, references to terms such as "some embodiments" or "example" indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0234] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method of resistance measurement of a superconducting quantum interference device including a first Josephson junction and a second Josephson junction in parallel, a first resistance of the first Josephson junction and a second resistance of the second Josephson junction being different, characterized in that, The method comprises: obtaining an equivalent resistance and an asymmetry of the superconducting quantum interference device; determining the first resistance and the second resistance based on the asymmetry and the equivalent resistance.

2. The method of resistance measurement of a superconducting quantum interference device according to claim 1, wherein, The determination of the first resistance and the second resistance based on the asymmetry and the equivalent resistance comprises: determining the first resistance and the second resistance according to a first correspondence relationship between the asymmetry and the first resistance and the second resistance and a second correspondence relationship between the equivalent resistance and the first resistance and the second resistance; wherein the asymmetry is inversely proportional to the sum of the first resistance and the second resistance and is proportional to the difference between the second resistance and the first resistance.

3. The method of resistance measurement of a superconducting quantum interference device according to claim 1, wherein, The obtaining of the equivalent resistance of the superconducting quantum interference device comprises: obtaining a first order transition frequency corresponding to a transition from a |0> state to a |1> state and a second order transition frequency corresponding to a transition from a |1> state to a |2> state of the superconducting quantum interference device; determining a self-capacitance parameter of the superconducting quantum interference device according to a difference between the first order transition frequency and the second order transition frequency; determining the equivalent resistance according to a square of the first order transition frequency and the self-capacitance parameter.

4. The method of resistance measurement of a superconducting quantum interference device according to claim 1, wherein, The obtaining of the asymmetry of the superconducting quantum interference device comprises: obtaining a first order transition frequency corresponding to a transition from a |0> state to a |1> state and a second order transition frequency corresponding to a transition from a |1> state to a |2> state of the superconducting quantum interference device; determining a non-harmonic parameter of the superconducting quantum interference device according to a difference between the first order transition frequency and the second order transition frequency; obtaining an upper degenerate point frequency and a lower degenerate point frequency of the superconducting quantum interference device; determining the asymmetry based on a sum of the non-harmonic parameter and the upper degenerate point frequency and a sum of the non-harmonic parameter and the lower degenerate point frequency.

5. The method of resistance measurement of a superconducting quantum interference device according to claim 4, wherein, The determination of the asymmetry based on the sum of the non-harmonic parameter and the upper degenerate point frequency and the sum of the non-harmonic parameter and the lower degenerate point frequency comprises: taking the sum of the non-harmonic parameter and the upper degenerate point frequency as a first sum and taking the sum of the non-harmonic parameter and the lower degenerate point frequency as a second sum; calculating a square of a quotient of the first sum and the second sum to obtain the asymmetry.

6. The method of resistance measurement of a superconducting quantum interference device according to claim 4, wherein, The obtaining of the upper degenerate point frequency and the lower degenerate point frequency of the superconducting quantum interference device comprises: applying only a Z signal to the superconducting quantum interference device to obtain a target curve of a cavity frequency of a reading cavity coupled with the superconducting quantum interference device varying with a voltage of the Z signal; according to the target curve, taking a voltage corresponding to a wave crest in the target curve as a first voltage and taking a voltage corresponding to a wave trough in the target curve as a second voltage; applying a Z signal with the first voltage to the superconducting quantum interference device and changing a voltage of an XY signal applied to the superconducting quantum interference device to obtain a frequency corresponding to a first transition of the superconducting quantum interference device as the upper degenerate point frequency; A Z signal with a voltage of the second voltage is applied to the superconducting quantum interference device, the voltage of the XY signal applied to the superconducting quantum interference device is changed, a frequency corresponding to a first transition of the superconducting quantum interference device is obtained, and the frequency is taken as the lower degenerate point frequency.

7. The method of resistance measurement of a superconducting quantum interference device according to claim 4, wherein, The non-harmonic parameter of the superconducting quantum interference device is determined according to a difference between the first step frequency and the second step frequency, and the method comprises the following steps: Half of the difference between the first step frequency and the second step frequency is taken as a value of the non-harmonic parameter.

8. The method of resistance measurement of a superconducting quantum interference device according to claim 1, wherein, The method for obtaining the asymmetry of the superconducting quantum interference device comprises the following steps: A voltage value corresponding to residual magnetism of the superconducting quantum interference device, an upper degenerate point frequency and a non-harmonic parameter are obtained. A plurality of Z signals satisfying a preset voltage range are applied to the superconducting quantum interference device, a first transition frequency of the superconducting quantum interference device from a |0> state to a |1> state corresponding to a voltage value of each Z signal is obtained, and a target spectrum curve is generated. An asymmetry of the superconducting quantum interference device is determined according to a target fitting formula and the target spectrum curve.

9. A resistance measuring device for a superconducting quantum interference device comprising a first Josephson junction and a second Josephson junction in parallel, a first resistance of the first Josephson junction and a second resistance of the second Josephson junction being different, characterized in that, The device comprises: An obtaining module is configured to obtain an equivalent resistance and an asymmetry of the superconducting quantum interference device. A resistance determining module is configured to determine the first resistance and the second resistance based on the asymmetry and the equivalent resistance.

10. Use of a method for measuring a resistance of a superconducting quantum interference device according to any one of claims 1 to 8 in manufacturing or measuring a quantum chip, wherein the quantum chip comprises a superconducting quantum bit, and the superconducting quantum bit comprises the superconducting quantum interference device.

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