Filter circuit, quantum device, quantum computer, method for manufacturing filter circuit, method for assembling filter circuit, method for filter reading frequency,

Abstract

A filter circuit (1) is provided with a readout resonator (11) that is coupled to a data qubit, and a filter resonator (12) that is coupled to an observation line. And the reading resonator 11 and the filtering resonator 12 are connected in parallel to realize electromagnetic coupling in a capacitive coupling and inductive coupling mode.

Description

Technical Field

[0001] This disclosure relates to filter circuits, quantum devices, quantum computers, methods for manufacturing filter circuits, methods for assembling filter circuits, filtering methods for readout frequencies, and methods for distributed readout of qubits. Background Technology

[0002] Qubit state determination is one of the key technologies in quantum computers. In superconducting quantum computing devices, qubit state determination typically employs a method known as "dispersed readout." Dispersed readout couples the electromagnetic field modes of the qubit to the electromagnetic field modes of the readout resonator in a state (dispersed region) that is sufficiently separated in frequency, and couples the readout resonator to the observation circuitry. When reading out the state of the qubit, microwaves at the frequency resonating with the readout resonator are incident through the observation circuitry, and their reflected phase is measured, thereby indirectly inferring the state of the qubit.

[0003] One problem with distributed readout is that the qubit's mode can also be indirectly coupled to the observation circuitry. This causes energy leakage from the qubit to the observation circuitry, resulting in a phenomenon known as "decoherence," which induces qubit relaxation (the Purcell effect). One way to address this is to use a filter circuit called a Purcell filter. That is, by adding a Purcell filter to the quantum device, it is possible to suppress qubit relaxation to the observation circuitry while maintaining the coupling between the readout resonator and the observation circuitry.

[0004] Existing technical documents

[0005] Non-patent literature Non-patent literature 1: “Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit”, MD Reed et al., Appl. Phys. Lett., 96(20), 203110(2010). Non-patent document 2: "Broadband Filters for Abatement of Spontaneous Emissionin Circuit Quantum Electrodynamics", N. Bronn et al., Applied PhysicsLetters, 107(17), 172601. (2015) Non-patent document 3: "Reducing spontaneous emission in circuit quantumelectrodynamics by a combined readout / filter technique", NT Bronn et al., IEEE Trans. Appl. Supercond. 25(5), 1-10. (2015) Non-patent document 4: "Fast Readout and Reset of a Superconducting QubitCoupled to a Resonator with an Intrinsic Purcell Filter", Y. Sunada et al., Phys Rev. Appl. 17, 044016. (2022) Non-patent literature 5: “Rapid high-fidelity multiplexed readout of superconducting qubits”, J. Heinsoo et al., Phys. Rev. Appl., 10(3), 034040.(2018) Non-patent document 6: “All-microwave leakage reduction units for quantum errorcorrection with superconducting transmon qubits”, JF Marques, arXivpreprint arXiv:2302.09876 (2023) Non-patent literature 7: “Analysis of multiconductor transmission lines.”, CRPaul (2007) Non-patent literature 8: “Solution of the transmission-line equations under the weak-coupling assumption.” CR Paul, IEEE Trans. Elec. Comp., 44(3), 413-423. (2002) Summary of the Invention The problem the invention aims to solve As a first implementation of the Purcell filter, there is a technique disclosed in Non-Patent Document 1. This technique couples a quarter-wavelength resonator to the observation circuit, effectively shorting the observation circuit. In this design, a single-notch stopband filter can be implemented as a filter characteristic, thereby suppressing energy relaxation at the qubit frequency. However, since this method requires additional implementation of the quarter-wavelength resonator in the circuit, additional physical circuit area is required. In large-scale superconducting quantum computers, even a small increase in circuit area becomes a practical problem due to the limited circuit area.

[0006] As a second implementation of the Purcell filter, there is a technique disclosed in Non-Patent Document 2. This technique achieves the desired function by inserting a broadband stopband filter, conventionally used in microwave filters, between the readout resonator and the observation line. In this approach, the filter circuit is fabricated on a chip independent of the qubit chip. One problem with this implementation is that impedance mismatch between the observation line and the filter can cause reflections. The signal loss accompanying this reflection can lead to a decrease in measurement efficiency. Another problem is that the circuit area increases significantly due to the need for a separate filter element.

[0007] As a third implementation of the Purcell filter, there is a technique disclosed in Non-Patent Document 3. In this method, capacitive direct coupling is introduced between the qubit and the observation line. This creates destructive interference on the coupling from the qubit to the observation line via the resonator, thus realizing a stopband filter. Such filters can be considered as filters "built-in" to the coupling, requiring no additional circuit components, and therefore have advantages in large-scale integrated applications with limited circuit area.

[0008] As another example of a built-in Purcell filter, there is a technique disclosed in Non-Patent Document 4. In this method, the built-in filter is implemented using a distributed constant circuit, and by adjusting the coupling position between the observation line and the resonator, dissipation at the qubit frequency can be suppressed. Similar to the previous example, this method also has the advantage of requiring no additional circuit components.

[0009] However, a common problem with the aforementioned methods is that the readout resonators are directly coupled to the observation line without any filtering. This can cause problems when multiplexing readouts and coupling multiple resonators to a common observation line. Multiplexing readouts significantly reduces wiring and microwave components within the dilution cooler, making it crucial for large-scale implementation. On the other hand, coupling a large number of readout resonators to a common observation line can introduce measurement crosstalk. In particular, the readout signal entering non-target resonators can degrade the phase coherence of the qubits, a serious problem.

[0010] Independent Purcell filter resonators are a method introduced to address readout crosstalk issues during multiplexing (see, for example, Non-Patent Documents 5 and 6). In readouts using independent Purcell filter resonators, multiple readout resonators are multiplexed onto a single observation line, with each readout resonator implemented in pairs with an independent Purcell filter resonator. This method has the advantage of simultaneously suppressing qubit relaxation and crosstalk between readout resonators, and has been first verified in Non-Patent Document 5 and used for eight-fold reuse of readouts in eight-qubit devices.

[0011] The independent filter resonator used in Non-Patent Documents 5 and 6 is implemented as a bandpass filter that allows passage near the readout frequency. This creates a structure that simultaneously suppresses energy relaxation of the qubit, but this presents a problem. Specifically, when the resonator is strongly coupled to the observation circuitry to accelerate readout, the filtering performance as a bandpass filter is insufficient, and it may not adequately suppress energy relaxation of the qubit.

[0012] The present invention was made in view of the above circumstances, and its purpose is to realize a filter circuit that has both a bandpass filter function that allows only the area near the readout frequency of the readout resonator to pass through, and a notch filter function that suppresses the energy relaxation of the qubit to the observation line.

[0013] Problem-solving methods To address the aforementioned problems, one aspect of the filtering circuit of the present invention includes a readout resonator coupled to the data qubits and a filter resonator coupled to the observation line. The readout resonator and the filter resonator are electromagnetically coupled by using capacitive and inductive coupling in parallel.

[0014] In one embodiment of the filter circuit, inductive coupling can be achieved by reading the mutual inductance between the resonator and the filter resonator.

[0015] In one embodiment of the filter circuit, a multi-core transmission line may be included, arranged between the readout resonator and the filter resonator. In this case, capacitive coupling and inductive coupling are achieved through the multi-core transmission line.

[0016] In one embodiment of the filter circuit, the readout resonator may be composed of a first readout resonator section whose first end is connected to the data qubit and a second readout resonator section whose first end is grounded; the filter resonator may be composed of a first filter resonator section whose first end is connected to the observation line and a second filter resonator section whose first end is grounded; the multi-core transmission line may be disposed between the second end of the first readout resonator section and the second end of the first filter resonator section, and the second end of the second readout resonator section and the second end of the second filter resonator section.

[0017] In one embodiment of the filter circuit, the length of the multi-core transmission line is assumed to be l.c The propagation speed of a wave along a multi-core transmission line is v. c The capacitance per unit length of the first and second cores of a multi-core transmission line is C. l The inductance per unit length of the first and second cores of a multi-core transmission line is L. l The capacitance per unit length between the first and second cores of a multi-core transmission line is C. m The inductance per unit length between the first and second cores of a multi-core transmission line is L. m The length of the second readout resonator section of the readout resonator 11 is l. r1-G The length of the second filter resonator section of the filter resonator is l. r2-G The length of the multi-core transmission line is l c When the variable of the distributed constant circuit is set to [Mathematical Expression 4] When, the notch frequency ω f The following expression is satisfied.

[0018] [Mathematical Expression 5]

[0019] In one embodiment of the filter circuit, the notch frequency ω f It can be expressed by the following formula.

[0020] [Mathematical Expression 10]

[0021] In one embodiment of the filter circuit, the coupling constant J between the readout resonator and the filter resonator can be expressed by the following formula.

[0022] [Mathematical Expression 11]

[0023] In one embodiment of the filter circuit, in addition to the multi-core transmission line, a coupling capacitor may also be arranged.

[0024] In one embodiment of the filter circuit, in addition to the multi-core transmission line, coupling capacitors and inductors may also be arranged.

[0025] In one embodiment of the filter circuit, a capacitor and an inductor may be arranged between the readout resonator and the filter resonator. In this case, capacitive coupling and inductive coupling are achieved through the capacitor and inductor arranged between the readout resonator and the filter resonator, respectively.

[0026] Another aspect of the present invention is a quantum device. This quantum device may include data qubits, observation lines, and any of the aforementioned filtering circuits. The filtering circuit is arranged between the data qubits and the observation lines.

[0027] Another aspect of the present invention is a quantum computer. This quantum computer includes the aforementioned quantum devices.

[0028] Another aspect of the present invention is a filtering circuit. The filtering circuit includes: one or more data qubits; one or more readout resonators corresponding to each data qubit; a filtering resonator having characteristics corresponding to the resonant frequency of the readout resonator; a coupling circuit arranged between the readout resonator and the filtering resonator, causing electromagnetic coupling between the readout resonator and the filtering resonator; and a common observation line. This filtering circuit combines bandpass filtering characteristics utilizing the resonant frequency of the filtering resonator near its resonant readout frequency with notch filtering characteristics utilizing the interference frequency of the qubits in the electromagnetic coupling circuit.

[0029] Another aspect of the present invention is a method for manufacturing a filter circuit. The method includes: forming a readout resonator; forming a filter resonator; coupling the readout resonator to a data qubit; coupling the filter resonator to an observation circuit; and electromagnetically coupling the readout resonator and the filter resonator by using capacitive coupling and inductive coupling in parallel.

[0030] Another aspect of the present invention is a method for assembling a filter circuit. The method includes: providing a readout resonator component coupled to a data qubit; providing a filter resonator component coupled to an observation line; and assembling the readout resonator component and the filter resonator component in an electromagnetic coupling manner by using capacitive coupling and inductive coupling in parallel.

[0031] Another aspect of the present invention is a filtering method for the readout frequency in the dispersed readout of a quantum bit to an observation line. The method includes: performing a bandpass filter using any of the above-described filtering circuits to allow only the area near the readout frequency of the readout resonator to pass through; and performing a notch filter to suppress energy relaxation of the quantum bit to the observation line.

[0032] Another aspect of the present invention is a method for distributing the readout of qubits to an observation line. The method includes: coupling the electromagnetic field mode of the qubit to the electromagnetic field mode of the readout resonator using any of the aforementioned filtering circuits; and coupling the readout resonator to the observation line.

[0033] Furthermore, any combination of the above-mentioned constituent elements, as well as solutions obtained by converting the description of this disclosure into methods, apparatus, systems, recording media, computer programs, etc., are also considered as effective implementations of this disclosure.

[0034] Invention Effects According to the present invention, a filter circuit can be implemented that combines a bandpass filter function that allows only the area near the readout frequency of the readout resonator to pass through, and a notch filter function that suppresses the energy relaxation of the qubits to the observation line. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the filter circuit involved in the first embodiment.

[0036] Figure 2 As Figure 1 A schematic diagram of a filter circuit as an example of the specific configuration of the circuit.

[0037] Figure 3 As Figure 1 A schematic diagram of a filter circuit, which is another specific example of the circuit configuration.

[0038] Figure 4 This is a schematic diagram of another filter circuit involved in the first embodiment.

[0039] Figure 5 It shows Figure 4 An example of implementing a filter circuit.

[0040] Figure 6 This is a schematic diagram of another filter circuit involved in the first embodiment.

[0041] Figure 7 This is a schematic diagram of the quantum device involved in the second embodiment.

[0042] Figure 8 It shows Figure 2 The frequency characteristics of the signal passed through the filter circuit.

[0043] Figure 9 The simulated radiative relaxation lifetime of the qubit is shown.

[0044] Figure 10 An example of an implementation of a filter circuit with a built-in notch filter for quadruple reuse readout of superconducting qubits is shown.

[0045] Figure 11 for Figure 10 A magnified view of the vicinity of the first qubit.

[0046] Figure 12 The frequency dependence of the radiative relaxation time of the first qubit is shown.

[0047] Figure 13 The frequency dependence of the radiative relaxation time of the second qubit is shown.

[0048] Figure 14 The frequency dependence of the radiative relaxation time of the third qubit is shown.

[0049] Figure 15 The frequency dependence of the radiative relaxation time of the fourth qubit is shown.

[0050] Figure 16 This is a schematic diagram of a multi-core transmission line.

[0051] Explanation of reference numerals in the attached figures 1. Filtering circuit 2. Filtering Circuit 3. Filtering Circuit 4. Filtering Circuit 5. Filtering Circuit 6. Filtering Circuit 11 Readout Resonator 11a First readout resonator section 11a1 First end 11a2 Second end 11b Second readout resonator section 11b1 First End 11b2 Second End 12 Filter Resonators 12a First filter resonator section 12a1 First end 12a2 Second end 12b Second Filter Resonator Section 12b1 First end 12b2 Second End 13. Coupling Circuit Section 14 Capacitors 15 Inductors 20+ core transmission lines 21 First core wire 22 Second core wire 30 capacitors 31 Inductor 80 quantum devices 81 data qubits 82 Observation Line 91 First qubit 92 second qubits 93 Third qubit 94 Fourth qubit 111 First Readout Resonator 111a First Readout Resonator Section 111b The second readout resonator section of the first readout resonator 112 Second Readout Resonator 113 Third Readout Resonator 114 Fourth readout resonator 121 First filter resonator 121a First filter resonator section 131b The second filter resonator section of the first filter resonator 122 Second filter resonator 123 Third filter resonator 124 Fourth filter resonator 200+ core transmission lines S1 forms a readout resonator S2 forms a filter resonator S3 couples the readout resonator with the data qubit. S4 couples the filter resonator to the observation line. S5 uses parallel capacitive and inductive coupling to electromagnetically couple the readout resonator and the filter resonator. S11 provides a readout resonator component coupled to the data qubit. S12 provides a filter resonator component coupled to the observation line. S13 assembles the readout resonator component and the filter resonator component via electromagnetic coupling using parallel capacitive and inductive coupling. S21 performs a bandpass filter that only allows frequencies near the readout frequency of the readout resonator to pass through. S22 performs notch filtering to suppress energy relaxation of the qubits into the observation circuit. S31 couples the electromagnetic field modes of the qubit with the electromagnetic field modes of the readout resonator. S32 couples the readout resonator to the observation line. Detailed Implementation [First Implementation Method] Figure 1 The filter circuit 1 according to the first embodiment is schematically shown. The filter circuit 1 includes a readout resonator 11 and a filter resonator 12. The readout resonator 11 is coupled to an external data qubit, and the filter resonator 12 is coupled to an external observation line. The readout resonator 11 and the filter resonator 12 are electromagnetically coupled by parallel connection using capacitive and inductive coupling. The filter resonator 12 is a bandpass filter that allows passage near the readout frequency of the readout resonator 11, thus functioning as an independent filter resonator.

[0052] For the resonator group consisting of readout resonator 11 and filter resonator 12, electromagnetic coupling is achieved by using capacitive and inductive coupling in parallel, thus realizing a built-in notch filter. The circuit model that uses capacitive and inductive coupling in parallel to electromagnetically couple the resonator group is referred to as the "lumped constant circuit model" below.

[0053] The working principle of this embodiment is explained below. Let C be the capacitive coupling and inductive coupling of the above coupling circuit, respectively. f With L f Then at the resonant frequency At this frequency, the impedance of the coupling circuit section 13 is infinite. Therefore, at this frequency, the readout resonator 11 and the filter resonator 12 behave as separate circuits. This hinders the signal transmission of the data qubits to the observation line, giving the circuit as a stopband filter function. However, at the frequency of the readout resonator 11, the impedance of the coupling circuit is finite, and the coupling between the readout resonator 11 and the observation line is preserved. Thus, while the frequency of the readout resonator can be distinguished by the filter resonator 12 (i.e., the independent Purcell filter circuit), a circuit with a stopband can be constructed through the electromagnetic coupling circuit.

[0054] As an example of this embodiment, a structure that functions as a notch filter at the qubit frequency can be built-in. In this case, the inductive coupling of the coupling circuit section 13 is achieved through the mutual inductance between the readout resonator 11 and the filter resonator 12. According to this embodiment, no special hardware needs to be added outside of the readout resonator 11 and the filter resonator 12; the bandpass readout frequency filtering of the original independent Purcell filter (filter resonator 12) can be used directly to achieve notch filtering. Therefore, when the readout resonator is more strongly coupled to the observation line, qubit relaxation can also be suppressed, achieving high-speed readout. This invention can improve the shortcomings of conventional bandpass independent Purcell filters in suppressing qubit relaxation.

[0055] Furthermore, according to this implementation example, the required filtering characteristics can be increased without increasing the physical circuit area. That is, in conventional methods, additional circuit area is required to obtain additional filtering performance, while the built-in implementation of this embodiment solves this problem, facilitating the integration of superconducting quantum bit chips.

[0056] Figure 2 Schematic illustration of as Figure 1 The specific configuration of the circuit is exemplified by filter circuit 2. Filter circuit 2 includes a readout resonator 11, a filter resonator 12, and a multi-core transmission line 20. Figure 2 In the example, both the readout resonator 11 and the filter resonator 12 are composed of quarter-wavelength resonators.

[0057] The readout resonator 11 of the filter circuit 2 is composed of a first readout resonator section 11a and a second readout resonator section 11b. The first readout resonator section 11a includes a first terminal 11a1 and a second terminal 11a2, and the second readout resonator section 11b includes a first terminal 11b1 and a second terminal 11b2. The first terminal 11a1 of the first readout resonator section 11a of the readout resonator 11 is connected to the data qubit, and the first terminal 11b1 of the second readout resonator section 11b of the readout resonator 11 is grounded.

[0058] The filter resonator 12 of the filter circuit 2 is composed of a first filter resonator section 12a and a second filter resonator section 12b. The first filter resonator section 12a includes a first terminal 12a1 and a second terminal 12a2, and the second filter resonator section 12b includes a first terminal 12b1 and a second terminal 12b2. The first terminal 12a1 of the first filter resonator section 12a of the filter resonator 12 is connected to the observation line, and the first terminal 12b1 of the second filter resonator section 12b of the filter resonator 12 is grounded.

[0059] The multi-core transmission line 20 includes a first core wire 21 and a second core wire 22. The multi-core transmission line 20 is arranged between the readout resonator 11 and the filter resonator 12. More specifically, the first core wire 21 of the multi-core transmission line 20 is connected to the second end 11a2 of the first readout resonator portion 11a of the readout resonator 11 and the second end 11b2 of the second readout resonator portion 11b. The second core wire 22 of the multi-core transmission line 20 is connected to the second end 12a2 of the first filter resonator portion 12a of the filter resonator 12 and the second end 12b2 of the second filter resonator portion 12b of the filter resonator 12. Thus, the multi-core transmission line 20 is positioned between the second end 11a2 of the first readout resonator portion 11a of the readout resonator 11 and the second end 12a2 of the first filter resonator portion 12a of the filter resonator 12, and the second end 11b2 of the second readout resonator portion 11b of the readout resonator 11 and the second end 12b2 of the second filter resonator portion 12b of the filter resonator 12. In this structure, the mutual inductance between the first core wire 21 and the second core wire 22 in the multi-core transmission line is utilized to achieve magnetic coupling.

[0060] According to this embodiment, a built-in notch filter circuit can be implemented using a multi-core transmission line.

[0061] Figure 3 Schematic illustration of as Figure 1 Another specific example of the circuit configuration is filter circuit 3. Filter circuit 3 in... Figure 2Based on the filter circuit 2 structure, a shunt capacitor 30 is arranged between the core wires adjacent to the multi-core transmission line 20. This structure also utilizes the multi-core transmission line 20 to achieve magnetic coupling and utilizes the capacitance of the multi-core transmission line 20 and the shunt capacitor 30 to achieve electrical coupling. By adding the shunt capacitor 30, it is possible to address situations where the capacitance of the multi-core transmission line section is insufficient or where separate adjustment of the electrical coupling is required.

[0062] The following explains how to utilize... Figure 2 The distributed constant circuit structure shown can reproduce Figure 1 A lumped constant circuit model is derived. Using multi-core transmission line analysis (e.g., see Non-Patent Document 7), the parameters of this distributed circuit are mapped to... Figure 1 The parameters of the lumped constant circuit were obtained. This shows that the two circuits have the same electrical response with high precision within the target frequency range. Furthermore, it is shown that the parameters of the lumped constant circuit can be realized to the desired values ​​using a multi-core transmission line with physical dimensions suitable for superconducting quantum circuits.

[0063] First, define the basic transmission line quantities. The behavior of a lossless transmission line can be described by the capacitance C per unit length. l and inductance per unit length L l This can be described using characteristic impedance Z0 and phase velocity v.

[0064] [Mathematical Expression 1]

[0065] A transmission line of length l with one end grounded has a fundamental resonant frequency ω. r = 2π / λ (where λ / 4 = l). Near this resonant frequency, the transmission line can be modeled as a lumped constant LC resonator, in which case its effective capacitance C and inductance are given by the following equation.

[0066] [Mathematical Expression 2]

[0067] In contrast to single-core transmission lines, multi-core transmission lines have n conductor lines and one ground reference point. For a lossless two-core transmission line, it can be described by six parameters: Capacitance C per unit length of conductor line 1 l,1 ; Capacitance C per unit length of conductor line 2 l,2 ; Inductance per unit length L of conductor line 1 l,1 ; Inductance per unit length L of conductor line 2 l,2 ; Capacitance C per unit length between two conductor lines m ;as well as Inductance per unit length L between two conductor lines m .

[0068] exist Figure 2 In this context, assume that the capacitance per unit length and the inductance per unit length to ground are the same for all conductor lines. Furthermore, assume C... l >>C m However, this is equivalent to the case of weak coupling between two conductor lines in a multi-core transmission line (the weak coupling assumption, also referred to below as the "weak coupling approximation"). This assumption is valid in multi-core transmission lines where the signal leaking to other cores is negligible compared to the signal transmitted in each core, the disturbance caused by coupling has a small impact, and it holds true under the typical coupling strength in superconducting quantum circuit applications (see, for example, Non-Patent Document 8). Even under this assumption, the resonant frequency ω of the notch filter... f It was also obtained through analysis.

[0069] Under the assumption that the above is true, the first readout resonator section 11a, the second readout resonator section 11b, and the multi-core transmission line segment 20 as a whole constitute the entire length l. r1-0 + l c + l r1-G The single-conductor transmission line operates. Since one end of the line is grounded, with λ / 4 = l r1-0 + l c + l r1-G Achieve λ / 4 resonance.

[0070] Similarly, the first filter resonator section 12a, the second filter resonator section 12b, and the multi-core transmission line segment 20 as a whole constitute the entire length l r2-0 + l c + l r2-G The line operates as a single conductor transmission line. This line operates with λ / 4 = l r2-0 + l c + l r2-G A λ / 4 resonance is achieved. Therefore, equation (1) gives the direction... Figure 2 The mapping of the capacitance and inductance of the two grounded LC resonators.

[0071] In summary, equation (1) gives the direction Figure 1 The mapping of the capacitance and inductance of the two grounded LC resonators.

[0072] To obtain the coupling capacitance C f and coupling inductor L f The mapping, first, find Figure 2The transfer impedance Z between the data qubit node and the detector node in the circuit 12 The frequency is zero. By assuming that at this frequency, Figure 1 The transfer impedance Z' of the lumped constant equivalent circuit 12 Also zero, the solution with the lowest frequency and the frequency Related.

[0073] Next, find Figure 1 The impedance of the coupling circuit element It satisfies the following formula.

[0074] [Mathematical Expression 3]

[0075] Here, Z r1 (ω f ) and Z r2 (ω f ) is based on frequency ω f The impedances of the lumped constant resonators r1 and r2 are evaluated. To utilize... Figure 2 Find Z from the circuit. f Map the right side of the above equation to Figure 2 The circuit. The capacitance and inductance of the lumped constant resonators r1 and r2 can be obtained from equation (1). Assume the transfer impedance Z' of the lumped constant equivalent circuit. 12 Near the resonant frequency and Figure 2 The transmission impedance Z of the distributed constant circuit 12 Consistent behavior, Z 12 Substitute Z' 12 Therefore, the right side of the above equation can be derived solely from... Figure 2 The circuit parameters are used to describe it.

[0076] Due to capacitance C m With inductor L m Completely determined by frequency ω f With impedance Z f OK, that's it, we're done. Figure 1 circuit and Figure 2 The corresponding circuit.

[0077] When a weak coupling approximation can be performed in a multi-core transmission line, the notch frequency ω f The analytical expression can be obtained as follows. For example, referring to non-patent literature 8, the transmission impedance Z under the weak coupling assumption is obtained. 12 The analytical expression is given by the following definition of each variable.

[0078] [Mathematical Expression 4]

[0079] Solving for the case where the transmission impedance is zero yields the information about the notch frequency ω. f The following formula.

[0080] [Mathematical Expression 5]

[0081] That is, let the length of the multi-core transmission line 20 be l. c The propagation speed of the wave along the multi-core transmission line 20 is v. c The capacitance per unit length of the first core 21 and the second core 22 of the multi-core transmission line 20 is C. l The inductance per unit length of the first core 21 and the second core 22 of the multi-core transmission line 20 is L. l The capacitance per unit length between the first core 21 and the second core 22 of the multi-core transmission line 20 is C. m The inductance per unit length between the first core 21 and the second core 22 of the multi-core transmission line 20 is L. m The length of the second readout resonator section 11b of the readout resonator 11 is l. r1-G The length of the second filter resonator section 12b of the filter resonator 12 is l. r2-G The length of the multi-core transmission line 20 is l c When the variable of the distributed constant circuit is set to [Mathematical Expression 4] At that time, determine Figure 2 The notch frequency ω of filter circuit 2 f The following expression is satisfied.

[0082] [Mathematical Expression 5]

[0083] According to this embodiment, in a multi-core transmission line system approximated by weak coupling, the parameters can be specifically determined to implement the filtering circuit.

[0084] Figure 4 Another filter circuit 4 according to the first embodiment is schematically shown. The filter circuit 4 includes a readout resonator 11, a filter resonator 12, a capacitor 30, and an inductor 31. The readout resonator 11 is composed of a first readout resonator section 11a and a second readout resonator section 11b, and the filter resonator 12 is composed of a first filter resonator section 12a and a second filter resonator section 12b. The capacitor 30 and the inductor 31 are disposed between the first readout resonator section 11a and the first filter resonator section 12a, and between the second readout resonator section 11b and the second filter resonator section 12b. That is, the filter circuit 4 includes the capacitor 30 and the inductor 31 to replace... Figure 2The filter circuit 2 has a multi-core transmission line 20. The other structures of the filter circuit 4 are the same as those of the filter circuit 2. The capacitive coupling and inductive coupling between the readout resonator 11 and the filter resonator 12 are achieved through the capacitor 30 and the inductor 31, respectively.

[0085] Figure 5 It shows Figure 4 Example of implementing filter circuit 4.

[0086] According to this embodiment, a filter circuit that achieves the desired function can be made using capacitors and inductors as circuit elements.

[0087] Figure 6 Another filter circuit 5 according to the first embodiment is schematically shown. The filter circuit 5 includes a readout resonator 11, a filter resonator 12, a multi-core transmission line 20, a capacitor 30, and an inductor 31. The multi-core transmission line 20 is arranged between the readout resonator 11 and the filter resonator 12, and the capacitor 30 and the inductor 31 are arranged adjacent to the multi-core transmission line 20.

[0088] Filter circuit 5 has the function of... Figure 2 Filter circuit 2 and Figure 4 The structure is composed of filter circuit 4. The capacitive and inductive coupling between the readout resonator 11 and the filter resonator 12 is achieved through the multi-core transmission line 20, capacitor 30 and inductor 31.

[0089] According to this embodiment, the structural degrees of freedom can be increased.

[0090] [Additional Examples] In the foregoing embodiments, Figure 2 The notch frequency ω of filter circuit 2 f Equation (4) represents the notch frequency as an implicit function. However, in practical applications, it is often more convenient to express the notch frequency explicitly. Such embodiments are described below.

[0091] In the following text, use Figure 16 Multi-core transmission line 200 to replace Figure 2 2. Multi-core transmission line 200. Let the capacitance per unit length of multi-core transmission line 200 be C. C Inductance per unit length is L C The capacitance per unit length between the first core 201 and the second core 202 of the multi-core transmission line 200 is C. m Inductance per unit length is L m When the variable of the distributed constant circuit is set to [Mathematical Expression 6] At that time, it was determined to adopt Figure 16The notch frequency ω of the filter circuit of the multi-core transmission line 200 f The following expression is satisfied.

[0092] [Mathematical Expression 7]

[0093] For multi-core transmission lines in a homogeneous medium, and multi-core coplanar lines, which are symmetrical in shape and each is composed of a homogeneous medium, the following approximation holds with extremely high accuracy.

[0094] [Mathematical Expression 8]

[0095] This is because, except in the extreme case of asymmetrical geometry, multi-core transmission lines with cores coupled to each other behave like multi-core transmission lines in a homogeneous medium.

[0096] According to equations (6) and (7), the following equation holds true.

[0097] [Mathematical Expression 9]

[0098] Therefore, the notch frequency ω f It can be explicitly represented as follows.

[0099] [Mathematical Expression 10]

[0100] According to this embodiment, since the notch frequency can be explicitly represented, the degree of freedom in the design and application of filter circuits can be improved.

[0101] Equation (7) can also give the following explicit expression for the J coupling constant J of the readout resonator and the filter resonator.

[0102] [Mathematical Expression 11]

[0103] Wherein, the coupling constant J is the Hamiltonian H through the following interaction. int A definite constant representing the coupling strength.

[0104] [Mathematical Expression 12]

[0105] here, [Mathematical Expression 13] To read out the generation operator of the resonator, [Mathematical Expression 14] For the generation operator of the filter resonator, [Mathematical Expression 15] To read out the annihilation operator of the resonator, [Mathematical Expression 16] This is the annihilation operator for the filter resonator.

[0106] Furthermore, the variables in equation (10) are defined as follows.

[0107] [Mathematical Expression 17]

[0108] [Mathematical Expression 18]

[0109] [Mathematical Expression 19]

[0110] According to this embodiment, since the coupling degrees of freedom can be explicitly represented, the degree of freedom in filter circuit design and practical application can be improved.

[0111] [Second Implementation] Figure 7 The quantum device 80 according to the second embodiment is schematically shown. The quantum device 80 includes data qubits 81, observation lines 82, and filter circuits 1.

[0112] The filter circuit 1 includes a readout resonator 11 and a filter resonator 12. The readout resonator 11 is coupled to external data qubits, and the filter resonator 12 is coupled to external observation lines. The readout resonator 11 and the filter resonator 12 are electromagnetically coupled via parallel connection using capacitive and inductive coupling. The filter resonator 12 is a bandpass filter that allows data to pass near the readout frequency of the readout resonator 11, thus functioning as an independent filter resonator.

[0113] The readout resonator 11 is coupled to the data qubit 81 to read out the state of the data qubit 81. The observation line 82 is coupled to the readout resonator 11 to transmit the information of the data qubit 81 read out by the readout resonator 11 to the observation equipment.

[0114] As mentioned earlier, in filter circuit 1, the readout resonator 11 and the filter resonator 12 are connected in parallel to achieve electromagnetic coupling through capacitive and inductive coupling, thereby realizing a notch filter. Other detailed operations and effects of filter circuit 1 are as described above.

[0115] According to this embodiment, a quantum device using a filter circuit can be realized, which combines a bandpass filter function that allows only the area near the readout frequency of the readout resonator to pass through, and a notch filter function that suppresses the relaxation of the qubits to the observation line.

[0116] Figure 7 The quantum device 80 can also be considered as a filter circuit. Specifically, the filter circuit 80 includes one or more data qubits 81, one or more readout resonators 11 corresponding to each data qubit, a filter resonator 12 having characteristics corresponding to the resonant frequency of the readout resonator, a coupling circuit 13 arranged between the readout resonator and the filter resonator to electromagnetically couple them, and a common observation line 82. This filter circuit 80 combines bandpass filtering characteristics utilizing the readout frequency of the filter resonator 12 with notch filtering characteristics utilizing the frequency of the interfering qubits in the electromagnetic coupling circuit.

[0117] [Third Implementation Method] The third embodiment is a quantum computer. This quantum computer includes the quantum devices of the second embodiment.

[0118] According to this embodiment, a quantum computer using a filtering circuit can be realized, which combines a bandpass filtering function that allows only the area near the readout frequency of the readout resonator to pass through, and a notch filtering function that suppresses the relaxation of the qubits to the observation line.

[0119] [Fourth Implementation Method] The fourth embodiment is a method for manufacturing a filter circuit. The method includes: step S1, forming a readout resonator; step S2, forming a filter resonator; step S3, coupling the readout resonator to a data qubit; step S4, coupling the filter resonator to an observation circuit; and step S5, electromagnetically coupling the readout resonator and the filter resonator by using capacitive coupling and inductive coupling in parallel.

[0120] According to this embodiment, a filter circuit can be manufactured that combines a bandpass filter function that allows only the area near the readout frequency of the readout resonator to pass through, and a notch filter function that suppresses energy relaxation of the qubits to the observation line.

[0121] [Fifth Implementation Method] The fifth embodiment is a method for assembling a filter circuit. The method includes: step S11, providing a readout resonator component coupled to a data qubit; step S12, providing a filter resonator component coupled to an observation line; and step S13, assembling the readout resonator component and the filter resonator component by electromagnetic coupling through parallel use of capacitive coupling and inductive coupling.

[0122] According to this embodiment, a filter circuit can be assembled by combining a readout resonator component and a filter resonator component. Furthermore, the readout resonator component and the filter resonator component can be inspected, repaired, or replaced for each component.

[0123] [Sixth Implementation Method] The fifth embodiment is a filtering method for the readout frequency in the dispersed readout of qubits to the observation line. The method includes: step S22, using any of the above-described filtering circuits to perform bandpass filtering that only allows the area near the readout frequency of the readout resonator to pass; and step S23, performing notch filtering to suppress energy relaxation of qubits to the observation line.

[0124] According to this embodiment, when the qubits are read out in a distributed manner into the observation line, the relaxation of the qubits into the observation line can be suppressed while maintaining the coupling between the readout resonator and the observation line.

[0125] [Seventh Implementation Method] The seventh embodiment is a method for distributed readout of qubits. The method includes: step S31, using any of the above-mentioned filter circuits to couple the electromagnetic field mode of the qubit with the electromagnetic field mode of the readout resonator; and step S32, coupling the readout resonator to the observation line.

[0126] According to this embodiment, the Purcell effect can be suppressed, and qubit readout can be performed in a distributed manner.

[0127] The present disclosure has been described above based on embodiments. Those skilled in the art should understand that the embodiments are examples, and various modifications may exist for the combination of each component and each processing step, and such modifications are also within the scope of the present disclosure.

[0128] [verify] To confirm the effectiveness of the implementation methods described above, the inventors conducted the following verification.

[0129] First, the accuracy of the above mapping was verified by comparing the transfer impedance of these circuits within the frequency range of superconducting circuit applications. Table 1 shows the parameter values ​​used in the simulation.

[0130] Table 1

[0131] Figure 8 It shows from Figure 2 Frequency characteristics of the signal transmitted from the port marked "to data qubits" to the port marked "to observation line". Figure 8 It shows Figure 1 The rigorous solution (solid line) of the lumped constant circuit model and Figure 2The weakly coupled approximation solution for a multi-core transmission line (single-dot dashed line) shows a high degree of consistency in frequency characteristics between the two solutions. Furthermore, it can be seen that the weak coupling assumption is sufficiently reasonable within the commonly used parameter range for superconducting quantum bit readout. The vertical dashed line indicates the notch frequency obtained from equation (4). It can be seen that the notch frequency is highly consistent with the frequency of the analytical solution.

[0132] Figure 9 The simulated radiative relaxation lifetime of the qubit is shown. The circuit parameters used are as follows: qubit frequency f qub = 4.75 GHz, readout resonator frequency f res = 6 GHz, external coupling strength of the readout resonator / 2π = 50 MHz, coupling between the quantum bit and the readout resonator g = 125 MHz, coupling between the readout resonator and the filter resonator J = 30 MHz. Figure 9 The paper compares the qubit lifetimes of circuits with built-in notch filters (with notch) and readout circuits with only independent Purcell filters (without notch) at the same coupling constant.

[0133] like Figure 9 As shown, it can be seen that in the circuit of this embodiment, by utilizing notch filtering, a much longer lifetime can be achieved at quantum bit frequencies above 4 GHz than that of circuits using conventional independent Purcell filters.

[0134] To best utilize the notch filtering function of this embodiment, the frequency of the notch filter needs to be sufficiently close to the frequency of the qubit. Because there are sufficient degrees of freedom for optimization, the frequency of the notch filter can be adjusted only while maintaining the readout resonator frequency and the coupling strength between the readout resonator and the filter resonator.

[0135] Next, for Figure 2 The experimental implementation method of the distributed constant circuit is illustrated below. As shown in the figure, it can be seen that through experimental implementation... Figure 2 The notch filter of this invention can be implemented in a built-in manner, given the structure of the filter circuit.

[0136] Figure 10An implementation example of a filter circuit 6 with a built-in notch filter for quadruple reuse readout of superconducting qubits is shown. The filter circuit 6 includes a first readout resonator 111, a second readout resonator 112, a third readout resonator 113, a fourth readout resonator 114, a first filter resonator 121, a second filter resonator 122, a third filter resonator 123, and a fourth filter resonator 124. The first readout resonator 111 is coupled to the first qubit 91, the second readout resonator 112 is coupled to the second qubit 92, the third readout resonator 113 is coupled to the third qubit 93, and the fourth readout resonator 114 is coupled to the fourth qubit 94. The first filter resonator 121, the second filter resonator 122, the third filter resonator 123, and the fourth filter resonator 124 are coupled to a common observation line.

[0137] Figure 11 for Figure 10 A magnified view near the first qubit 91. The first readout resonator 111 includes a first readout resonator section 111a and a second readout resonator section 111b, and the first filter resonator 111 includes a first filter resonator section 121a and a second filter resonator section 121b. A multi-core transmission line 20 is arranged between the first readout resonator 111 and the first filter resonator 112.

[0138] Figure 12 The frequency dependence of the radiative relaxation time T1 of the first qubit 91 is shown. Figure 13 The frequency dependence of the radiative relaxation time T1 of the second qubit 92 is shown. Figure 14 The frequency dependence of the radiative relaxation time T1 of the third qubit 93 is shown. Figure 15 The frequency dependence of the radiative relaxation time T1 of the fourth qubit 94 is shown. In any figure, cross markers indicate experimental results, and circles indicate simulation results; the experimental results are in high agreement with the simulations. Figure 12-15 As shown, each qubit exhibits a radiative relaxation time peak around 8.2 GHz–9 GHz. This experimentally verifies that, through filter circuit 6, each independent Purcell filter can also function as a notch filter, achieving the desired filtering effect.

[0139] When understanding the abstracted technical concept of the implementation methods and variations, this technical concept should not be limited to the content of the implementation methods and variations. The aforementioned implementation methods and variations are merely specific examples, and various design changes can be made, such as altering, adding, or deleting constituent elements. In the implementation methods, content that allows for such design changes is emphasized by the word "implementation method." However, even content without such wording is permitted to undergo design changes.

[0140] Industrial applicability This disclosure can be applied to filter circuits, quantum devices, and quantum computers.

Claims

1. A filter circuit, characterized by, comprises: a readout resonator coupled to a data qubit; and a filter resonator coupled to an observation line; wherein the readout resonator and the filter resonator are electromagnetically coupled by parallel use of capacitive coupling and inductive coupling.

2. The filter circuit of claim 1, wherein, The inductive coupling is realized by mutual inductance between the readout resonator and the filter resonator.

3. The filter circuit of claim 1, wherein, comprises a multi-core transmission line arranged between the readout resonator and the filter resonator; The capacitive coupling and the inductive coupling are realized by the multi-core transmission line.

4. The filter circuit according to claim 3, wherein the readout resonator is composed of a first readout resonator part having a first end connected to the data qubit and a second readout resonator part having a first end grounded; the filter resonator is composed of a first filter resonator part having a first end connected to the observation line and a second filter resonator part having a first end grounded; the multi-core transmission line is arranged between a second end of the first readout resonator part and a second end of the first filter resonator part, and between a second end of the second readout resonator part and a second end of the second filter resonator part.

5. The filter circuit according to claim 4, wherein Let the length of the multicore transmission line be l c , The propagation speed of the wave propagating along the multicore transmission line is v c , The unit length capacitance of the first core wire and the second core wire of the multi-core transmission line is C l , The unit length inductance of the first core wire and the second core wire of the multi-core transmission line is L l , The unit length capacitance between the first core and the second core of the multi-core transmission line is C m , The unit length inductance between the first core wire and the second core wire of the multi-core transmission line is L m , The length of the second readout resonator part of the readout resonator 11 is l r1-G , The length of the second filter resonator part of the filter resonator is l r2-G , The length of the multicore transmission line is l c , when variables of a distributed constant circuit are set as [mathematical formula 4] [mathematical formula 5] Notch frequency ω f Satisfies [mathematical formula 10] 。 6. The filter circuit of claim 5, wherein, The notch frequency ω f By is represented. A coupling constant J of the readout resonator and the filter resonator is represented by 7. The filter circuit of claim 6, wherein, [mathematical formula 11] In addition to the multi-core transmission line, a coupling capacitor is arranged. In addition to the multi-core transmission line, a coupling capacitor and an inductor are arranged.

8. The filter circuit of claim 3, wherein, comprises a capacitor and an inductor arranged between the readout resonator and the filter resonator; 9. The filter circuit of claim 3, wherein, The capacitive coupling and the inductive coupling are realized by the capacitor and the inductor arranged between the readout resonator and the filter resonator, respectively.

10. The filter circuit of claim 9, wherein, comprises: a data qubit; 11. A quantum device, characterized in that, an observation line; and a filter circuit according to any one of claims 1 to 10; wherein the filter circuit is arranged between the data qubit and the observation line.

12. A quantum computer comprising the quantum device according to claim 11. comprises: one or more data qubits; 13. A filter circuit, characterized by one or more readout resonators corresponding to the respective data qubits; a filter resonator having a characteristic corresponding to a resonance frequency of the readout resonator; a coupling circuit arranged between the readout resonator and the filter resonator so that the readout resonator and the filter resonator are electromagnetically coupled; and a common observation line; wherein the filter circuit has both a bandpass filter characteristic in a vicinity of a readout frequency using resonance of the filter resonator, and a notch filter characteristic in a vicinity of a qubit frequency using interference in the electromagnetically coupling circuit. The filter circuit comprises a readout resonator and a filter resonator, and the method comprises: forming a readout resonator; 14. A method of manufacturing a filter circuit, characterized by, forming a filter resonator; coupling the readout resonator to a data qubit; coupling the filter resonator to an observation line; and ​ ​ The readout resonator is electromagnetically coupled to the filter resonator by using both capacitive coupling and inductive coupling in parallel.

15. A method of assembling a filter circuit, characterized by Comprising: providing a readout resonator component coupled to a data qubit; providing a filter resonator component coupled to an observation line; and assembling the readout resonator component and the filter resonator component in an electromagnetically coupled manner by using both capacitive coupling and inductive coupling in parallel.

16. A method of filtering a readout frequency in a dispersive readout of a qubit-to-observation line, characterized by, Comprising: using a filter circuit according to any one of claims 1 to 7, performing bandpass filtering that only allows a readout frequency of the readout resonator to pass through; and performing notch filtering that suppresses energy relaxation of the qubit to the observation line.

17. A method of dispersively reading out a quantum bit to an observation line, characterized by, Comprising: using a filter circuit according to any one of claims 1 to 7, coupling an electromagnetic field mode of the qubit to an electromagnetic field mode of the readout resonator; and coupling the readout resonator to the observation line.

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