Method for determining an equivalent critical current and a qubit frequency

Abstract

The application discloses a method for determining an equivalent critical current and a method for determining a quantum bit frequency, and belongs to the technical field of quantum computing. The method comprises the following steps: determining a Josephson junction as a first Josephson junction and determining an adjacent Josephson junction as a second Josephson junction in the parallel structure; determining the critical current of a superconducting quantum interference device formed by the first Josephson junction and the second Josephson junction in parallel; judging whether the parallel structure contains a Josephson junction adjacent to the superconducting quantum interference device; if yes, taking the superconducting quantum interference device as the first Josephson junction and returning to the step of determining an adjacent Josephson junction as the second Josephson junction; and if no, determining the critical current of the superconducting quantum interference device as the equivalent critical current. The scheme disclosed by the application can determine the critical current of the parallel structure formed by a plurality of Josephson junctions in parallel with each other.

Description

Technical Field

[0001] This application belongs to the field of quantum information, especially the field of quantum computing technology. In particular, this application relates to a method for determining the equivalent critical current and a method for determining the frequency of a quantum bit. Background Technology

[0002] A Josephson junction is a three-layer structure consisting of two superconductors separated by a thin insulating layer. When the insulating layer is thin enough to clearly demonstrate the quantum tunneling effect of Cooper pairs, the Josephson junction exhibits behaviors different from those of ordinary superconductors or insulators. For this superconductor-insulator-superconductor (SIS) Josephson junction, the maximum permissible overcurrent is the critical current. When the current through the Josephson junction is less than the critical current, the junction behaves differently from ordinary devices; when the current exceeds the critical current, the junction behaves similarly to a typical resistor.

[0003] A quantum bit is a two-level system composed of a capacitor and a Josephson junction with nonlinear inductance. Determining the critical current of the Josephson junction connected in parallel with the capacitor is a key step in determining the frequency of the quantum bit. However, for parallel structures formed by multiple Josephson junctions connected in parallel, how to determine the critical current of the parallel structure is an urgent problem to be solved. Invention Content

[0004] The purpose of this application is to provide a method for determining the equivalent critical current of a parallel structure and a method for determining the frequency of a quantum bit, so as to solve the problem in the prior art that it is impossible to determine the critical current of a parallel structure formed by multiple Josephson junctions connected in parallel.

[0005] One embodiment of this application provides a method for determining the equivalent critical current, applied to a parallel structure comprising multiple Josephson junctions, wherein the Josephson junctions are arranged sequentially and connected in parallel with each other, the method comprising the following steps:

[0006] In the parallel structure, one Josephson knot is designated as the first Josephson knot, and a Josephson knot adjacent to the first Josephson knot is designated as the second Josephson knot;

[0007] The first and second Josephson junctions connected in parallel are used as a superconducting quantum interference device, and the critical current of the superconducting quantum interference device is determined.

[0008] Determine whether the parallel structure contains a Josephson junction adjacent to the superconducting quantum interference device;

[0009] If yes, then the superconducting quantum interference device is used as the first Josephson junction and the step of determining a Josephson junction adjacent to the first Josephson junction as the second Josephson junction is returned; if no, then the critical current of the superconducting quantum interference device is determined as the equivalent critical current of the parallel structure.

[0010] In some embodiments of the equivalent critical current determination method described above, the step of determining the critical current of the superconducting quantum interference device includes:

[0011] Obtain the critical current of the first Josephson junction and the critical current of the second Josephson junction, as well as the magnetic flux through the enclosed region of the first Josephson junction and the second Josephson junction.

[0012] The critical current of the superconducting quantum interference device is calculated based on the critical current of the first Josephson junction, the critical current of the second Josephson junction, and the magnetic flux.

[0013] In some embodiments of the equivalent critical current determination method described above, the critical current of the superconducting quantum interference device satisfies:

[0014]

[0015] In the formula: I a I is the critical current of the first Josephson junction. b The critical current of the second Josephson junction. For magnetic flux, Called the magnetic flux quantum, taking

[0016] In some embodiments of the equivalent critical current determination method described above, the critical current of each Josephson junction in the parallel structure is determined based on the ratio of an empirical value to the room-temperature resistance of the Josephson junction. For example, this empirical value is 230 µV.

[0017] In some embodiments of the equivalent critical current determination method described above, the critical current of each Josephson junction in the parallel structure is determined according to the following formula:

[0018]

[0019] Where R is the room temperature resistance of the Josephson junction, e is the elementary charge, and Δ is the superconducting band gap.

[0020] In some embodiments of the equivalent critical current determination method described above, the number of Josephson junctions in the parallel structure is at least three. For example, the critical currents of the Josephson junctions in the parallel structure are not the same.

[0021] Another embodiment of this application provides a method for determining the frequency of a quantum bit, characterized in that the quantum bit includes a capacitor and a parallel structure as described above, the parallel structure being connected in parallel with the capacitor, and the frequency determination method includes:

[0022] To obtain the charging energy of the capacitor;

[0023] The Josephson junction energy in the parallel structure is determined based on the equivalent critical current. Among them: I c0 This is the equivalent critical current. It is a magnetic flux quantum;

[0024] The frequency of the quantum bit is determined as Among them, E J For the Josephson junction energy, E c Let be the charging energy of the capacitor, and h be Planck's constant.

[0025] For a parallel structure formed by multiple Josephson junctions connected in parallel, this application first identifies one Josephson junction as the first Josephson junction in the parallel structure, and then identifies a Josephson junction adjacent to the first Josephson junction as the second Josephson junction; then, the parallel first Josephson junction and the second Josephson junction are used as a superconducting quantum interference device (SQFID), and the critical current of the SQFID is determined; next, it is determined whether the parallel structure contains a Josephson junction adjacent to the SQFID. If it is, the SQFID is used as the first Josephson junction and the process returns to the step of identifying a Josephson junction adjacent to the first Josephson junction as the second Josephson junction. If it is not, the critical current of the SQFID is determined as the equivalent critical current of the parallel structure. This achieves the determination of the critical current of the parallel structure and solves the problem in the prior art that the critical current of a parallel structure formed by multiple Josephson junctions connected in parallel cannot be determined. Attached Figure Description

[0026] Figure 1 A schematic diagram of a parallel structure provided in this application;

[0027] Figure 2 A flowchart illustrating a method for determining the equivalent critical current provided in this application;

[0028] Figure 3 A schematic diagram of a quantum bit structure provided in this application. Detailed Implementation

[0029] 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.

[0030] A qubit (qubit) is a two-level system that obeys the laws of quantum mechanics and can exist in any superposition of 0 and 1 states; it is the fundamental unit of quantum computing. In superconducting systems, qubits are typically constructed based on Josephson junctions (JJs), which are two superconductors coupled by a weak link, such as two superconductors coupled by a thin insulating barrier layer. Josephson junctions can be fabricated using an insulating tunnel barrier (e.g., Al₂O₃) between superconducting electrodes. For such a superconductor-insulator-superconductor (SIS) Josephson junction, the maximum permissible superconducting current is the critical current I. c Josephson Energy E j =I c Φ0 / 2π (where Φ0 is the magnetic flux quantum). Critical current I c The JJ area and insulator thickness are determined and fixed through sample manufacturing.

[0031] Transmon qubits typically employ a critical current I0. c1 The single Josephson junction. Tunable qubits have advantages in quantum computing because E can be tuned using an external magnetic field. j An external magnetic field can reduce the ratio of Josephson junction energy to charging energy, thereby introducing sensitivity to charge noise. The frequency of a quantum bit during operation can be modulated at the sweet point, which is insensitive to external magnetic flux noise and typically has a relatively high decoherence time.

[0032] To make the critical current adjustable, a device with a critical current Ic is used in the Squid loop of the superconducting quantum interference device. c2 and I c3 A scheme using a pair of Josephson junctions, and adjusting the magnetic flux in the loop via an external field transmission line, is used to determine the critical current of the combined junction at I. c2 I c3 The frequency of a qubit is generally determined by calculations based on the energy of the Josephson junction and the charging energy of the capacitor. Therefore, for parallel structures formed by three or more Josephson junctions connected in parallel, determining the critical current of the parallel structure for the application of the Josephson junction (e.g., determining the frequency of the qubit) is crucial.

[0033] Figure 1 This is a schematic diagram of a parallel structure provided in this application. Figure 1The diagram schematically illustrates a parallel structure 1 formed by Josephson junctions 11, 12, 13, and 14 arranged sequentially and connected in parallel. The magnetic flux through the enclosed region of the parallel loops of Josephson junctions 11 and 12 is Φ1, the magnetic flux through the enclosed region of the parallel loops of Josephson junctions 12 and 13 is Φ2, and the magnetic flux through the enclosed region of the parallel loops of Josephson junctions 13 and 14 is Φ3. It is understood that the parallel structure 1 is not limited to... Figure 1 The form can also include a structure consisting of only three Josephson knots 11, 12, and 13 connected in parallel, or a structure that includes more Josephson knots connected in parallel.

[0034] Figure 2 This is a flowchart illustrating a method for determining the equivalent critical current provided in this application.

[0035] Reference Figure 1 and Figure 2 As shown, for a parallel structure 1 comprising multiple Josephson junctions, in which the Josephson junctions are arranged sequentially and connected in parallel, embodiments of this application provide a method for determining the equivalent critical current of the parallel structure 1, the method comprising the following steps S100 to S500:

[0036] Step S100: In the parallel structure 1, determine a Josephson knot (such as Josephson knot 11) as the first Josephson knot;

[0037] Step S200: In the parallel structure 1, determine a Josephson node (such as Josephson node 12) adjacent to the first Josephson node as the second Josephson node;

[0038] Step S300: Use the parallel first Josephson junction and the second Josephson junction as a superconducting quantum interference device, and determine the critical current of the superconducting quantum interference device;

[0039] Step S400: Determine whether the parallel structure 1 contains a Josephson junction adjacent to the superconducting quantum interference device;

[0040] If yes, in step S500, the superconducting quantum interference device is designated as the first Josephson junction, and the process returns to the step of determining a Josephson junction adjacent to the first Josephson junction as the second Josephson junction, i.e., Josephson junction 13 is designated as the second Josephson junction, and then steps S300, S400, and S500 are executed; if no, the critical current of the superconducting quantum interference device is determined as the equivalent critical current of the parallel structure.

[0041] For a parallel structure 1 formed by multiple Josephson junctions connected in parallel, the embodiments provided in this application determine the critical current of the parallel structure 1 through steps S100 to S500, solving the problem in the prior art that the critical current of a parallel structure 1 formed by multiple Josephson junctions connected in parallel cannot be determined. In the embodiments provided in this application, a pair of adjacent Josephson junctions in the parallel structure are first treated as a superconducting quantum interference device (SQU), and the critical current of the SQU is determined. Then, the SQU is treated as an equivalent Josephson junction, and a Josephson junction adjacent to the equivalent Josephson junction is selected. The critical current of the SQU formed by the equivalent Josephson junction and the equivalent Josephson junction is then determined. This process is repeated to determine the critical current of the parallel structure 1.

[0042] The specific implementation methods for each step are described below.

[0043] In some embodiments of this application, the step of determining the critical current of the superconducting quantum interference device in step S300 includes: first obtaining the critical currents of the first Josephson junction and the second Josephson junction, and the magnetic flux of the enclosed region formed by the parallel first and second Josephson junctions. The magnetic flux of the enclosed region is typically controlled by the induced magnetic field generated by the magnetic flux control signal line transmitting the current. Therefore, the magnetic flux can be determined based on the mutual inductance between the corresponding enclosed region and the magnetic flux control signal line, and the current intensity of the magnetic flux control signal line. Then, the critical current of the superconducting quantum interference device is calculated based on the critical currents of the first and second Josephson junctions and the magnetic flux. For example, the critical currents of the superconducting quantum interference devices corresponding to the first and second Josephson junctions satisfy the following:

[0044]

[0045] In the formula: I a I is the critical current of the first Josephson junction; b This is the critical current of the second Josephson junction; It is magnetic flux; For magnetic flux quanta, The usual value is 2.068 × 10⁻⁶. -15 Webber.

[0046] In some embodiments of this application, the critical current of each Josephson junction in the parallel structure 1 is determined based on an empirical value and the ratio of this value to the room-temperature resistance of the Josephson junction. For example, this empirical value is 230 μV (microvolts), i.e., I... c R = 230, where R (Ω) is the resistance of the Josephson junction at room temperature, which is usually measured and determined in advance. c(uA) is the critical current of the Josephson junction. In some other embodiments of this application, the critical current of each Josephson junction in the parallel structure 1 is determined according to the following formula: Where: R is the room temperature resistance of the Josephson junction; e is the elementary charge, i.e., the charge of one electron; Δ is the superconducting band gap, which is 3.53 J (joules).

[0047] In some embodiments of this application, the number of Josephson junctions in the parallel structure 1 is at least three. Exemplarily, the critical currents of the Josephson junctions in the parallel structure 1 are not the same.

[0048] Figure 3 A schematic diagram of a quantum bit structure provided in this application.

[0049] Reference Figure 3 and combined Figure 1 and Figure 2 As shown, embodiments of this application also provide a method for determining the frequency of a quantum bit, wherein the quantum bit includes a capacitor 2 and a parallel structure 1 as described in the above embodiment of the equivalent critical current determination method. The parallel structure 1 is connected in parallel with the capacitor 2, and one end of the parallel structure is grounded. Figure 3 (Not shown in the image), the determination method includes:

[0050] First, obtain the charging energy of capacitor 2, and then determine the Josephson junction energy of the parallel structure 1 based on the equivalent critical current. Then the frequency of the quantum bit is determined as Among them, I c0 The equivalent critical current for parallel structure 1 is... For magnetic flux quantum, E J For the Josephson junction energy, E c Let h be the charging energy of capacitor 2, and h be Planck's constant. The parallel structure 1 is formed by multiple Josephson junctions connected in parallel. The Josephson junction energy determined according to the equivalent critical current is the total energy of the Josephson junction combination in the parallel structure 1.

[0051] For the parallel structure 1 consisting of two Josephson junctions connected in parallel, the scheme provided in this application can determine the Josephson junction energy based on the determined equivalent critical current. Then, combined with the charging energy of capacitor 2, the frequency of the quantum bit can be calculated according to the formula.

[0052] The above description, based on the embodiments shown in the drawings, details the structure, features, and effects of this application. The above description is only a preferred embodiment of this application, but this application does not limit the scope of implementation to what is shown in the drawings. Any changes made in accordance with the concept of this application, or modifications to equivalent embodiments, that do not exceed the spirit covered by the specification and drawings, should be within the protection scope of this application.

Claims

1. A method for determining the equivalent critical current, applied to a parallel structure comprising multiple Josephson junctions, wherein the Josephson junctions are arranged sequentially and connected in parallel, characterized in that, The method includes: In the parallel structure, one Josephson junction is designated as the first Josephson junction; Identify a Josephson node adjacent to the first Josephson node as the second Josephson node; The first and second Josephson junctions connected in parallel are used as a superconducting quantum interference device, and the critical current of the superconducting quantum interference device is determined. Determine whether the parallel structure contains a Josephson junction adjacent to the superconducting quantum interference device; If yes, then the superconducting quantum interference device is used as the first Josephson junction and the step of determining a Josephson junction adjacent to the first Josephson junction as the second Josephson junction is returned; if no, then the critical current of the superconducting quantum interference device is determined as the equivalent critical current of the parallel structure.

2. The method according to claim 1, characterized in that, The step of determining the critical current of the superconducting quantum interference device includes: Obtain the critical current of the first Josephson junction and the critical current of the second Josephson junction, as well as the magnetic flux through the enclosed region of the first Josephson junction and the second Josephson junction. The critical current of the superconducting quantum interference device is calculated based on the critical current of the first Josephson junction, the critical current of the second Josephson junction, and the magnetic flux.

3. The method according to claim 2, characterized in that, The critical current of a superconducting quantum interference device satisfies: In the formula: I a I is the critical current of the first Josephson junction. b The critical current of the second Josephson junction. For magnetic flux, It is a magnetic flux quantum.

4. The method according to claim 1, characterized in that, The critical current of each Josephson junction in the parallel structure is determined based on the ratio of an empirical value to the room-temperature resistance of the Josephson junction.

5. The method according to claim 4, characterized in that, The empirical value is 230uV.

6. The method according to claim 1, characterized in that, The critical current of each Josephson junction in the parallel structure is determined according to the following formula: Where R is the room temperature resistance of the Josephson junction, e is the elementary charge, and Δ is the superconducting band gap.

7. The method according to claim 1, characterized in that, The number of Josephson knots in the parallel structure is at least three.

8. The method according to claim 7, characterized in that, The critical currents of each Josephson junction in the parallel structure are different.

9. A method for determining the frequency of a quantum bit, characterized in that, The quantum bit includes a capacitor and a parallel structure as described in any one of claims 1 to 8, wherein the parallel structure is connected in parallel with the capacitor, and the frequency determination method includes: To obtain the charging energy of the capacitor; The Josephson junction energy in the parallel structure is determined based on the equivalent critical current. Among them: I c0 This is the equivalent critical current. It is a magnetic flux quantum; The frequency of the quantum bit is determined as Among them, E J For the Josephson junction energy, E c Let be the charging energy of the capacitor, and h be Planck's constant.

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