Electronic circuits and computers

Abstract

To improve an electronic circuit and a calculator in which characteristics can be improved.SOLUTION: An electronic circuit comprises a band-pass filter and at least one first circuit. The band-pass filter includes a plurality of filter resonators. Two adjacent filter resonators included in the plurality of filter resonators can be mutually coupled. The first circuit includes a first qubit and a first readout resonator. The first readout resonator can be coupled with the first qubit and one of the plurality of filter resonators. A passband of the band-pass filter includes a first passband and a second passband. A magnitude of a first ripple of the first passband is equal to or less than 1 / 10 of a magnitude of a second ripple of the second passband.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] FIELD OF THE INVENTION Embodiments of the present invention relate to electronic circuits and computers. [Background technology]

[0002] For example, electronic circuits including quantum bits are used in computers, and improvements in the characteristics of such electronic circuits are desired. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] E. Jeffrey et al., Phys. Rev. Lett., 112, 190504 (2014). Summary of the Invention [Problem to be solved by the invention]

[0004] Embodiments of the present invention provide electronic circuits and computers that can have improved performance. [Means for solving the problem]

[0005] According to an embodiment of the present invention, an electronic circuit includes a bandpass filter and at least one first circuit. The bandpass filter includes a plurality of filter resonators. Two adjacent filter resonators in the plurality of filter resonators are couplable with each other. The first circuit includes a first quantum bit and a first readout resonator. The first readout resonator is couplable with the first quantum bit and one of the plurality of filter resonators. The passband of the bandpass filter includes a first passband and a second passband. The magnitude of the first ripple in the first passband is 1 / 10 or less of the magnitude of the second ripple in the second passband. [Brief explanation of the drawings]

[0006] [Figure 1]FIG. 1 is a schematic view illustrating an electronic circuit according to the first embodiment. [Figure 2] 2(a) and 2(b) are graphs illustrating the characteristics of the electronic circuit according to the first embodiment. [Figure 3] FIG. 3 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. [Figure 4] FIG. 4 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. [Figure 5] FIG. 5 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. [Figure 6] 6(a) and 6(b) are graphs illustrating the characteristics of an electronic circuit. [Figure 7] 7(a) and 7(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 8] 8(a) and 8(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 9] 9(a) and 9(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 10] 10(a) and 10(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 11] FIG. 11 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 12] FIG. 12 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 13] FIG. 13 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 14] FIG. 14 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 15] FIG. 15 is a graph illustrating the characteristics of an electronic circuit. [Figure 16] 16(a) and 16(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 17] 17(a) and 17(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 18]18(a) and 18(b) are graphs illustrating the characteristics of the electronic circuit. [Figure 19] FIG. 19 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 20] FIG. 20 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 21] FIG. 21 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 22] FIG. 22 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 23] FIG. 23 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 24] FIG. 24 is a schematic view illustrating the electronic circuit according to the first embodiment. [Figure 25] FIG. 25 is a schematic plan view illustrating the electronic circuit according to the first embodiment. [Figure 26] 26(a) and 26(b) are schematic cross-sectional views illustrating a part of the electronic circuit according to the first embodiment. [Figure 27] FIG. 27 is a schematic diagram illustrating a computer according to the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0007] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The drawings are schematic or conceptual, and the relationship between the thickness and width of each part, the size ratio between parts, etc. are not necessarily the same as those in reality. Even when the same part is shown, the dimensions and ratios may be different depending on the drawing. In this specification and in each drawing, elements similar to those previously described with reference to the previous drawings are designated by the same reference numerals, and detailed descriptions thereof will be omitted where appropriate.

[0008] (First embodiment) FIG. 1 is a schematic view illustrating an electronic circuit according to the first embodiment. As shown in FIG. 1, the electronic circuit 110 according to the embodiment includes a band-pass filter 50 and at least one first circuit 31.

[0009] The bandpass filter 50 includes a plurality of filter resonators 58r. Two adjacent ones of the plurality of filter resonators 58r can be coupled to each other. Two adjacent ones of the plurality of filter resonators 58r are, for example, electromagnetically coupled. The electromagnetic field coupling includes, for example, at least one of electric field coupling and magnetic field coupling. The electromagnetic field coupling may include, for example, at least one of capacitive coupling and inductive coupling. In one example, two adjacent ones of the plurality of filter resonators 58r can be, for example, capacitively coupled. At least two of the plurality of filter resonators 58r are connected in series. At least two of the plurality of filter resonators 58r are coupled to each other in series.

[0010] The plurality of filter resonators 58r includes, for example, a first filter resonator R(1), a second filter resonator R(2), a third filter resonator R(3), ..., and an Nth filter resonator R(N), where "N" is, for example, an integer equal to or greater than 4.

[0011] The first circuit 31 includes a first quantum bit 11 and a first readout resonator 21. The first readout resonator 21 is capable of coupling to the first quantum bit 11 and one of the plurality of filter resonators 58r. The first readout resonator 21 is capable of electromagnetic field coupling to the first quantum bit 11. The first readout resonator 21 is capable of electromagnetic field coupling to one of the plurality of filter resonators 58r.

[0012] For example, a plurality of first circuits 31 may be provided. One of the plurality of first circuits 31 may be coupled to one of the plurality of filter resonators 58r. Another of the plurality of first circuits 31 may be coupled to another of the plurality of filter resonators 58r. For example, the plurality of first circuits 31 may be coupled to each of the plurality of filter resonators 58r.

[0013] 1, the band-pass filter 50 may further include a first portion 61P. The first portion 61P can receive a signal. 。 The first portion 61P is couplable to one of the plurality of filter resonators 58r. In this example, the first portion 61P is couplable to the first filter resonator R(1).

[0014] 1, the bandpass filter 50 may further include a second portion 62P. The second portion 62P may output the above-described signal. The second portion 62P may be coupled to another one of the plurality of filter resonators 58r. In this example, the second portion 62P may be coupled to the Nth filter resonator R(N).

[0015] The first portion 61P corresponds to, for example, an input port. The second portion 62P corresponds to, for example, an output port. For example, an input signal generator 61 (SG: Signal Generator) is provided. The first portion 61P can receive signals from the input signal generator 61 and supply them to the plurality of filter resonators 58r. For example, an output signal amplifier 62 (AMP: Amplifier) ​​is provided. The second portion 62P can output output signals of the plurality of filter resonators 58r to the output signal amplifier 62.

[0016] For example, the state of a first quantum bit 11 included in a first circuit 31 is read out via a first readout resonator 21 and a plurality of filter resonators 58r. In a readout operation, a signal from an input signal generator 61 passes through a bandpass filter 50 and is amplified by an output signal amplifier 62.

[0017] In the read operation, information about multiple states of the first quantum bit 11 is obtained. The multiple states of the first quantum bit 11 include, for example, a first state and a second state. For example, the difference in signal phase between the first state and the second state is read. This determines the state of the first quantum bit 11. For example, in a computer, the first state corresponds to one of "0" and "1." The second state corresponds to the other of "0" and "1."

[0018] In the embodiment, each of the plurality of filter resonators 58r may be, for example, a wave guide resonator (WGR). The bandpass filter 50 functions as, for example, a Purcell filter. The bandpass filter 50 may be, for example, a Chebyshev filter.

[0019] 2(a) and 2(b) are graphs illustrating the characteristics of the electronic circuit according to the first embodiment. The horizontal axis of these figures is frequency fr1 (GHz), and the vertical axis is signal strength Int1 (dB).

[0020] 2(a) illustrates the pass characteristic 50p of the band-pass filter 50. As shown in FIG. 2(a), the band-pass filter 50 includes a pass band 50pb and a non-pass band. The non-pass band includes a low-frequency non-pass band 50lb and a high-frequency non-pass band 50hb. The pass band 50pb is located between the low-frequency non-pass band 50lb and the high-frequency non-pass band 50hb.

[0021] The signal strength Int1 (eg, the amount of transmission) in the passband 50pb is higher than the signal strength Int1 in the low frequency non-passband 50lb. The signal strength Int1 (eg, the amount of transmission) in the passband 50pb is higher than the signal strength Int1 in the high frequency non-passband 50hb.

[0022] For example, the signal strength Int1 in the passband 50pb is 100 times or more (e.g., a difference of 20dB or more) the signal strength Int1 in the low-frequency non-passband 50lb. For example, the signal strength Int1 in the passband 50pb is 100 times or more (e.g., a difference of 20dB or more) the signal strength Int1 in the high-frequency non-passband 50hb.

[0023] As shown in FIG. 2(a), the passband 50pb of the bandpass filter 50 includes a first passband w1 and a second passband w2. In this example, the frequency of the first passband w1 is higher than the frequency of the second passband w2. The ripple (first ripple R1) of the first passband w1 is smaller than the ripple (second ripple R2) of the second passband w2. The first passband w1 is a passband with substantially constant pass characteristics. The second passband w2 is a passband with variable pass characteristics.

[0024] By providing such a first passband w1 and a second passband w2, for example, high steepness can be obtained in the change in characteristics between the passband 50 pb and the non-passband. For example, the out-of-band suppression amount Δ50 in the non-passband can be made larger. For example, a faster readout operation can be realized. For example, a readout operation with lower error can be realized. For example, the number of multiple first circuits 31 provided corresponding to the non-passband (i.e., the number of multiple first quantum bits 11) can be increased. For example, the multiple first quantum bits 11 can be provided at a higher density.

[0025] In a general filter (first reference example), a design is applied in which the signal strength Int1 (e.g., the amount of transmission) is constant throughout the entire 50 pb passband. This allows signals to pass with uniform signal strength Int1 (e.g., the amount of transmission) throughout the entire 50 pb passband. In the first reference example, ripples are small throughout the entire 50 pb passband. In the first reference example, a first passband w1 and a second passband w2, in which the magnitude of ripples differ from each other, are not provided. In this first reference example, a multi-stage filter using many resonators is required to sufficiently increase the out-of-band suppression amount Δ50. In the first reference example, the circuit area becomes too large when multiple bits are used. Practical problems arise in the first reference example.

[0026] In contrast, in the embodiment, a first passband w1 and a second passband w2 having different ripple magnitudes are provided. As a result, it has been found that the out-of-band suppression amount Δ50 can be made larger compared to the first reference example. This enables faster readout operations. For example, the number of multiple first quantum bits 11 can be increased. For example, multiple first quantum bits 11 can be provided at a higher density. According to the embodiment, an electronic circuit capable of improving characteristics can be provided.

[0027] In this example, the passband 50 pb further includes a third passband w3. The first passband w1 is located between the second passband w2 and the third passband w3. The magnitude of the first ripple R1 is smaller than the ripple (third ripple R3) in the third passband w3.

[0028] 2(b) illustrates the pass characteristic Ch1 between the first portion 61P and the second portion 62P. In this example, the number of the multiple first circuits 31 is four. FIG. 2(b) illustrates the resonant frequencies 11p of the four first quantum bits 11 and the resonant frequencies 21p of the four first readout resonators 21.

[0029] The resonant frequency 21p of the first readout resonator 21 is included in the first passband w1. The resonant frequency 21p of the first readout resonator 21 can pass through the band-pass filter 50 with low loss. One of the multiple resonant frequencies 21p has a frequency width (linewidth 21w). The width of the product of the number of first circuits 31 and the linewidth 21w is included in the first passband w1.

[0030] The resonant frequency 11p of the first quantum bit 11 is included in the non-pass band of the band-pass filter 50 (e.g., low-frequency non-pass band 501b). The resonant frequency 11p of the first quantum bit 11 is in the non-pass band of the band-pass filter 50. The resonant frequency 11p of the first quantum bit 11 does not substantially pass through the band-pass filter 50. One of the multiple first quantum bits 11 has a frequency width (linewidth 11w). The width of the product of the number of first circuits 31 and the linewidth 11w is included in the non-pass band (e.g., low-frequency non-pass band 501b).

[0031] According to the embodiment, for example, it is possible to appropriately measure the frequency change of the first readout resonator 21 in response to the state change of the first quantum bit 11 while suppressing the attenuation of the first quantum bit 11.

[0032] FIG. 3 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. Fig. 3 illustrates the characteristics of a passband of 50 pb. The horizontal axis of Fig. 3 represents frequency fr1. The vertical axis of Fig. 3 represents signal strength Int1.

[0033] In the first ripple R1 in the first passband w1, the difference between the maximum and minimum values ​​of the signal strength Int1 corresponds to the magnitude Rp1 of the first ripple R1. In the second passband w2, the difference between the maximum and minimum values ​​of the signal strength Int1 corresponds to the magnitude Rp2 of the second ripple R2. In the third passband w3, the difference between the maximum and minimum values ​​of the signal strength Int1 corresponds to the magnitude Rp3 of the third ripple R3.

[0034] In the embodiment, for example, the magnitude Rp1 of the first ripple R1 is 1 / 10 or less of the magnitude Rp2 of the second ripple R2. For example, the magnitude Rp1 of the first ripple R1 is 1 / 10 or less of the magnitude Rp3 of the third ripple R3. The magnitude Rp1 of the first ripple R1 may be 1 / 5 or less of the magnitude Rp2 of the second ripple R2. For example, the magnitude Rp1 of the first ripple R1 may be 1 / 5 or less of the magnitude Rp3 of the third ripple R3.

[0035] FIG. 4 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. The horizontal axis of Figure 4 is the ripple ratio RR1. R1 The second ripple of magnitude Rp1 R2 4 is the ratio (Rp1 / Rp2) of the magnitude of Rp1 to the magnitude Rp2 of the first readout resonator 21. The vertical axis of FIG.

[0036] As shown in FIG. 4, as the ripple ratio RR1 increases, the insertion loss IL increases. In practice, the insertion loss IL is preferably 0.1 or less. In the embodiment, the ripple ratio RR1 is preferably 1 / 10 or less. The ripple ratio RR1 may be 0.05 or less. A smaller insertion loss IL can be obtained.

[0037] In this embodiment, a first pass band w1 with a small ripple and a second pass band w2 with a large ripple are provided. A band-pass filter 50 having such characteristics can be applied to a first circuit 31 having various configurations. For example, in the design concept of the first reference example described above, if the design of the first circuit 31 is different, the inter-resonator coupling must be changed. In the first reference example, the design of the band-pass filter 50 must be changed.

[0038] In contrast, in the embodiment, it is sufficient that the first pass band w1 with small ripples is applicable to first circuits 31 with various characteristics. The band-pass filter 50 according to the embodiment can accommodate first circuits 31 with various designs. For example, high design efficiency can be achieved.

[0039] The above-described characteristics of the bandpass filter 50 can be obtained by appropriately controlling the amount of coupling (for example, coupling coefficient) among the plurality of filter resonators 58r.

[0040] 1, the band-pass filter 50 has a plurality of coupling coefficients kx. One of the plurality of coupling coefficients kx is a coupling coefficient between two adjacent filter resonators included in the plurality of filter resonators 58r. For example, the plurality of coupling coefficients kx include a first coupling coefficient k(1), a second coupling coefficient k(2), ..., and an (N-1)th coupling coefficient k(N-1).

[0041] The first coupling coefficient k(1) is the coupling coefficient between the first filter resonator R(1) and the second filter resonator R(2). The second coupling coefficient k(2) is the coupling coefficient between the second filter resonator R(2) and the third filter resonator R(3). The (N-1)th coupling coefficient k(N-1) is the coupling coefficient between the (N-1)th filter resonator R(N-1) and the Nth filter resonator R(N). The (i-1)th coupling coefficient k(i-1) is the coupling coefficient between the (i-1)th filter resonator R(i-1) and the ith filter resonator R(i), where "i" is an integer between 1 and N.

[0042] In the embodiment, when the number (N) of the plurality of filter resonators 58r is an even number, the difference between the minimum value of the plurality of coupling coefficients kx and the maximum value of the plurality of coupling coefficients kx is 0.1 times or less the average value of the plurality of coupling coefficients kx. For example, the plurality of coupling coefficients kx are substantially the same. With this configuration, the first pass band w1, the second pass band w2, and the third pass band w3 described above are effectively obtained. An example in which the number (N) of the plurality of filter resonators 58r is an odd number will be described later.

[0043] 1, the bandpass filter 50 has a first portion external Qe. The first portion external Qe is an external Q between the first portion 61P and one of the multiple filter resonators 58r (in this example, the first filter resonator R(1)) that can be coupled to the first portion 61P. The "external Q" (external Q value) represents the degree of coupling between an external circuit and a filter resonator. The "external Q" (external Q value) corresponds to, for example, the ratio of the resonant frequency to the bandwidth.

[0044] 1, in this example, the bandpass filter 50 has a second section external Qf, which is an external Q between the second section 62P and another one of the plurality of filter resonators 58r (in this example, the Nth filter resonator R(N)) that can be coupled to the second section 62P.

[0045] The multiple coupling coefficients kx may be different from the first portion external Qe. The multiple coupling coefficients kx may be different from the second portion external Qf. For example, the second portion external Qf may be substantially the same as the first portion external Qe.

[0046] FIG. 5 is a graph illustrating the characteristics of the electronic circuit according to the first embodiment. 5 corresponds to the case where the number (N) of the plurality of filter resonators 58r is an even number. The horizontal axis of FIG. 5 represents the coupling coefficient difference Δk. The coupling coefficient difference Δk is the ratio of the difference between the minimum value of the plurality of coupling coefficients kx and the maximum value of the plurality of coupling coefficients kx to the average value of the plurality of coupling coefficients kx. The vertical axis of FIG. 5 represents the worst value Vr1(d B ) It is preferable that the worst value Vr1 of the reflection characteristic is small.

[0047] As shown in Fig. 5, as the coupling coefficient difference Δk increases, the worst value Vr1 of the reflection characteristics increases. It is practically preferable that the worst value Vr1 of the reflection characteristics be -10 dB or less. Therefore, it is preferable that the coupling coefficient difference Δk be 10% or less. In other words, it is preferable that the difference between the minimum value of the multiple coupling coefficients kx and the maximum value of the multiple coupling coefficients kx be 1 / 10 or less of the average value of the multiple coupling coefficients kx.

[0048] An example of the results of simulating the characteristics of the electronic circuit 110 will now be described. 6(a), 6(b), 7(a), 7(b), 8(a), 8(b), 9(a) and 9(b) are graphs illustrating the characteristics of the electronic circuit. These figures illustrate the characteristics of the bandpass filter 50. The horizontal axis of these figures is frequency fr1. Figures 6(a), 7(a), 8(a), and 9(a) illustrate the pass characteristic S21. Figures 6(b), 7(b), 8(b), and 9(b) illustrate the reflection characteristic S11. In these examples, the multiple coupling coefficients kx are the same, 0.053. The first portion external Qe is 20.0. The second portion external Qf is 20.0. In these examples, the number (N) of the multiple filter resonators 58r is an even number.

[0049] 6(a) and 6(b), the number (N) of the plurality of filter resonators 58r is 4. In this example, the ripple ratio RR1 (i.e., Rp1 / Rp2) is 0.016.

[0050] 7(a) and 7(b), the number (N) of the plurality of filter resonators 58r is 8. In this example, the ripple ratio RR1 is 0.006.

[0051] 8(a) and 8(b), the number (N) of the plurality of filter resonators 58r is 20. In this example, the ripple ratio RR1 is 0.005.

[0052] 9(a) and 9(b), the number (N) of the plurality of filter resonators 58r is 80. In this example, the ripple ratio RR1 is 0.005.

[0053] The greater the number (N) of filter resonators 58r, the greater the abruptness of the transition between passband 50pb and non-passband (eg, low frequency non-passband 50lb).

[0054] In an embodiment, when the number (N) of the multiple filter resonators 58r is an even number, by appropriately setting the multiple coupling coefficients kx, it is easy to obtain an appropriate first pass band w1, an appropriate second pass band w2, and an appropriate third pass band w3.

[0055] 10(a) and 10(b) are graphs illustrating the characteristics of the electronic circuit. These figures illustrate simulation results when multiple coupling coefficients kx are changed. In this example, the second portion external Qf is the same as the first portion external Qe. The horizontal axis of these figures is the first portion external Qe. The vertical axis of these figures is multiple coupling coefficients kx.

[0056] In these figures, the parameter FBW is changed. The parameter FBW is the center frequency f0 (see FIG. 2(a)) of the passband 50pb, which is the product of the frequency width (line width 21w) of the plurality of resonant frequencies 21p and the number of the plurality of resonant frequencies 21p. (see) is a ratio to. In practice, the parameter FBW is preferably 10% or less. For example, the number of the multiple first circuits 31 can be increased. When the parameter FBW is 10% or less, the width of the first passband w1 is prevented from becoming excessively large. For example, an appropriate width of the first passband w1 can increase the out-of-band suppression amount Δ50. For example, the steepness of the change in characteristics can be increased between the passband 50 pb and the non-passband. The parameter FBW may be, for example, 1% or more. The parameter FBW may be, for example, 0.1% or more.

[0057] 10(a) shows examples where the parameter FBW is 1%, 3.08%, and 10%, and FIG. 10(b) shows examples where the parameter FBW is 1.54% and 6.15%.

[0058] The characteristic when the parameter FBW is 1% as shown in FIG. 10(a) can be approximately expressed by the following first equation. kx=(2×10 -7 )×Qe 4 -(2×10 -5 )×Qe 3 +0.0009×Qe 2 -0.0211×Qe+0.2361 …(1) The characteristic when the parameter FBW is 10% as shown in FIG. 10(a) can be approximately expressed by the following first equation. kx=0.0003×Qe 2 -0.014×Qe+0.2216 … (2) Therefore, in an embodiment, when the number (N) of the plurality of filter resonators 58r is an even number, it is preferable that one of the plurality of coupling coefficients kx (each of the plurality of coupling coefficients kx) is equal to or greater than a first value and equal to or less than a second value. The first value is (2×10 -7 )×Qe 4 -(2×10 -5 )×Qe 3+0.0009×Qe 2 -0.0211×Qe+0.2361. The second value is 0.0003×Qe 2 -0.014×Qe+0.2216.

[0059] Such a plurality of coupling coefficients kx makes it possible to obtain an appropriate first passband w1 with a small ripple.

[0060] For example, the second portion 62P may be provided. In this case, it is preferable that one of the multiple coupling coefficients kx (each of the multiple coupling coefficients kx) is equal to or greater than a third value and equal to or less than a fourth value. The third value is (2×10 -7 )×Qf 4 -(2×10 -5 )×Qf 3 +0.0009×Qf 2 -0.0211×Qf+0.2361. The fourth value is 0.0003×Qf 2 -0.014×Qf+0.2216.

[0061] As described above, when the number (N) of the plurality of filter resonators 58r is an even number, the plurality of coupling coefficients kx can be set to be substantially the same as one another. In one example, the plurality of filter resonators 58r can be set to be substantially the same as one another. This allows the plurality of coupling coefficients kx to be set to be substantially the same as one another.

[0062] FIG. 11 is a schematic view illustrating the electronic circuit according to the first embodiment. 11, the bandpass filter 50 has a plurality of distances dx. One of the plurality of distances dx is the distance between two adjacent ones of the plurality of filter resonators 58r. For example, the plurality of distances dx includes a first distance d(1), a second distance d(2), ..., and an (N-1)th distance d(N-1). The (i-1)th distance d(i-1) is the distance between the (i-1)th filter resonator R(i-1) and the ith filter resonator R(i). "i" is an integer between 1 and N.

[0063] When the number (N) of the plurality of filter resonators 58r is an even number, the difference between the minimum value of the plurality of distances dx and the maximum value of the plurality of distances dx is preferably 0.1 times or less the average value of the plurality of distances dx. By using a uniform plurality of distances dx, a first passband w1 with small ripples can be appropriately obtained.

[0064] When the number (N) of the plurality of filter resonators 58r is odd, it has been found that a first passband w1 with small ripples can be appropriately obtained by making the coupling coefficient kx of some of the plurality of filter resonators 58r different from that of the others.

[0065] FIG. 12 is a schematic view illustrating the electronic circuit according to the first embodiment. 12, the bandpass filter 50 also includes a plurality of filter resonators 58r. Adjacent two of the plurality of filter resonators 58r are capable of coupling to each other. The first circuit 31 includes a first quantum bit 11 and a first readout resonator 21. The first readout resonator 21 is capable of coupling to the first quantum bit 11 and one of the plurality of filter resonators 58r.

[0066] In the electronic circuit 111, the number (N) of the multiple filter resonators 58r is an odd number. The multiple filter resonators 58r include a first filter resonator R(1) to an N-th filter resonator R(N). "N" is (2n+1). "n" is an integer equal to or greater than 2. For example, the number (N) of the multiple filter resonators 58r is an odd number equal to or greater than 5.

[0067] FIG. 13 is a schematic view illustrating the electronic circuit according to the first embodiment. 13, the first circuit 31 is omitted. The plurality of filter resonators 58r includes an (n-1)th filter resonator R(n-1), an nth filter resonator R(n), an (n+1)th filter resonator R(n+1), an (n+2)th filter resonator R(n+2), and an (n+3)th filter resonator R(n+3). The (n+1)th filter resonator R(n+1) is the middle filter resonator 58r among the plurality of filter resonators 58r.

[0068] The coupling coefficient between the (n-1)th filter resonator R(n-1) and the nth filter resonator R(n) is the (n-1)th coupling coefficient k(n-1). The coupling coefficient between the nth filter resonator R(n) and the (n+1)th filter resonator R(n+1) is the nth coupling coefficient k( n) The coupling coefficient between the (n+1)th filter resonator R(n+1) and the (n+2)th filter resonator R(n+2) is the (n+1)th coupling coefficient k(n+1). The coupling coefficient between the (n+2)th filter resonator R(n+2) and the (n+3)th filter resonator R(n+3) is the (n+2)th coupling coefficient k(n+2).

[0069] In the electronic circuit 111, the n-th coupling coefficient k(n) is different from the (n-1)-th coupling coefficient k(n-1). The (n+1)-th coupling coefficient k(n+1) is different from the (n+2)-th coupling coefficient k(n+ 2) It is different from the (n+2) coupling coefficient k(n+ 2) is substantially the same as the (n-1)th coupling coefficient k(n-1). For example, in the (n+1)th filter resonator R(n+1) provided at the center, the coupling coefficient kx between the (n+1)th filter resonator R(n+1) and the adjacent filter resonator 58r is set to be smaller than the other coupling coefficients kx.

[0070] For example, the n-th coupling coefficient k(n) is preferably 0.7 to less than 0.9 times the (n-1)-th coupling coefficient k(n-1).For example, the n-th coupling coefficient k(n) is preferably 0.7 to less than 0.9 times the (n+2)-th coupling coefficient k(n+2).

[0071] For example, the (n+1)th coupling coefficient k(n+1) is preferably 0.7 times or more and less than 0.9 times the (n-1)th coupling coefficient k(n-1). For example, the (n+2)th coupling coefficient k(n+2) is preferably 0.7 times or more and less than 0.9 times the (n-2)th coupling coefficient k(n+2). With such a coupling coefficient kx, a first passband w1 with small ripples can be appropriately obtained when the number (N) of the plurality of filter resonators 58r is odd.

[0072] The nth coupling coefficient k(n) may be substantially the same as the (n+1)th coupling coefficient k(n+1). The nth coupling coefficient k(n) may be, for example, 0.95 to 1.05 times the (n+1)th coupling coefficient k(n+1). The (n-1)th coupling coefficient k(n-1) may be substantially the same as the (n+2)th coupling coefficient k(n+2). The coupling coefficient k(n-1) may be 0.95 to 1.05 times the (n+2)th coupling coefficient k(n+2).

[0073] For example, in the electronic circuit 111, "n" may be equal to or greater than 3. For example, the number (N) of the plurality of filter resonators 58r is equal to or greater than 7.

[0074] 13, the band-pass filter 50 has a plurality of first-type coupling coefficients ks1 and a plurality of second-type coupling coefficients ks2. One of the plurality of first-type coupling coefficients ks1 is a coupling coefficient between two adjacent filter resonators included in the first filter resonator R(1) to the n-th filter resonator R(n). The plurality of first-type coupling coefficients ks1 are the first coupling coefficient k(1) to the (n-1)-th coupling coefficient k(n-1). The difference between the minimum value of the plurality of first-type coupling coefficients ks1 and the maximum value of the plurality of first-type coupling coefficients ks1 is 0.1 times or less the average value of the plurality of first-type coupling coefficients ks1. For example, the plurality of first-type coupling coefficients ks1 are substantially the same as one another.

[0075] One of the multiple second-type coupling coefficients ks2 is a coupling coefficient between two adjacent filter resonators included in the (n+2)th filter resonator R(n+2) to the (2n+1)th filter resonator R(2n+1). The multiple second-type coupling coefficients ks2 include the (n+2)th coupling coefficient k(n+2) to the (2n)th coupling coefficient k(2n). The difference between the minimum value of the multiple second-type coupling coefficients ks2 and the maximum value of the multiple second-type coupling coefficients ks2 is 0.1 times or less the average value of the multiple second-type coupling coefficients ks2. For example, the multiple second-type coupling coefficients ks2 are substantially the same as each other.

[0076] By using a plurality of first-type coupling coefficients ks1 that are substantially the same as one another and a plurality of second-type coupling coefficients ks2 that are substantially the same as one another, a first passband w1 with a small ripple can be effectively obtained when the number (N) of the plurality of filter resonators 58r is an odd number equal to or greater than 7.

[0077] FIG. 14 is a schematic view illustrating the electronic circuit according to the first embodiment. As shown in FIG. 14, in the electronic circuit 111, the band-pass filter 50 has a plurality of first type distances ds1 and a plurality of second type distances ds2.

[0078] One of the plurality of first type distances ds1 is the distance between two adjacent ones of the first filter resonators R(1) to n-th filter resonators R(n). The difference between the minimum value of the plurality of first type distances ds1 and the maximum value of the plurality of first type distances ds1 is 0.1 times or less the average value of the plurality of first type distances ds1. The plurality of first type distances ds1 may be substantially the same as one another.

[0079] One of the plurality of second type distances ds2 is the distance between two adjacent filter resonators included in the (n+2)th filter resonator R(n+2) to the (2n+1)th filter resonator R(2n+1). The difference between the minimum value of the plurality of second type distances ds2 and the maximum value of the plurality of second type distances ds2 is 0.1 times or less the average value of the plurality of second type distances ds2. The plurality of second type distances ds2 may be substantially the same as one another.

[0080] In the electronic circuit 111, the distance between the nth filter resonator R(n) and the (n+1)th filter resonator R(n+1) is shorter than the plurality of first type distances ds1 and shorter than the plurality of second type distances ds2. The distance between the (n+1)th filter resonator R(n+1) and the (n+2)th filter resonator R(n+2) is shorter than the plurality of first type distances ds1 and shorter than the plurality of second type distances ds2.

[0081] Below, we will explain an example of simulation results of characteristics when the coupling coefficient is changed when the number (N) of multiple filter resonators 58r is an odd number equal to or greater than 7. In the simulation, the multiple first-type coupling coefficients ks1 are the same as each other. The multiple second-type coupling coefficients ks2 are the same as each other. The multiple second-type coupling coefficients ks2 are the same as the multiple first-type coupling coefficients ks1. In the simulation, the (n+1)th coupling coefficient k(n+1) is the same as the nth coupling coefficient k(n).

[0082] FIG. 15 is a graph illustrating the characteristics of an electronic circuit. The horizontal axis of FIG. 15 represents the normalized coupling coefficient difference Dk1. The normalized coupling coefficient difference Dk1 is the ratio (k(n) / ks1) of the n-th coupling coefficient k(n) to the first type coupling coefficient ks1. The vertical axis represents the worst value Vr1(d B ) It is preferable that the worst value Vr1 of the reflection characteristic is small.

[0083] 15, when the normalized coupling coefficient difference Dk1 is 80%, the worst value Vr1 of the reflection characteristics is smallest. The normalized coupling coefficient difference Dk1 is preferably, for example, 70% or more and 90% or less. The normalized coupling coefficient difference Dk1 is more preferably, for example, 75% or more and 85% or less.

[0084] That is, for example, the n-th coupling coefficient k(n) is preferably 0.7 to 0.9 times the first type coupling coefficient ks1, and more preferably 0.75 to 0.85 times the first type coupling coefficient ks1.

[0085] For example, the n-th coupling coefficient k(n) is the (n-1)-th coupling coefficient k(n- 1) The n-th coupling coefficient k(n) is preferably 0.7 times or more and less than 0.9 times the (n+2)-th coupling coefficient. double The (n+1)-th coupling coefficient k(n+1) is preferably 0.7 times or more and less than 0.9 times the (n-1)-th coupling coefficient k(n-1). doubleThe (n+1)-th coupling coefficient k(n+1) is preferably 0.7 times or more and less than 0.9 times the (n+2)-th coupling coefficient. double It is preferable that it is less than 10 ...

[0086] The plurality of first-type coupling coefficients ks1 and the plurality of second-type coupling coefficients ks2 may be equal to or greater than the first value and equal to or less than the second value described with reference to FIG. 10(a). The first value is (2×10 -7 )×Qe 4 -(2×10 -5 )×Qe 3 +0.0009×Qe 2 -0.0211×Qe+0.2361. The second value is 0.0003×Qe 2 The multiple first-type coupling coefficients ks1 and multiple second-type coupling coefficients ks2 may be equal to or greater than the third value and equal to or less than the fourth value. The third value is (2×10 -7 )×Qf 4 -(2×10 -5 )×Qf 3 +0.0009×Qf 2 -0.0211×Qf+0.2361. The fourth value is 0.0003×Qf 2 -0.014×Qf+0.2216.

[0087] 16(a) and 16(b) are graphs illustrating the characteristics of the electronic circuit. These figures correspond to the first configuration CF1. In the first configuration CF1, the number (N) of the plurality of filter resonators 58r is 17. The n-th coupling coefficient k(n) is the same as the first type coupling coefficient ks1. The (n+1)-th coupling coefficient k(n+1) is the same as the n-th coupling coefficient k(n). The second type coupling coefficient ks2 is the same as the first type coupling coefficient ks1.

[0088] 17(a) and 17(b) are graphs illustrating the characteristics of the electronic circuit. These figures correspond to the second configuration CF2. In the second configuration CF2, the number (N) of the plurality of filter resonators 58r is 17. The n-th coupling coefficient k(n) is 0.8 times the first-type coupling coefficient ks1. The (n+1)-th coupling coefficient k(n+1) is the same as the n-th coupling coefficient k(n). The second-type coupling coefficient ks2 is the same as the first-type coupling coefficient ks1. Figures 16(a) and 17(a) illustrate the pass characteristic S21. Figures 16(b) and 17(b) illustrate the reflection characteristic S11.

[0089] 18(a) and 18(b) are graphs illustrating the characteristics of the electronic circuit. Figure 18(a) shows an enlarged view of a part of Figure 16(a), and Figure 18(b) shows an enlarged view of a part of Figure 17(a).

[0090] As shown in Figures 16(a) and 17(a), relatively good pass characteristic S21 is obtained in the first configuration CF1 and the second configuration CF2. As shown in the enlarged view of Figure 18(a), the pass characteristic S21 in the first configuration CF1 is substantially zero within the required band. On the other hand, as shown in the enlarged view of Figure 18(b), the pass characteristic S21 in the second configuration CF2 is approximately 0.15 dB larger than that in the first configuration CF1. In other words, the loss in the second configuration CF2 is smaller than the loss in the first configuration CF1.

[0091] As described above, by making the n-th coupling coefficient k(n) smaller than the first-type coupling coefficient ks1, it is possible to obtain a frequency width wx in which the bandpass characteristic S21 is substantially 0.

[0092] FIG. 19 is a schematic view illustrating the electronic circuit according to the first embodiment. As shown in FIG. 19, in the electronic circuit 112 according to the embodiment, the passband 50pb of the bandpass filter 50 includes a first passband w1 and a second passband w2. The third passband w3 does not have to be provided. In the electronic circuit 112, the frequency of the first passband w1 is higher than the frequency of the second passband w2. By providing the first passband w1 and the second passband w2, which have different ripple magnitudes, the out-of-band suppression amount Δ50 can be increased. For example, a faster read operation is possible. For example, a plurality of first quantum bits 11 can be provided at a higher density.

[0093] FIG. 20 is a schematic view illustrating the electronic circuit according to the first embodiment. As shown in FIG. 20 , in the electronic circuit 113 according to the embodiment, the passband 50pb of the bandpass filter 50 includes a first passband w1 and a second passband w2. A third passband w3 is not provided. In the electronic circuit 113, the frequency of the first passband w1 is higher than the frequency of the second passband w2. By providing the first passband w1 and the second passband w2, which have different ripple magnitudes, the out-of-band suppression amount Δ50 can be increased. For example, a faster readout operation is possible. For example, a plurality of first quantum bits 11 can be provided at a higher density.

[0094] FIG. 21 is a schematic view illustrating the electronic circuit according to the first embodiment. 21, in the electronic circuit 120 according to the embodiment, two of the plurality of filter resonators 58r that are not adjacent to each other can be coupled. Except for this, the configuration of the electronic circuit 120 may be similar to the configurations of the electronic circuits 110 to 113.

[0095] In the electronic circuit 120, for example, two filter resonators 58r that are not adjacent to each other can be coupled to each other by the conductive member 65a and the conductive member 65b. By "cross-coupling," for example, high steepness can be easily obtained in the pass characteristic 50p of the band-pass filter 50.

[0096] FIG. 22 is a schematic view illustrating the electronic circuit according to the first embodiment. 22 , in an electronic circuit 121 according to the embodiment, the bandpass filter 50 further includes a first waveguide 66. An end of the first waveguide 66 can be coupled to one of two of the plurality of filter resonators 58r that are not adjacent to each other. The other end of the first waveguide 66 can be coupled to the other of the two of the plurality of filter resonators 58r that are not adjacent to each other. The remaining configuration of the electronic circuit 121 may be the same as that of the electronic circuits 110 to 113 or 120.

[0097] For example, the length of the first waveguide 66 is substantially 0.9 to 1.1 times an odd multiple ((2m+1) times) of ¼ of the wavelength λ corresponding to the center frequency of the passband 50 pb of the bandpass filter 50, where "m" is an integer greater than or equal to 0. For example, good and realistic "cross-coupling" characteristics can be obtained.

[0098] In the above electronic circuit, the length of each of the plurality of filter resonators 58r may be, for example, substantially λ / 2. The length of each of the plurality of filter resonators 58r may be, for example, 0.9 to 1.1 times λ / 2. For example, each of the plurality of filter resonators 58r may be a half-wavelength waveguide resonator. For example, each of the plurality of filter resonators 58r may be a quarter-wavelength waveguide resonator.

[0099] FIG. 23 is a schematic view illustrating the electronic circuit according to the first embodiment. 23, the electronic circuit 122 according to the embodiment includes a circulator 67. Other configurations of the electronic circuit 122 may be similar to those of the electronic circuits 110 to 113, 120, or 121.

[0100] The circulator 67 can supply an input signal SI1 to the band-pass filter 50. The circulator 67 can obtain an output signal SO1 from the band-pass filter 50. For example, the circulator 67 includes a first port 67a, a second port 67b, and a third port 67c. In the circulator 67, a signal (input signal SI1) input from the first port 67a is output to the second port 67b. At this time, the third port 67c is isolated. On the other hand, a signal (output signal SO1) input from the second port 67b is output to the third port 67c. At this time, the first port 67a is isolated. A signal input from the third port 67c is output to the first port 67a. At this time, the second port 67b is isolated. The circulator 67 passes the input signal SI1 to the second port 67b. For example, the circulator 67 outputs the output signal SO1 input from the second port 67b to the third port 67c, but does not output it to the first port 67a.

[0101] FIG. 24 is a schematic view illustrating the electronic circuit according to the first embodiment. 24, an electronic circuit 123 according to this embodiment includes a directional coupler 69. Other configurations of the electronic circuit 123 may be similar to those of the electronic circuits 110 to 113, 120, or 121.

[0102] The directional coupler 69 includes an input section 69I and an output section 69O. The directional coupler 69 can supply an input signal SI1 input to the input section 69I to the band-pass filter 50. The output section 69O can output an output signal SO1 obtained from the band-pass filter 50.

[0103] FIG. 25 is a schematic plan view illustrating the electronic circuit according to the first embodiment. FIG. 25 shows an example of an electronic circuit 121. For example, a plurality of filter resonators 58r, a plurality of first quantum bits 11, and a plurality of first readout resonators 21 can be formed by the conductive layer 10L. In this example, a first waveguide 66 is also provided by the conductive layer 10L. As shown in FIG. 25, a plurality of Josephson junctions (such as a first Josephson junction J1 and a second Josephson junction J2) are provided in each of the plurality of first quantum bits 11. A current path including the plurality of Josephson junctions forms a closed loop. The current path forms a dc-SQUID (superconducting quantum interference device). A space surrounded by a current path including the plurality of Josephson junctions corresponds to, for example, a SQUID loop. The plurality of first quantum bits 11 correspond to, for example, Transmon resonators.

[0104] 26(a) and 26(b) are schematic cross-sectional views illustrating a part of the electronic circuit according to the first embodiment. 26(a) illustrates a first Josephson junction J1. For example, a first conductive layer 10a and a second conductive layer 10b are provided on a first surface 10f of a substrate 10s. A first insulating layer 10i is provided between a portion of the first conductive layer 10a and a portion of the second conductive layer 10b. These conductive layers and the first insulating layer 10i form the first Josephson junction J1.

[0105] 26(b) illustrates a second Josephson junction J2. For example, a third conductive layer 10c and a fourth conductive layer 10d are provided on a first surface 10f of a substrate 10s. A second insulating layer 10j is provided between a portion of the third conductive layer 10c and a portion of the fourth conductive layer 10d. These conductive layers and the second insulating layer 10j form the second Josephson junction J2.

[0106] The third conductive layer 10c may be connected to or continuous with one of the first conductive layer 10a and the second conductive layer 10b. The fourth conductive layer 10d may be connected to or continuous with the other of the first conductive layer 10a and the second conductive layer 10b. The second insulating layer 10j may be continuous with the first insulating layer 10i.

[0107] The direction from a portion of the first conductive layer 10a to a portion of the second conductive layer 10b is defined as the Z-axis direction. A direction perpendicular to the Z-axis direction is defined as the X-axis direction. A direction perpendicular to the Z-axis direction and the X-axis direction is defined as the Y-axis direction. The first conductive layer 10a, the second conductive layer 10b, the third conductive layer 10c, and the fourth conductive layer 10d correspond to a portion of the conductive layer 10L. The conductive layer 10L is aligned along the XY plane (see FIG. 25).

[0108] An appropriate coupling coefficient k can be obtained by appropriately controlling the first distance d(1), the second distance d(2), ..., and the (N-1)th distance d(N-1) shown in Fig. 25. If these distances are short, the coupling coefficient k becomes high.

[0109] The length Ln1 over which the plurality of filter resonators 58r face each other is appropriately determined as shown in Fig. 25. If the length Ln1 is long, the coupling coefficient k becomes high.

[0110] In the electronic circuit 121, a transmon qubit including multiple Josephson junctions is applied to each of the multiple first qubits 11. In an embodiment, at least one of the multiple first qubits 11 may be a transmon qubit including one Josephson junction.

[0111] In an embodiment, a base conductive member 10M may be provided on the second surface 10g of the substrate 10s. The first surface 10f is between the second surface 10g and the conductive layer 10L. The second surface 10g is between the base conductive member 10M and the first surface 10f. The second surface 10g is the surface opposite to the first surface 10f. The base conductive member 10M may be set to a fixed potential, for example. The base conductive member 10M may be a ground plane, for example. The second surface 10g may be in contact with a conductive housing. The base conductive member 10M may be at least a part of the conductive housing. The base conductive member 10M and a part of the conductive layer 10L may be electrically connected by a connecting member. The connecting member may be a via that penetrates the substrate 10s.

[0112] Some of the conductive layers 10L are provided around the resonators and signal lines. Some of the conductive layers 10L serve as ground layers. Do The plurality of conductive layers 10L corresponding to the layers may be electrically connected to each other by connecting conductive members 10C. The connecting conductive members 10C may include, for example, wires. The connecting conductive members 10C may include at least a portion of the base conductive member 10M. The connecting conductive members 10C may include conductive vias (connecting members) that penetrate the substrate 10s.

[0113] (Second embodiment) The second embodiment relates to a computer. FIG. 27 is a schematic diagram illustrating a computer according to the second embodiment. As shown in FIG. 27 , a computer 210 according to an embodiment includes an electronic circuit according to the first embodiment (electronic circuit 110 in this example) and a control unit 70. The control unit 70 is capable of controlling the state of the first quantum bit. For example, a control conductive member 60 is provided in the electronic circuit or the computer. The control conductive member 60 may be provided in the vicinity of the first quantum bit 11. The control unit 70 supplies an alternating current to the control conductive member 60. A magnetic field generated from the control conductive member 60 is applied to the first quantum bit 11. The control unit 70 is capable of controlling the state of the first quantum bit by controlling the alternating current. The computer 210 is capable of performing calculation operations.

[0114] According to the embodiments, for example, an electronic circuit capable of reading quantum bit information at high speed can be provided. According to the embodiments, for example, a computer capable of performing complex calculations can be provided. According to the embodiments, for example, a computer capable of performing calculations at high speed can be provided.

[0115] The embodiment may include the following configurations (e.g., technical solutions). (Configuration 1) a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first quantum bit and a first readout resonator, the first readout resonator being couplable to the first quantum bit and one of the plurality of filter resonators; Equipped with the passband of the bandpass filter includes a first passband and a second passband; an electronic circuit, wherein a magnitude of the first ripple in the first passband is 1 / 10 or less of a magnitude of the second ripple in the second passband;

[0116] (Configuration 2) the passband further includes a third passband; the first passband is between the second passband and the third passband; 2. The electronic circuit of claim 1, wherein the magnitude of the first ripple is less than or equal to 1 / 10 of the magnitude of the third ripple in the third passband.

[0117] (Configuration 3) 3. The electronic circuit of claim 1 or 2, wherein the resonant frequency of the first readout resonator is included in the first passband.

[0118] (Configuration 4) 4. The electronic circuit of configuration 3, wherein the frequency of the first passband is higher than the frequency of the second passband.

[0119] (Configuration 5) 4. The electronic circuit of claim 3, wherein the frequency of the first passband is lower than the frequency of the second passband.

[0120] (Configuration 6) 6. The electronic circuit according to any one of configurations 1 to 5, wherein the resonant frequency of the first quantum bit is included in the non-pass band of the band-pass filter.

[0121] (Configuration 7) a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first quantum bit and a first readout resonator, the first readout resonator being couplable to the first quantum bit and one of the plurality of filter resonators; Equipped with the number of the plurality of filter resonators is an even number equal to or greater than four; the bandpass filter has a plurality of coupling coefficients; one of the plurality of coupling coefficients is a coupling coefficient between two adjacent ones of the plurality of filter resonators; An electronic circuit, wherein a difference between the minimum value of the plurality of coupling coefficients and the maximum value of the plurality of coupling coefficients is 0.1 times or less of an average value of the plurality of coupling coefficients.

[0122] (Configuration 8) the bandpass filter further includes a first portion to which a signal can be input; the first portion is couplable with one of a plurality of filter resonators; an external Q between the first section and the one of the plurality of filter resonators coupleable with the first section is a first section external Qe; the one coupling coefficient of the plurality of coupling coefficients is equal to or greater than a first value and equal to or less than a second value, The first value is (2×10 -7 )×Qe 4 -(2×10 -5 )×Qe 3 +0.0009×Qe 2 -0.0211×Qe+0.2361, The second value is 0.0003×Qe 2 8. The electronic circuit of claim 7, wherein Qe is −0.014×Qe+0.2216.

[0123] (Configuration 9) the bandpass filter further includes a second portion capable of outputting the signal; the second portion is couplable with another one of the plurality of filter resonators; an external Q between the second section and the other one of the plurality of filter resonators coupleable with the second section is a second section external Qf; the one coupling coefficient of the plurality of coupling coefficients is equal to or greater than a third value and equal to or less than a fourth value, The third value is (2×10 -7 )×Qf 4 -(2×10 -5 )×Qf 3 +0.0009×Qf 2 -0.0211×Qf+0.2361, The fourth value is 0.0003×Qf 2 9. The electronic circuit of claim 8, wherein Qf is −0.014×Qf+0.2216.

[0124] (Configuration 10) the bandpass filter has a plurality of distances; one of the plurality of distances is a distance between two adjacent ones of the plurality of filter resonators; 10. The electronic circuit according to any one of configurations 7 to 9, wherein the difference between the minimum value of the plurality of distances and the maximum value of the plurality of distances is 0.1 times or less the average value of the plurality of distances.

[0125] (Configuration 11) a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first qubit and a first readout resonator, the first readout resonator being couplable to the first qubit and one of the plurality of filter resonators; Equipped with the plurality of filter resonators include a first filter resonator to an N-th filter resonator, where N is (2n+1), and n is an integer equal to or greater than 2; the plurality of filter resonators include an (n-1)th resonator, an nth resonator, an (n+1)th resonator, an (n+2)th resonator, and an (n+3)th resonator; The coupling coefficient between the (n-1)th resonator and the nth resonator is the (n-1)th coupling coefficient, The coupling coefficient between the n-th resonator and the (n+1)-th resonator is the n-th coupling coefficient, the coupling coefficient between the (n+1)-th resonator and the (n+2)-th resonator is the (n+1)-th coupling coefficient, the coupling coefficient between the (n+2)-th resonator and the (n+3)-th resonator is the (n+2)-th coupling coefficient, The n-th coupling coefficient is 0.7 times or more and less than 0.9 times the (n-1)-th coupling coefficient, and is 0.7 times or more and less than 0.9 times the (n+2)-th coupling coefficient. double is less than The (n+1) coupling coefficient is 0.7 times or more and 0.9 times or less than the (n-1) coupling coefficient. double and is 0.7 times or more and 0.9 times or less than the (n+2) coupling coefficient. double An electronic circuit that is less than

[0126] (Configuration 12) wherein n is 3 or more; the band-pass filter has a plurality of first-type coupling coefficients and a plurality of second-type coupling coefficients; one of the plurality of first-type coupling coefficients is two adjacent coupling coefficients included in the first filter resonator to the n-th filter resonator, a difference between the minimum value of the plurality of first-type coupling coefficients and the maximum value of the plurality of first-type coupling coefficients is 0.1 times or less of an average value of the plurality of first-type coupling coefficients; one of the plurality of second-type coupling coefficients is two adjacent coupling coefficients included in the (n+2)th filter resonator to the (2n+1)th filter resonator, 12. The electronic circuit according to configuration 11, wherein a difference between the minimum value of the plurality of second-type coupling coefficients and the maximum value of the plurality of second-type coupling coefficients is 0.1 times or less of an average value of the plurality of second-type coupling coefficients.

[0127] (Configuration 13) the bandpass filter further includes a first portion to which a signal can be input; the first portion is couplable with one of a plurality of filter resonators; an external Q between the first section and the one of the plurality of filter resonators coupleable with the first section is a first section external Qe; the plurality of first-type coupling coefficients and the plurality of second-type coupling coefficients are equal to or greater than a first value and equal to or less than a second value, The first value is (2×10 -7 )×Qe 4 -(2×10 -5 )×Qe 3 +0.0009×Qe 2 -0.0211×Qe+0.2361, The second value is 0.0003×Qe 2 13. The electronic circuit of claim 12, wherein Qe is −0.014×Qe+0.2216.

[0128] (Configuration 14) the bandpass filter further includes a second portion through which the signal can be output; the second portion is couplable with another one of the plurality of filter resonators; an external Q between the second section and the other one of the plurality of filter resonators coupleable with the second section is a second section external Qf; the plurality of first-type coupling coefficients and the plurality of second-type coupling coefficients are equal to or greater than a third value and equal to or less than a fourth value, The third value is (2×10 -7 )×Qf 4 -(2×10 -5 )×Qf 3 +0.0009×Qf 2 -0.0211×Qf+0.2361, The fourth value is 0.0003×Qf 2 14. The electronic circuit of claim 13, wherein Qf is −0.014×Qf+0.2216.

[0129] (Configuration 15) the bandpass filter has a plurality of first type distances and a plurality of second type distances; one of the plurality of first-type distances is a distance between two adjacent resonators included in the first to n-th filter resonators, a difference between the minimum value of the plurality of first type distances and the maximum value of the plurality of first type distances is 0.1 times or less of an average value of the plurality of first type distances, one of the plurality of second-type distances is a distance between two adjacent filter resonators included in the (n+2)th to (2n+1)th filter resonators; The electronic circuit according to any one of configurations 11 to 14, wherein the difference between the minimum value of the plurality of second kind distances and the maximum value of the plurality of second kind distances is 0.1 times or less the average value of the plurality of second kind distances.

[0130] (Configuration 16) 16. The electronic circuit according to any one of configurations 1 to 15, wherein two of the plurality of filter resonators that are not adjacent to each other are coupleable.

[0131] (Configuration 17) the bandpass filter further includes a first waveguide; an end of the first waveguide can be coupled to one of two non-adjacent filter resonators of the plurality of filter resonators; 16. The electronic circuit according to any one of configurations 1 to 15, wherein the other end of the first waveguide is capable of being coupled to the other of the two filter resonators that are not adjacent to each other.

[0132] (Configuration 18) Further comprising a circulator; the circulator is capable of providing an input signal to the bandpass filter; 18. The electronic circuit according to any one of configurations 1 to 17, wherein the circulator is capable of obtaining an output signal obtained from the band-pass filter.

[0133] (Configuration 19) a directional coupler including an input and an output; the directional coupler is capable of supplying an input signal input to the input section to the band-pass filter; 18. The electronic circuit according to any one of configurations 1 to 17, wherein the output section is capable of outputting an output signal obtained from the band-pass filter.

[0134] (Configuration 20) The electronic circuit according to any one of configurations 1 to 19, a control unit capable of controlling the state of the first quantum bit; A calculator equipped with.

[0135] According to the embodiment, it is possible to provide an electronic circuit and a computer that can improve the characteristics.

[0136] The embodiments of the present invention have been described above with reference to examples. However, the present invention is not limited to these examples. For example, the specific configurations of elements such as bandpass filters, filter resonators, circuits, quantum bits, resonators, waveguides, and control units included in electronic circuits or computers are within the scope of the present invention as long as a person skilled in the art can implement the present invention in a similar manner and obtain similar effects by appropriately selecting them from known ranges.

[0137] Any combination of two or more elements of each example within the scope of technical feasibility is also included within the scope of the present invention as long as it encompasses the gist of the present invention.

[0138] All electronic circuits and computers that can be implemented by a person skilled in the art by appropriately modifying the design based on the electronic circuits and computers described above as embodiments of the present invention also fall within the scope of the present invention, as long as they include the gist of the present invention.

[0139] Within the scope of the concept of the present invention, a person skilled in the art may conceive of various modifications and alterations, and it is understood that these modifications and alterations also fall within the scope of the present invention.

[0140] Although several embodiments of the present invention have been described, these embodiments are presented as examples and are not intended to limit the scope of the invention. These novel embodiments can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the spirit of the invention. These embodiments and their modifications are included within the scope and spirit of the invention, and are also included in the scope of the invention and its equivalents as defined in the claims. [Explanation of symbols]

[0141] 10C...connecting conductive member, 10L...conductive layer, 10M...base conductive member, 10a-10d...first to fourth conductive layers, 10f, 10g...first and second surfaces, 10i, 10j...first and second insulating layers, 10s...substrate, 11...first quantum bit, 11p...resonant frequency, 11w...linewidth, 21...first readout resonator, 21p...resonant frequency, 21w...linewidth, 31...first circuit, 50...bandpass filter, 50hb...high frequency non-passband, 50lb...low frequency non-passband, 50p...pass characteristic, 50pb...passband, 58r...filter resonator, 60...control conductive member, 61...input signal generator, 61P...first portion, 62...output signal amplifier, 62P...second portion, 65a, 65b...conductive member, 66...first waveguide, 67...circulator, 67a to 67c...first to third ports, 69...directional coupler, 69I...input section, 69O...output section, 70...control section, Δ50...out-of-band suppression amount, Δk...coupling coefficient difference, 110 to 113, 120 to 123...electronic circuits, 210...computer, CF1, CF2...first and second configurations, Ch1...pass characteristics, Dk1...normalized coupling coefficient difference, FBW...parameter, IL...insertion loss, Int1...signal strength, J1, J2...first and second Josephson junctions, Ln1...length, Qe, Qf...first and second partial coupling coefficients, R(1) to R(N)...first to Nth filter resonators, R1 to R3...first to third ripples, RR1...ripple ratio, Rp1~Rp3...magnitude, S11...reflection characteristics, S21...pass characteristics, SI1...input signal, SO1...output signal, Vr1...worst value, d(1)~d(N-1)...1st to (N-1)th distance, ds1, ds2...1st and 2nd type distance, dx...distance, f0...center frequency, fr1...frequency, k...coupling coefficient, ks1, ks2...1st and 2nd type coupling coefficient, kx...coupling coefficient, w1~w3...1st to 3rd passband, wx...frequency width

Claims

1. a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first qubit and a first readout resonator, the first readout resonator being couplable to the first qubit and one of the plurality of filter resonators; Equipped with the passband of the bandpass filter includes a first passband and a second passband; An electronic circuit, wherein a magnitude of the first ripple in the first passband is 1 / 10 or less of a magnitude of the second ripple in the second passband.

2. the passband further includes a third passband; the first passband is between the second passband and the third passband; The electronic circuit of claim 1 , wherein the magnitude of the first ripple is less than or equal to 1 / 10 of the magnitude of the third ripple in the third passband.

3. 3. The electronic circuit of claim 1, wherein the resonant frequency of the first readout resonator is included in the first passband.

4. The electronic circuit of claim 3 , wherein the first passband has a higher frequency than the second passband.

5. The electronic circuit of claim 3 , wherein the first passband has a lower frequency than the second passband.

6. The electronic circuit of claim 3 , wherein the resonant frequency of the first quantum bit is included in a non-passband of the bandpass filter.

7. a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first qubit and a first readout resonator, the first readout resonator being couplable to the first qubit and one of the plurality of filter resonators; Equipped with the number of the plurality of filter resonators is an even number equal to or greater than four; the bandpass filter has a plurality of coupling coefficients; one of the plurality of coupling coefficients is a coupling coefficient between two adjacent ones of the plurality of filter resonators; An electronic circuit, wherein a difference between the minimum value of the plurality of coupling coefficients and the maximum value of the plurality of coupling coefficients is 0.1 times or less of an average value of the plurality of coupling coefficients.

8. the bandpass filter further includes a first portion to which a signal can be input; the first portion is coupleable to one of a plurality of filter resonators; an external Q between the first section and the one of the plurality of filter resonators coupleable with the first section is a first section external Qe; the one coupling coefficient of the plurality of coupling coefficients is equal to or greater than a first value and equal to or less than a second value, The first value is (2×10 －７ ) × Qe ４ -(2 x 10 －５ ) × Qe ３ +0.0009 x Qe ２ −0.0211×Qe+0.2361, The second value is 0.0003×Qe ２ 8. The electronic circuit of claim 7, wherein Qe is −0.014×Qe+0.2216.

9. the bandpass filter further includes a second portion capable of outputting the signal; the second portion is couplable with another one of the plurality of filter resonators; an external Q between the second section and the other one of the plurality of filter resonators coupleable with the second section is a second section external Qf; the one coupling coefficient of the plurality of coupling coefficients is equal to or greater than a third value and equal to or less than a fourth value, The third value is (2×10 －７ ) × Qf ４ -(2 x 10 －５ ) × Qf ３ +0.0009 x Qf ２ −0.0211×Qf+0.2361, The fourth value is 0.0003×Qf ２ 9. The electronic circuit of claim 8, wherein Qf is −0.014×Qf+0.2216.

10. the bandpass filter has a plurality of distances; one of the plurality of distances is a distance between two adjacent ones of the plurality of filter resonators; 10. The electronic circuit according to claim 7, wherein a difference between the minimum value of the plurality of distances and the maximum value of the plurality of distances is 0.1 times or less the average value of the plurality of distances.

11. a bandpass filter including a plurality of filter resonators, wherein two adjacent filter resonators included in the plurality of filter resonators are mutually coupleable; at least one first circuit, the first circuit including a first qubit and a first readout resonator, the first readout resonator being couplable to the first qubit and one of the plurality of filter resonators; Equipped with the plurality of filter resonators include a first filter resonator to an N-th filter resonator, where N is (2n+1), and n is an integer equal to or greater than 2; the plurality of filter resonators include an (n-1)th resonator, an nth resonator, an (n+1)th resonator, an (n+2)th resonator, and an (n+3)th resonator; The coupling coefficient between the (n-1)th resonator and the nth resonator is the (n-1)th coupling coefficient, The coupling coefficient between the n-th resonator and the (n+1)-th resonator is the n-th coupling coefficient, the coupling coefficient between the (n+1)-th resonator and the (n+2)-th resonator is the (n+1)-th coupling coefficient, the coupling coefficient between the (n+2)-th resonator and the (n+3)-th resonator is the (n+2)-th coupling coefficient, the n-th coupling coefficient is 0.7 times or more and less than 0.9 times the (n-1)-th coupling coefficient, and 0.7 times or more and less than 0.9 times the (n+2)-th coupling coefficient; The (n+1) coupling coefficient is 0.7 times or more and less than 0.9 times the (n-1) coupling coefficient, and 0.7 times or more and less than 0.9 times the (n+2) coupling coefficient.

12. wherein n is 3 or more; the band-pass filter has a plurality of first-type coupling coefficients and a plurality of second-type coupling coefficients; one of the plurality of first-type coupling coefficients is two adjacent coupling coefficients included in the first filter resonator to the n-th filter resonator, a difference between the minimum value of the plurality of first-type coupling coefficients and the maximum value of the plurality of first-type coupling coefficients is 0.1 times or less of an average value of the plurality of first-type coupling coefficients, one of the plurality of second-type coupling coefficients is two adjacent coupling coefficients included in the (n+2)th filter resonator to the (2n+1)th filter resonator, 12. The electronic circuit according to claim 11, wherein a difference between the minimum value of the plurality of second-type coupling coefficients and the maximum value of the plurality of second-type coupling coefficients is 0.1 times or less an average value of the plurality of second-type coupling coefficients.

13. the bandpass filter further includes a first portion to which a signal can be input; the first portion is coupleable to one of a plurality of filter resonators; an external Q between the first section and the one of the plurality of filter resonators coupleable with the first section is a first section external Qe; the plurality of first-type coupling coefficients and the plurality of second-type coupling coefficients are equal to or greater than a first value and equal to or less than a second value, The first value is (2×10 －７ ) × Qe ４ -(2 x 10 －５ ) × Qe ３ +0.0009 x Qe ２ −0.0211×Qe+0.2361, The second value is 0.0003×Qe ２ 13. The electronic circuit of claim 12, wherein Qe is −0.014×Qe+0.2216.

14. the bandpass filter further includes a second portion through which the signal can be output; the second portion is couplable with another one of the plurality of filter resonators; an external Q between the second section and the other one of the plurality of filter resonators coupleable with the second section is a second section external Qf; the plurality of first-type coupling coefficients and the plurality of second-type coupling coefficients are equal to or greater than a third value and equal to or less than a fourth value, The third value is (2×10 －７ ) × Qf ４ -(2 x 10 －５ ) × Qf ３ +0.0009 x Qf ２ −0.0211×Qf+0.2361, The fourth value is 0.0003×Qf ２ 14. The electronic circuit of claim 13, wherein Qf is −0.014×Qf+0.2216.

15. the bandpass filter has a plurality of first type distances and a plurality of second type distances; one of the plurality of first type distances is a distance between two adjacent resonators included in the first to n-th filter resonators, a difference between a minimum value of the plurality of first type distances and a maximum value of the plurality of first type distances is equal to or less than 0.1 times an average value of the plurality of first type distances, one of the plurality of second-type distances is a distance between two adjacent resonators included in the (n+2)th filter resonator to the (2n+1)th filter resonator, 15. The electronic circuit according to claim 11, wherein a difference between the minimum value of the plurality of second type distances and the maximum value of the plurality of second type distances is 0.1 times or less of an average value of the plurality of second type distances.

16. 15. The electronic circuit of claim 1, wherein two of the plurality of filter resonators that are not adjacent to each other are coupleable.

17. the bandpass filter further includes a first waveguide; an end of the first waveguide is capable of being coupled to one of two of the plurality of filter resonators that are not adjacent to each other; 15. The electronic circuit according to claim 1, wherein the other end of the first waveguide is capable of being coupled to the other of the two filter resonators that are not adjacent to each other.

18. Further comprising a circulator; the circulator is capable of providing an input signal to the bandpass filter; 15. The electronic circuit according to claim 1, wherein the circulator is capable of obtaining an output signal obtained from the band-pass filter.

19. a directional coupler including an input and an output; the directional coupler is capable of supplying an input signal input to the input section to the band-pass filter; 15. The electronic circuit according to claim 1, wherein the output section is capable of outputting an output signal obtained from the band-pass filter.

20. an electronic circuit according to any one of claims 1, 2, 7, 8, 9, 11, 12, 13, and 14; a control unit capable of controlling the state of the first quantum bit; A calculator equipped with.

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