Filter circuit, quantum device, quantum computer, filter circuit manufacturing method, filter circuit assembly method, readout frequency filtering method, and quantum bit dispersive readout method

Abstract

A filter circuit 1 comprises: a readout resonator 11 that is coupled to data quantum bits; and a filter resonator 12 that is configured and is coupled to an observation line. The readout resonator 11 and the filter resonator 12 are electrically and magnetically coupled by using capacitive coupling and inductive coupling in parallel.

Description

Filter circuit, quantum device, quantum computer, filter circuit manufacturing method, filter circuit assembly method, readout frequency filtering method, and quantum bit distributed readout method

[0001] The present disclosure relates to a filter circuit, a quantum device, a quantum computer, a method for manufacturing a filter circuit, a method for assembling a filter circuit, a method for filtering a readout frequency, and a method for distributed readout of quantum bits.

[0002] Measuring the state of qubits is one of the key technologies in quantum computers. A technique commonly known as "distributed readout" is used to measure the state of qubits in superconducting quantum computer devices. In distributed readout, the electromagnetic field mode of the qubit is coupled to the electromagnetic field mode of the readout resonator in a state where they are sufficiently separated in frequency (dispersive region), and the readout resonator is then coupled to an observation line. When reading out the state of the qubit, microwaves with a frequency that resonates with the readout resonator are incident from the observation line, and the reflected phase is measured to indirectly estimate the state of the qubit.

[0003] One of the challenges of distributed readout is that the quantum bit modes can indirectly couple to the observation line. This causes quantum bit energy to leak into the observation line, resulting in a phenomenon called decoherence, which causes quantum bit relaxation (the Purcell effect). One approach to address this is to use a filter circuit called a Purcell filter. By adding a Purcell filter to the quantum device, it is possible to suppress quantum bit relaxation into the observation line while maintaining coupling between the readout resonator and the observation line.

[0004] "Fast Reset and Suppressing Spontaneous Emission of a Superconducting Qubit", M. D. Reed et al., Appl. Phys. Lett., 96(20), 203110 (2010)"Broadband Filters for Abatement of Spontaneous Emission in Circuit Quantum Electrodynamics", N. Bronn et al., Applied Physics Letters, 107(17), 172601. (2015)"Reducing spontaneous emission in circuit quantum electrodynamics by a combined readout / filter technique", N. T. Bronn et al., IEEE Trans. Appl. Supercond. 25(5), 1-10. (2015)"Fast Readout and Reset of a Superconducting Qubit Coupled to a Resonator with an Intrinsic Purcell Filter", Y. Sunada et al., Phys Rev. Appl. 17, 044016. (2022)"Rapid high-fidelity multiplexed readout of superconducting qubits", J. Heinsoo et al., Phys. Rev. Appl., 10(3), 034040. (2018)"All-microwave leakage reduction units for quantum error correction with superconducting transmon qubits", J. F. Marques, arXiv preprint arXiv:2302.09876 (2023)"Analysis of multiconductor transmission lines.", C. R.Paul (2007)"Solution of the transmission-line equations under the weak-coupling assumption." CR Paul, IEEE Trans. Elec. Comp., 44(3), 413-423. (2002).

[0005] A first implementation example of a Purcell filter is the technology disclosed in Non-Patent Document 1. This technology involves coupling a quarter-wave resonator to the observation line, effectively shorting the observation line. This design achieves a single-notch stopband filter as a filter characteristic. This enables suppression of energy relaxation at the quantum bit frequency. However, this method requires the implementation of an additional quarter-wave resonator in the circuit, which requires additional physical circuit area. In large-scale superconducting quantum computers, the circuit area is limited, so even a small increase in circuit area can pose an implementation problem.

[0006] A second implementation example of a Purcell filter is the technology disclosed in Non-Patent Document 2. This technology achieves the desired functionality by inserting a wideband stopband filter, which is conventionally used in microwave filters, between the readout resonator and the observation line. In this method, the filter circuit is fabricated on a chip separate from the qubit chip. One problem with this implementation method is the possibility of reflection due to impedance mismatch between the observation line and the filter. Signal loss associated with such reflection can reduce measurement efficiency. Another issue is the significant increase in circuit area due to the need for a separate filter element.

[0007] A third implementation example of a Purcell filter is the technology disclosed in Non-Patent Document 3. This approach introduces a direct capacitive coupling between the quantum bit and the observation line. This implements a stopband filter that causes destructive interference in the coupling from the quantum bit to the observation line via the resonator. This type of filter can be considered an "intrinsic" filter in the coupling and does not require any additional circuit elements. Therefore, it is considered advantageous for large-scale integration applications where circuit area is limited.

[0008] Another example of an intrinsic Purcell filter is the technology disclosed in Non-Patent Document 4. Here, the intrinsic filter is realized as a distributed constant circuit. By adjusting the coupling position between the observation line and the resonator, it is possible to suppress dissipation at the quantum bit frequency. This method, like the above, has the advantage of not requiring additional circuit elements.

[0009] However, a common issue with these approaches is that the readout resonator is directly coupled to the observation line, with no filtering performed on the readout resonator itself. This can be problematic when multiplexing the readout and coupling multiple resonators to a common observation line. Multiplexing readout significantly reduces the wiring and microwave components within the dilution refrigerator, making it crucial for large-scale implementations. However, coupling multiple readout resonators to a common observation line can cause measurement crosstalk. In particular, the readout signal can enter resonators other than the target resonator, degrading the phase coherence of the qubits.

[0010] Individual Purcell filter resonators are a technique introduced to address the issue of readout crosstalk during multiplexing (see, for example, Non-Patent Documents 5 and 6). In individual Purcell filter resonator readout, multiple readout resonators are multiplexed onto a single observation line, while each readout resonator is paired with an individual Purcell filter resonator. This technique has the advantage of simultaneously suppressing qubit relaxation and crosstalk between readout resonators. This technique was first demonstrated in Non-Patent Document 5 and has been used for 8-qubit readout multiplexing in an 8-qubit device.

[0011] The individual filter resonators used in Non-Patent Documents 5 and 6 are implemented as bandpass filters that transmit frequencies near the readout frequency. As a result, they are designed to simultaneously suppress the energy relaxation of the quantum bit, but this also poses a problem. That is, if the resonator is coupled very strongly to the observation line in order to speed up the readout, the filter performance as a bandpass filter may not be sufficient, and it may not be possible to fully suppress the energy relaxation of the quantum bit.

[0012] The present invention has been made in light of these circumstances, and its purpose is to realize a filter circuit that combines a bandpass filter function that transmits only frequencies near the readout frequency of the readout resonator, and a notch filter function that suppresses energy relaxation of the quantum bit to the observation line.

[0013] In order to achieve the above object, a filter circuit according to one aspect of the present invention includes a readout resonator coupled to a data quantum bit and a filter resonator coupled to an observation line, the readout resonator and the filter resonator being electromagnetically coupled using capacitive coupling and inductive coupling in parallel.

[0014] In an embodiment of the filter circuit, the inductive coupling may be realized by the mutual inductance between the readout resonator and the filter resonator.

[0015] In some embodiments, the filter circuit may include a multi-core transmission line disposed between the readout resonator and the filter resonator, where the capacitive and inductive couplings are realized by the multi-core transmission line.

[0016] In an embodiment of the filter circuit, the readout resonator may be composed of a first readout resonator section having a first end connected to the data quantum bit and a second readout resonator section having a first end grounded, the filter resonator may be composed of a first filter resonator section having a first end connected to the observation line and a second filter resonator section having a first end grounded, and the multicore transmission line may be installed between the second end of the first readout resonator section and the second end of the first filter resonator section, and between the second end of the second readout resonator section and the second end of the second filter resonator section.

[0017] In a filter circuit according to an embodiment, the length of the multi-core transmission line is l ｃ , the propagation speed of the wave propagating through the multi-core transmission line is v ｃ , the capacitance per unit length of the first and second cores of the multi-core transmission line is C ｌ , the inductance per unit length of the first core wire and the second core wire of the 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 core and the second core of the multi-core transmission line is L ｍ , the length of the second readout resonator portion of the readout resonator 11 is l ｒ１－Ｇ , the length of the second filter resonator portion of the filter resonator is l ｒ２－Ｇ , the length of the multi-core transmission line is l ｃ , and the variables of the distributed constant circuit are Then, the notch frequency ω ｆ is expressed as follows: Meet the following.

[0018] In one embodiment of the filter circuit, the notch frequency ω ｆ is expressed as follows: It may be expressed as:

[0019] In one embodiment of the filter circuit, the coupling constant J between the readout resonator and the filter resonator is expressed by the following formula: It may be expressed as:

[0020] In a filter circuit according to an embodiment, a coupling capacitor may be disposed in addition to the multi-core transmission line.

[0021] In a filter circuit according to an embodiment, coupling capacitors and inductors may be arranged in addition to the multi-core transmission line.

[0022] In an embodiment, the filter circuit may include a capacitor and an inductor disposed between the readout resonator and the filter resonator, whereby the capacitive coupling and the inductor are realized by the capacitor and the inductor disposed between the readout resonator and the filter resonator, respectively.

[0023] Another aspect of the present invention is a quantum device. The quantum device may include a data qubit, an observation line, and any of the filter circuits described above. The filter circuit is disposed between the data qubit and the observation line.

[0024] Yet another aspect of the present invention is a quantum computer, which includes the quantum device described above.

[0025] Yet another aspect of the present invention is a filter circuit comprising: one or more data quantum bits; one or more readout resonators corresponding to each of the data quantum bits; a filter resonator having characteristics corresponding to the resonant frequency of the readout resonator; a coupler circuit disposed between the readout resonator and the filter resonator for electrically and magnetically coupling the readout resonator and the filter resonator; and a common observation line. The filter circuit has both a bandpass filter characteristic near the readout frequency utilizing the resonance of the filter resonator and a notch filter characteristic near the quantum bit frequency utilizing interference in the electrical and magnetic coupler circuit.

[0026] Yet another aspect of the invention is a method for fabricating a filter circuit, the method including forming a readout resonator, forming a filter resonator, coupling the readout resonator to a data qubit, coupling the filter resonator to an observation line, and electromagnetically coupling the readout resonator and the filter resonator using parallel capacitive and inductive coupling.

[0027] Yet another aspect of the invention is a method of assembling a filter circuit, the method comprising the steps of 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 so that they are electromagnetically coupled using parallel capacitive and inductive coupling.

[0028] Yet another aspect of the present invention is a method for filtering a readout frequency in distributed readout of a quantum bit onto an observation line, the method including the steps of: performing bandpass filtering using any of the filter circuits described above to transmit only frequencies near the readout frequency of the readout resonator; and performing notch filtering to suppress energy relaxation of the quantum bit onto the observation line.

[0029] Yet another aspect of the present invention is a method for distributed readout of qubits onto an observation line, the method comprising the steps of: using a filter circuit as described above to couple an electromagnetic mode of the qubit to an electromagnetic mode of a readout resonator; and coupling the readout resonator to the observation line.

[0030] Any combination of the above components, and conversion of the present disclosure into a method, device, system, recording medium, computer program, etc., are also valid aspects of the present disclosure.

[0031] According to the present invention, it is possible to realize a filter circuit that combines a bandpass filter function that transmits only frequencies near the readout frequency of the readout resonator and a notch filter function that suppresses energy relaxation of the quantum bit to the observation line.

[0032] 1. A schematic diagram of a filter circuit according to a first embodiment. 2. A schematic diagram of a filter circuit that is a specific configuration example of the circuit of FIG. 1. 3. A schematic diagram of a filter circuit that is another specific configuration example of the circuit of FIG. 1. 4. A schematic diagram of yet another filter circuit according to the first embodiment. 5. A diagram showing an implementation example of the filter circuit of FIG. 4. 6. A schematic diagram of yet another filter circuit according to the first embodiment. 7. A schematic diagram of a quantum device according to a second embodiment. 8. A diagram showing the frequency characteristics of a transmitted signal of the filter circuit of FIG. 2. 9. A diagram showing the radiative relaxation lifetime of a quantum bit obtained by simulation. 10. A diagram showing an implementation example of a filter circuit with an intrinsic notch used for four-way multiplexed readout of superconducting quantum bits. 11. A magnified view of the vicinity of the first quantum bit in FIG. 10. 12. A diagram showing the frequency dependence of the radiative relaxation time for the first quantum bit. 13. A diagram showing the frequency dependence of the radiative relaxation time for the second quantum bit. 14. A diagram showing the frequency dependence of the radiative relaxation time for the third quantum bit. 15. A diagram showing the frequency dependence of the radiative relaxation time for the fourth quantum bit. 16. A schematic diagram of a multi-core transmission line.

[0033] 1 schematically shows a filter circuit 1 according to a first embodiment. The filter circuit 1 includes a readout resonator 11 and a filter resonator 12. The readout resonator 11 is coupled to an external data quantum bit. The filter resonator 12 is coupled to an external observation line. The readout resonator 11 and the filter resonator 12 are electromagnetically coupled using parallel capacitive and inductive couplings. The filter resonator 12 is a bandpass filter that transmits frequencies near the readout frequency of the readout resonator 11 and functions as an individual filter resonator.

[0034] An inherent notch filter can be realized by electromagnetically coupling a pair of resonators consisting of a readout resonator 11 and a filter resonator 12 using capacitive and inductive coupling in parallel. Hereinafter, such a circuit model in which a pair of resonators is electromagnetically coupled using capacitive and inductive coupling in parallel is referred to as a "lumped parameter circuit model."

[0035] The operation principle of this embodiment will be described. The capacitive coupling and inductive coupling of the above coupling circuit are respectively denoted as C ｆ and L ｆ Then, the resonant frequency ω ｆ = 1 / √(C ｆ L ｆ ), the impedance of the coupling circuit portion 13 becomes infinite. Therefore, at this frequency, the readout resonator 11 and the filter resonator 12 behave as isolated circuits. As a result, signal transmission from the data quantum bit to the observation line is inhibited, and the circuit as a whole functions as a stopband filter. At the frequency of the readout resonator 11, the impedance of the coupling circuit is finite, so coupling between the readout resonator 11 and the observation line remains. This allows the filter resonator 12 (i.e., the individual Purcell filter circuit) to discriminate the readout resonator frequency, while at the same time configuring a circuit with a stopband using the electromagnetic coupling circuit.

[0036] As an example of realizing this embodiment, a component that functions as a notch filter at the quantum bit frequency is internally added. In this case, the inductive coupling of the coupling circuit portion 13 is realized by the mutual inductance between the readout resonator 11 and the filter resonator 12. According to this example, no special hardware is required other than the readout resonator 11 and the filter resonator 12. Instead, the bandpass-like readout frequency filtering provided by the original individual Purcell filter (filter resonator 12) can be utilized to provide the notch function. As a result, even when the readout resonator is more strongly coupled to the observation line, quantum bit relaxation can be suppressed, enabling high-speed readout. The present invention improves the quantum bit relaxation suppression function, which was insufficient with conventional bandpass-type individual Purcell filters.

[0037] Furthermore, this implementation allows for the addition of desired filter characteristics without increasing the physical circuit area. That is, in conventional approaches, additional circuit area is required to obtain additional filter performance. However, the inherent implementation approach of this embodiment solves this problem, facilitating the integration of superconducting qubit chips.

[0038] Fig. 2 schematically shows a filter circuit 2 as a specific example of the configuration of the circuit in Fig. 1. The filter circuit 2 includes a readout resonator 11, a filter resonator 12, and a multi-core transmission line 20. In the example of Fig. 2, the readout resonator 11 and the filter resonator 12 are both configured as quarter-wave resonators.

[0039] The readout resonator 11 of the filter circuit 2 is composed of a first readout resonator portion 11a and a second readout resonator portion 11b. The first readout resonator portion 11a has a first end 11a1 and a second end 11a2. The second readout resonator portion 11b has a first end 11b1 and a second end 11b2. The first end 11a1 of the first readout resonator portion 11a of the readout resonator 11 is connected to the data quantum bit. The first end 11b1 of the second readout resonator portion 11b of the readout resonator 11 is grounded.

[0040] The filter resonator 12 of the filter circuit 2 is composed of a first filter resonator portion 12a and a second filter resonator portion 12b. The first filter resonator portion 12a has a first end 12a1 and a second end 12a2. The second filter resonator portion 12b has a first end 12b1 and a second end 12b2. The first end 12a1 of the first filter resonator portion 12a of the filter resonator 12 is connected to the observation line. The first end 12b1 of the second filter resonator portion 12b of the filter resonator 12 is grounded.

[0041] The multi-core transmission line 20 includes a first core 21 and a second core 22. The multi-core transmission line 20 is disposed between the readout resonator 11 and the filter resonator 12. More specifically, the first core 21 of the multi-core transmission line 20 connects the second end 11a2 of the first readout resonator portion 11a of the readout resonator 11 to the second end 11b2 of the second readout resonator portion 11b. The second core 22 of the multi-core transmission line 20 connects the second end 12a2 of the first filter resonator portion 12a of the filter resonator 12 to the second end 12b2 of the second filter resonator portion 12b. In this way, the multi-core transmission line 20 is installed 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 configuration, mutual inductance between the first core wire 21 and the second core wire 22 in the multi-core transmission line is utilized to obtain magnetic coupling.

[0042] According to this embodiment, an inherent notch filter circuit can be realized using a multi-core transmission line.

[0043] Fig. 3 schematically shows a filter circuit 3 as another specific example of the circuit of Fig. 1. In addition to the configuration of the filter circuit 2 of Fig. 2, the filter circuit 3 has a shunt capacitor 30 disposed between the cores adjacent to the multi-core transmission line 20. In this configuration, the multi-core transmission line 20 is used to obtain magnetic coupling. The capacitance of the multi-core transmission line 20 and the shunt capacitor 30 is used to obtain electrical coupling. Adding the shunt capacitor 30 makes it possible to deal with cases where the capacitance of the multi-core transmission line section is insufficient or where it is desired to individually adjust the electrical coupling.

[0044] Next, we explain how the lumped-element circuit model of Figure 1 can be reproduced by using the distributed-element circuit configuration shown in Figure 2. Using multicore transmission line analysis (see, for example, Non-Patent Document 7), we map the parameters of this distributed circuit to the parameters of the lumped-element circuit of Figure 1. This shows that both circuits have the same electrical response with high precision over the target frequency range. Furthermore, we show that desired values ​​for the parameters of the lumped-element circuit can be achieved by using a multicore transmission line with a physical size suitable for superconducting quantum circuits.

[0045] First, let us define the basic transmission line quantities. The behavior of a lossless transmission line is characterized by a capacitance per unit length, C ｌ and the inductance per unit length L ｌ Equivalently, the characteristic impedance Z ０ and the phase velocity v.

[0046] A transmission line with a total length l and one end grounded has a fundamental resonant frequency ω ｒ = 2π / λ, where λ / 4 = 1. Near this resonant frequency, the transmission line can be modeled as a lumped-element LC resonator. In this case, the effective capacitance C and inductance are given by

[0047] In contrast to a single-core transmission line, a multi-core transmission line has n conductor lines and one ground reference point. In the case of a lossless two-core transmission line, the line has six parameters: ｌ，１ , the capacitance C per unit length of the conductor line 2 ｌ，２ , the inductance L per unit length of the conductor line 1 ｌ，１ , the inductance L per unit length of the conductor line 2 ｌ，２ , the capacitance C per unit length between two conductor lines ｍ , the inductance L per unit length between two conductor lines ｍ , is described by

[0048] In Figure 2, the capacitance per unit length and the inductance per unit length to ground are assumed to be the same for all conductor lines. ｌ >>C ｍ This corresponds to the case where two conductor lines of a multi-core transmission line are weakly coupled (weak coupling assumption) (hereinafter also referred to as "weak coupling approximation"). This assumption is valid when the signal leaking to each core in the multi-core transmission line is negligibly small compared to the signal transmitted through each core, and the influence of perturbations due to coupling is small, and it holds true for typical coupling strengths in applications of superconducting quantum circuits (see, for example, Non-Patent Document 8). Even under this assumption, the resonant frequency ω of the notch filter ｆ is found analytically.

[0049] If the above assumptions hold, the first readout resonator portion 11a, the second readout resonator portion 11b, and the multicore transmission line section 20 of the readout resonator 11 together have a total length l ｒ１－０ +l ｃ +l ｒ１－Ｇ Since one end of this line is grounded, it operates as a single conductor transmission line with a ｒ１－０ +l ｃ +l ｒ１－Ｇ It resonates at λ / 4.

[0050] Similarly, the first filter resonator portion 12a, the second filter resonator portion 12b of the filter resonator 12, and the multicore transmission line section 20 together have a total length l ｒ２－０ +l ｃ +l ｒ２－Ｇ This line operates as a single conductor transmission line with a λ / 4 = l ｒ２－０ +l ｃ +l ｒ２－Ｇ Then, equation (1) gives the mapping to the capacitance and inductance of the two grounded LC resonators in FIG.

[0051] From the above, equation (1) gives the mapping to the capacitance and inductance of the two grounded LC resonators of FIG.

[0052] Coupling capacitance C ｆ and coupling inductance L ｆ To find the mapping to １２ This frequency is determined by the transfer impedance Z' of the lumped parameter equivalent circuit in Figure 1. １２ Also, by assuming that ｆ = 1 / √(C ｆ L ｆ ) and associate it with

[0053] Next, the impedance Z of the coupling circuit element in FIG. ｆ =√(L ｆ / C ｆ ) is found, which satisfies the following equation: Here, Z ｒ１ (ω ｆ ) and Z ｒ２ (ω ｆ ) is the frequency ω ｆ is the impedance of the lumped constant resonators r1 and r2 evaluated by Z ｆ To find the capacitance and inductance of the lumped resonators r1 and r2, the right-hand side of this equation is mapped onto the circuit in Figure 2. The transfer impedance Z' of the lumped equivalent circuit is found using equation (1). １２is the transfer impedance Z of the distributed constant circuit in Figure 2 near the resonant frequency. １２ Assume that Z' behaves similarly to １２ Z １２ As a result, the right-hand side can be described using only the parameters of the circuit in Figure 2.

[0054] Capacitance C ｍ and inductance L ｍ is the frequency ω ｆ and impedance Z ｆ 1 and 2 are now completely determined.

[0055] When a multi-core transmission line can be approximated as weakly coupled, the notch frequency ω ｆ The analytical expression for can be obtained as follows: For example, referring to Non-Patent Document 8, the transfer impedance Z １２ Here, each variable is defined as follows: When this transfer impedance becomes zero, the notch frequency ω ｆ The following equation for

[0056] That is, the length of the multi-core transmission line 20 is l ｃ , the propagation velocity of the wave propagating through the multi-core transmission line 20 is v ｃ , the capacitance per unit length of the first core wire 21 and the second core wire 22 of the multi-core transmission line 20 is C ｌ , the inductance per unit length of the first core wire 21 and the second core wire 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 portion 11b of the readout resonator 11 is l ｒ１－Ｇ , the length of the second filter resonator portion 12b of the filter resonator 12 is l ｒ２－Ｇ , the length of the multi-core transmission line 20 is l ｃ , and the variables of the distributed constant circuit are When the notch frequency ω of the filter circuit 2 in FIG. ｆ is determined to satisfy the following equation:

[0057] According to this embodiment, in a system of multi-core transmission lines approximated by weak coupling, parameters can be specifically determined to realize a filter circuit.

[0058] FIG. 4 schematically illustrates another filter circuit 4 according to the first embodiment. The filter circuit 4 includes a readout resonator 11, a filter resonator 12, a capacitor 30, and an inductor 31. The readout resonator 11 includes a first readout resonator portion 11a and a second readout resonator portion 11b. The filter resonator 12 includes a first filter resonator portion 12a and a second filter resonator portion 12b. The capacitor 30 and the inductor 31 are disposed between the first readout resonator portion 11a and the first filter resonator portion 12a and between the second readout resonator portion 11b and the second filter resonator portion 12b. That is, the filter circuit 4 includes the capacitor 30 and the inductor 31 instead of the multicore transmission line 20 of the filter circuit 2 in FIG. 2. The remaining configuration of the filter circuit 4 is similar to that of the filter circuit 2. The capacitive and inductive coupling between the readout resonator 11 and the filter resonator 12 is realized by a capacitor 30 and an inductor 31, respectively.

[0059] FIG. 5 shows an example of implementation of the filter circuit 4 of FIG.

[0060] According to this embodiment, a filter circuit that achieves a desired function can be fabricated using capacitors and inductors as circuit elements.

[0061] 6 schematically shows another filter circuit 5 according to the first embodiment. 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 disposed between the readout resonator 11 and the filter resonator 12. The capacitor 30 and the inductor 31 are disposed adjacent to the multi-core transmission line 20.

[0062] The filter circuit 5 has a structure that combines the filter circuit 2 of Fig. 2 and the filter circuit 4 of Fig. 4. The capacitive coupling and inductive coupling between the readout resonator 11 and the filter resonator 12 are realized by a multi-core transmission line 20, a capacitor 30, and an inductor 31.

[0063] According to this embodiment, the degree of freedom in the configuration can be increased.

[0064] [Additional Embodiment] In the above-described embodiment, the notch frequency ω of the filter circuit 2 of FIG. ｆ is expressed implicitly by equation (4). However, in practice, it is often easier to use if the notch frequency is expressed explicitly. An example of such an embodiment will be described below.

[0065] In the following description, the multi-core transmission line 200 shown in FIG. 16 is used instead of the multi-core transmission line 2 shown in FIG. 2. The capacitance per unit length of the multi-core transmission line 200 is defined as C Ｃ , the inductance per unit length of the multi-core transmission line 200 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 , the inductance per unit length between the first core 201 and the second core 202 of the multi-core transmission line 200 is L ｍ The variables of the distributed constant circuit are When the notch frequency ω of the filter circuit using the multi-core transmission line 200 of FIG. ｆ is determined to satisfy the following equation:

[0066] For a multi-core transmission line in a uniform medium or a multi-core transmission line such as a multi-core coplanar line, where the top and bottom shapes of the line are symmetrical and each is made of a uniform medium, the following approximation holds with very good accuracy. This is because a multi-core transmission line in which the cores are coupled behaves like a multi-core transmission line in a homogeneous medium, except in extreme cases where the geometric shape is asymmetric.

[0067] From equations (6) and (7), the following holds true: Therefore, the notch frequency ω ｆ can be explicitly expressed as follows:

[0068] According to this embodiment, the notch frequency can be explicitly expressed, which increases the degree of freedom in designing and practically using a filter circuit.

[0069] Equation (7) also gives an explicit expression for the J-coupling constant J between the readout and filter resonators: where the coupling constant J is calculated by the following interaction Hamiltonian H ｉｎｔ is a constant that represents the strength of the bond, determined by where: is the generation operator of the readout resonator, is the generating operator of the filter resonator, is the annihilation operator of the readout cavity, is the annihilation operator of the filter resonator. Furthermore, each variable in equation (10) is defined as follows:

[0070] According to this embodiment, the degree of freedom of coupling can be explicitly expressed, which increases the degree of freedom in designing and using a filter circuit.

[0071] 7 is a schematic diagram of a quantum device 80 according to a second embodiment. The quantum device 80 includes a data quantum bit 81, an observation line 82, and a filter circuit 1.

[0072] The filter circuit 1 includes a readout resonator 11 and a filter resonator 12. The readout resonator 11 is coupled to an external data quantum bit. The filter resonator 12 is coupled to an external observation line. The readout resonator 11 and the filter resonator 12 are electromagnetically coupled using parallel capacitive coupling and inductive coupling. The filter resonator 12 is a bandpass filter that transmits frequencies near the readout frequency of the readout resonator 11 and functions as an individual filter resonator.

[0073] Readout resonator 11 is coupled to data quantum bit 81 and reads out the state of data quantum bit 81. Observation line 82 is coupled to readout resonator 11 and transmits information about data quantum bit 81 read out by readout resonator 11 to an observation device.

[0074] As described above, in the filter circuit 1, the readout resonator 11 and the filter resonator 12 are electromagnetically coupled using capacitive coupling and inductive coupling in parallel, thereby realizing a notch filter. Other detailed operations and effects of the filter circuit 1 are as described above.

[0075] According to this embodiment, a quantum device can be realized using a filter circuit that combines a bandpass filter function that transmits only frequencies near the readout frequency of the readout resonator and a notch filter function that suppresses relaxation of the quantum bit to the observation line.

[0076] 7 can also be considered as a filter circuit, as described below. That is, this filter circuit 80 includes one or more data quantum bits 81, one or more readout resonators 11 corresponding to each of these data quantum bits, a filter resonator 12 having characteristics corresponding to the resonant frequency of the readout resonator, a coupler circuit 13 disposed between the readout resonator and the filter resonator to electrically and magnetically couple the readout resonator and the filter resonator, and a common observation line 82. This filter circuit 80 has both a bandpass filter characteristic near the readout frequency utilizing the resonance of the filter resonator 12 and a notch filter characteristic near the quantum bit frequency utilizing interference in the electrical and magnetic coupler circuit.

[0077] Third Embodiment A third embodiment is a quantum computer, which includes the quantum device of the second embodiment.

[0078] According to this embodiment, a quantum computer can be realized using a filter circuit that combines a bandpass filter function that transmits only frequencies near the readout frequency of the readout resonator and a notch filter function that suppresses relaxation of the quantum bit to the observation line.

[0079] Fourth Embodiment A fourth embodiment is a method for manufacturing a filter circuit, which includes steps S1 forming a readout resonator, S2 forming a filter resonator, S3 coupling the readout resonator to a data qubit, S4 coupling the filter resonator to an observation line, and S5 electromagnetically coupling the readout resonator and the filter resonator using capacitive and inductive coupling in parallel.

[0080] According to this embodiment, it is possible to manufacture a filter circuit that combines a bandpass filter function that transmits only frequencies near the readout frequency of the readout resonator and a notch filter function that suppresses energy relaxation of the quantum bit to the observation line.

[0081] Fifth Embodiment A fifth embodiment is a method of assembling a filter circuit, comprising the steps of providing a readout resonator component coupled to a data qubit (S11), providing a filter resonator component coupled to an observation line (S12), and assembling the readout resonator component and the filter resonator component so that they are electromagnetically coupled using parallel capacitive and inductive coupling (S13).

[0082] According to this embodiment, a filter circuit can be assembled by combining a readout resonator component and a filter resonator component, and the readout resonator component and the filter resonator component can be inspected, repaired, replaced, etc., individually.

[0083] Sixth Embodiment A fifth embodiment is a method for filtering a readout frequency in distributed readout of a quantum bit onto an observation line, which includes step S22 of performing bandpass filtering using any of the filter circuits described above to transmit only frequencies near the readout frequency of the readout resonator, and step S23 of performing notch filtering to suppress energy relaxation of the quantum bit onto the observation line.

[0084] According to this embodiment, when quantum bits are distributed and read out onto the observation line, it is possible to suppress relaxation of the quantum bits onto the observation line while maintaining the coupling between the readout resonator and the observation line.

[0085] A seventh embodiment is a method for distributed readout of quantum bits, which includes step S31 of coupling an electromagnetic field mode of a quantum bit to an electromagnetic field mode of a readout resonator using any of the filter circuits described above, and step S32 of coupling the readout resonator to an observation line.

[0086] According to this embodiment, the Purcell effect can be suppressed and distributed readout of quantum bits can be performed.

[0087] The present disclosure has been described above based on the embodiments. These embodiments are merely examples, and it will be understood by those skilled in the art that various modifications are possible in the combination of the respective components and the respective treatment processes, and that such modifications are also within the scope of the present disclosure.

[0088] [Verification] The inventors conducted the following verification to confirm the effectiveness of the above-described embodiment.

[0089] First, we verified the accuracy of the above mapping by comparing the transfer impedances of these circuits over the frequency range used in superconducting circuit applications. The parameter values ​​used in the simulations are listed in Table 1.

[0090] Figure 8 shows the frequency characteristics of the transmitted signal from the port labeled "To the data qubit" in Figure 2 to the port labeled "To the observation line." Figure 8 shows the exact solution (solid line) of the lumped-element circuit model in Figure 1 and the approximate weakly coupled solution (dashed-dotted line) of the multicore transmission line in Figure 2. The frequency characteristics of the two are in good agreement. Furthermore, it can be seen that the weakly coupled assumption is quite valid in the parameter range typically used for reading out superconducting qubits. The vertical dashed line shows the notch frequency calculated from Equation (4). It can be seen that the notch frequency is in good agreement with the frequency of the analytical solution.

[0091] Figure 9 shows the radiative relaxation lifetime of the quantum bit obtained by simulation. The circuit parameters used are as follows: quantum bit frequency f ｑｕｂ = 4.75 GHz, readout resonator frequency f ｒｅｓ = 6 GHz, readout resonator external coupling strength / 2π = 50 MHz, qubit-to-readout resonator coupling g = 125 MHz, readout resonator-to-filter resonator coupling J = 30 MHz. Figure 9 compares the qubit lifetimes for a circuit including an intrinsic notch filter (with a notch) and a readout circuit with only a discrete Purcell filter (without a notch), with the same coupling constants.

[0092] As shown in FIG. 9, in the circuit of this embodiment, by utilizing notches, it is possible to achieve a significantly longer lifetime than circuits using conventional individual Purcell filters at quantum bit frequencies of 4 GHz or higher.

[0093] To optimally utilize the notch filtering capabilities of this embodiment, the notch filter frequency must be tuned sufficiently close to the qubit frequency. Because there are sufficient parameter degrees of freedom for optimization, it is possible to adjust only the notch filter frequency while maintaining the readout resonator frequency and the coupling strength between the readout resonator and the filter resonator.

[0094] Next, we will describe an experimental realization method for the distributed constant circuit shown in Fig. 2. As will be shown below, by experimentally realizing the filter circuit of the configuration shown in Fig. 2, it can be seen that the notch filter of the present invention can be implemented in an inherent form.

[0095] 10 shows an example implementation of a filter circuit 6 with an intrinsic notch for use in four-way readout of superconducting qubits. 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. 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 single common observation line.

[0096] 11 is an enlarged view of the first quantum bit 91 and its vicinity in FIG. 10 . The first readout resonator 111 includes a first readout resonator portion 111 a and a second readout resonator portion 111 b. The first filter resonator 111 includes a first filter resonator portion 121 a and a second filter resonator portion 121 b. A multicore transmission line 20 is disposed between the first readout resonator 111 and the first filter resonator 112.

[0097] FIG. 12 shows the frequency dependence of the radiative relaxation time T1 for the first quantum bit 91. FIG. 13 shows the frequency dependence of the radiative relaxation time T1 for the second quantum bit 92. FIG. 14 shows the frequency dependence of the radiative relaxation time T1 for the third quantum bit 93. FIG. 15 shows the frequency dependence of the radiative relaxation time T1 for the fourth quantum bit 94. In each figure, crosses indicate experimental results, and circles indicate simulation results. The experimental results and simulations are in good agreement. As shown in FIGS. 12 to 15, it can be seen that the radiative relaxation time for each quantum bit peaks around frequencies of 8.2 GHz to 9 GHz. In this way, it was experimentally verified that the filter circuit 6 allows each individual Purcell filter to also function as a notch filter, thereby realizing the desired filter function.

[0098] When understanding the abstract technical ideas of the embodiments and modifications, the technical ideas should not be interpreted as being limited to the contents of the embodiments and modifications. The above-described embodiments and modifications are merely illustrative examples, and many design modifications, such as changes, additions, and deletions of components, are possible. In the embodiments, the contents in which such design modifications are possible are emphasized by adding the notation "embodiment." However, design modifications are also permitted even in contents without such notation.

[0099] The present disclosure is applicable to filter circuits, quantum devices, and quantum computers.

[0100] REFERENCE SIGNS LIST 1. Filter circuit, 2. Filter circuit, 3. Filter circuit, 4. Filter circuit, 5. Filter circuit, 6. Filter circuit, 11. Readout resonator, 11a. First readout resonator portion, 11a1. First end, 11a2. Second end, 11b. Second readout resonator portion, 11b1. First end, 11b2. Second end, 12. Filter resonator, 12a. First filter resonator portion, 12a1. First end, 12a2. Second end, 12b. Second filter resonator portion, 12b1. First end, 12b2. Second end, 13. Coupling circuit portion, 14. Capacitor, 15. Inductor, 20. Multicore transmission line, 21. First core wire, 22: Second core wire, 30: Capacitor, 31: Inductor, 80: Quantum device, 81: Data quantum bit, 82: Observation line, 91: First quantum bit, 92: Second quantum bit, 93: Third quantum bit, 94: Fourth quantum bit 111: First readout resonator, 111a: First readout resonator portion of first readout resonator, 111b: Second readout resonator portion of first readout resonator, 112: Second readout resonator, 113: Third readout resonator, 114: Fourth readout resonator, 121: First filter resonator, 121a: First filter resonator portion of first filter resonator, 131b: Second filter resonator portion of first filter resonator 122: Second filter resonator; 123: Third filter resonator; 124: Fourth filter resonator; 200: Multicore transmission line; S1: Forming a readout resonator; S2: Forming a filter resonator; S3: Coupling the readout resonator to a data qubit; S4: Coupling the filter resonator to an observation line; S5: Electromagnetically coupling the readout resonator and the filter resonator using capacitive and inductive coupling in parallel; S11: Providing a readout resonator component that couples to a data qubit;S12: A step of providing a filter resonator component to be coupled to the observation line; S13: A step of assembling the readout resonator component and the filter resonator component so that they are electromagnetically coupled using capacitive coupling and inductive coupling in parallel; S21: A step of performing bandpass filtering to transmit only frequencies near the readout frequency of the readout resonator; S22: A step of performing notch filtering to suppress energy relaxation of the quantum bit to the observation line; S31: A step of coupling the electromagnetic field mode of the quantum bit to the electromagnetic field mode of the readout resonator; S32: A step of coupling the readout resonator to the observation line.

Claims

1. A filter circuit comprising: a readout resonator coupled to a data quantum bit; and a filter resonator coupled to an observation line, wherein the readout resonator and the filter resonator are electromagnetically coupled using capacitive coupling and inductive coupling in parallel.

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

3. The filter circuit according to claim 1, further comprising a multi-core transmission line disposed between the readout resonator and the filter resonator, wherein the capacitive coupling and the inductive coupling are realized by the multi-core transmission line.

4. The filter circuit of claim 3, wherein the readout resonator is composed of a first readout resonator portion having a first end connected to a data quantum bit and a second readout resonator portion having a first end grounded, the filter resonator is composed of a first filter resonator portion having a first end connected to an observation line and a second filter resonator portion having a first end grounded, and the multi-core transmission line is installed between the second end of the first readout resonator portion and the second end of the first filter resonator portion, and the second end of the second readout resonator portion and the second end of the second filter resonator portion.

5. Let the length of the multi-core transmission line be l. ｃ The propagation speed of the wave propagating through the multi-core transmission line is v ｃ The capacitance per unit length of the first core wire and the second core wire of the multi-core transmission line is C ｌ The inductance per unit length of the first core wire and the second core wire of the multi-core transmission line is L ｌ The capacitance per unit length between the first core and the second core of the multi-core transmission line is C ｍ The inductance per unit length 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 portion 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 multi-core transmission line is l ｃ , and the variables of the distributed constant circuit are Then, the notch frequency ω ｆ is expressed as follows:

5. The filter circuit according to claim 4, wherein the following is satisfied:

6. The notch frequency ω ｆ is expressed as follows:

6. The filter circuit according to claim 5, wherein the filter circuit is expressed by the following formula:

7. The coupling constant J between the readout resonator and the filter resonator is expressed by the following formula:

7. The filter circuit according to claim 6, characterized in that it is expressed by:

8. The filter circuit according to claim 3, further comprising a coupling capacitor disposed in addition to said multi-core transmission line.

9. The filter circuit according to claim 3, further comprising a coupling capacitor and an inductor arranged in addition to the multi-core transmission line.

10. The filter circuit of claim 9, further comprising a capacitor and an inductor disposed between the readout resonator and the filter resonator, wherein the capacitive coupling and the inductive coupling are realized by a capacitor and an inductor disposed between the readout resonator and the filter resonator, respectively.

11. A quantum device comprising: a data quantum bit; an observation line; and a filter circuit according to any one of claims 1 to 10, wherein the filter circuit is disposed between the data quantum bit and the observation line.

12. A quantum computer comprising the quantum device according to claim 11.

13. A filter circuit comprising: one or more data quantum bits; one or more readout resonators corresponding to each of the data quantum bits; a filter resonator having characteristics corresponding to the resonant frequency of the readout resonator; a coupler circuit disposed between the readout resonator and the filter resonator for electrically and magnetically coupling the readout resonator and the filter resonator; and a common observation line, wherein the filter circuit has both a bandpass filter characteristic near the readout frequency utilizing the resonance of the filter resonator, and a notch filter characteristic near the quantum bit frequency utilizing interference in the electrical and magnetic coupler circuit.

14. A method for manufacturing a filter circuit having a readout resonator and a filter resonator, comprising the steps of: forming a readout resonator; forming a filter resonator; coupling the readout resonator to a data quantum bit; coupling the filter resonator to an observation line; and electromagnetically coupling the readout resonator and the filter resonator using capacitive coupling and inductive coupling in parallel.

15. A method of assembling a filter circuit, comprising the steps of: providing a readout resonator component for coupling to a data quantum bit; providing a filter resonator component for coupling to an observation line; and assembling the readout resonator component and the filter resonator component so as to be electromagnetically coupled using capacitive coupling and inductive coupling in parallel.

16. A method for filtering a readout frequency in distributed readout of a quantum bit onto an observation line, comprising the steps of: performing bandpass filtering using a filter circuit as defined in any one of claims 1 to 7, which transmits only frequencies near the readout frequency of the readout resonator; and performing notch filtering to suppress energy relaxation of the quantum bit onto the observation line.

17. A method for distributed readout of a quantum bit onto an observation line, comprising the steps of: coupling an electromagnetic field mode of the quantum bit to an electromagnetic field mode of a readout resonator using a filter circuit as defined in any one of claims 1 to 7; and coupling the readout resonator to the observation line.