Multiplexed readout system

Abstract

A circuit is presented that includes a first amplifier having an input, a transmission line having a first end and a second end. The first end of the transmission line is coupled to the input of the first amplifier and a plurality of channels. Each channel includes a plurality of resonators arranged to read out a plurality of qubits, respectively, and a readout line arranged to receive readout signals from the plurality of resonators. The readout line of each channel is coupled to the transmission line, and each channel is configured to output a respective signal in a respective frequency band that is different from frequency bands of other channels of the plurality of channels.

Description

Technical Field

[0001] This topic relates to qubit readout systems. Background Technology

[0002] Large-scale quantum computers have the potential to provide rapid solutions to certain types of difficult problems. However, multiple challenges in designing and implementing quantum architectures to control, program, and maintain quantum hardware hinder the realization of large-scale quantum computing. Summary of the Invention

[0003] This invention describes a technique for multiplexing readout systems for qubits.

[0004] Generally, an innovative aspect of the subject matter of this invention can be embodied in a circuit comprising: a first amplifier having an input; a transmission line having a first end and a second end, wherein the first end of the transmission line is coupled to the input of the first amplifier; and a plurality of channels, each channel comprising: a plurality of resonators arranged to read out a plurality of qubits respectively, and a readout line arranged to receive readout signals from the plurality of resonators, wherein the readout line of each channel is coupled to the transmission line, and wherein each channel is configured to output a corresponding signal in a corresponding frequency band different from the frequency bands of the other channels in the plurality of channels.

[0005] The above and other implementations may each optionally include one or more of the following features individually or in combination.

[0006] In some implementations, the transmission line is a first transmission line and the readout line included in each channel is a second transmission line, and each of the multiple channels also includes: a second amplifier connected to the second transmission line, configured to amplify the readout signals from the multiple readout resonators before they are coupled to the first transmission line.

[0007] In some implementations, the second amplifier is a Josephson junction parametric amplifier.

[0008] In some implementations, the Josephson junction parametric amplifier is any one of a JPC amplifier, a non-degenerate parametric amplifier, or a traveling wave amplifier.

[0009] In some implementations, each of the multiple channels further includes a circulator disposed between the output of the second transmission line and the Josephson junction parametric amplifier, configured to receive and direct the readout signal to the second transmission line toward the multiple resonators, and to direct the readout signal reflected from the multiple resonators to the Josephson junction parametric amplifier.

[0010] In some implementations, each second amplifier is configured to shift the frequency of the readout signal to a different corresponding frequency band.

[0011] In some implementations, the first amplifier has a first frequency bandwidth and each of the plurality of channels has a different corresponding second frequency bandwidth, and each second frequency bandwidth is smaller than the first frequency bandwidth, does not overlap with another second frequency bandwidth, and spans a frequency range within the first frequency bandwidth.

[0012] In some implementations, each of the multiple channels further includes a directional multiplexer configured to couple a readout signal from the readout line or the second transmission line to the first transmission line toward the first amplifier.

[0013] In some implementations, the directional multiplexer is arranged such that the readout signal travels unidirectionally toward the first amplifier in the first transmission line.

[0014] In some implementations, the directional multiplexer includes at least one ring resonator, and the directional multiplexer further includes: a first port arranged to receive signals from a plurality of readout resonators via a second transmission line; a second port connected to a termination resistor; a third port coupled to the first transmission line; and a fourth port coupled to the first transmission line.

[0015] In some implementations, the directional multiplexer is arranged such that: in response to a readout signal received at a first port and resonating with at least one ring resonator, the readout signal is directed to a fourth port and subsequently into a first transmission line toward a first amplifier; in response to a readout signal received at the first port and detuned from at least one ring resonator, the readout signal is directed to a second port and terminated at a termination resistor; in response to a signal received at a third port from a first transmission line and detuned from at least one ring resonator, the received signal is directed via the fourth port to the first transmission line toward the first amplifier; and in response to a first transmission line signal received at the third port and resonating with at least one ring resonator, the received signal is directed to a second port and terminated at a termination resistor.

[0016] In some implementations, the directional multiplexer includes: a first directional coupler; a second directional coupler; a first quarter-wavelength connector; and a second quarter-wavelength connector, wherein the first directional coupler includes a first port, a second port, a third port, and a fourth port, wherein the second directional coupler includes a first port, a second port, a third port, and a fourth port, wherein the first port of the directional multiplexer includes the first port of the second directional coupler, the second port of the directional multiplexer includes the second port of the second directional coupler, the third port of the directional multiplexer includes the second port of the first directional coupler, and the fourth port of the directional multiplexer includes the first port of the first directional coupler, wherein the fourth port of the first directional coupler is connected to the fourth port of the second directional coupler via the first quarter-wavelength connector, and wherein the third port of the first directional coupler is connected to the third port of the second directional coupler via the second quarter-wavelength connector.

[0017] In some implementations, the directional multiplexer includes: a first directional coupler; a second directional coupler; a third directional coupler; a first quarter-wavelength connector; a second quarter-wavelength connector; a third quarter-wavelength connector; and a fourth quarter-wavelength connector, wherein the first directional coupler includes a first port, a second port, a third port, and a fourth port; the second directional coupler includes a first port, a second port, a third port, and a fourth port; the third directional coupler includes a first port, a second port, a third port, and a fourth port; wherein the first port of the directional multiplexer includes the first port of the third directional coupler; and the second port of the directional multiplexer includes the first port of the third directional coupler. The second-port directional multiplexer has a third port including a fourth port of the first directional coupler, and the fourth port of the directional multiplexer includes a third port of the first directional coupler, wherein the first port of the first directional coupler is connected to the first port of the second directional coupler via a first quarter-wavelength connector, wherein the second port of the first directional coupler is connected to the second port of the second directional coupler via a second quarter-wavelength connector, wherein the third port of the second directional coupler is connected to the third port of the third directional coupler via a third quarter-wavelength connector, and wherein the fourth port of the second directional coupler is connected to the fourth port of the third directional coupler via a fourth quarter-wavelength connector.

[0018] In some implementations, the first amplifier is a HEMT (High Electron Mobility Transistor) amplifier or a silicon-germanium amplifier.

[0019] In some implementations, the first transmission line is impedance matched at 50 Ohms.

[0020] Details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will be apparent from the specification, drawings, and claims. Attached Figure Description

[0021] Figure 1 This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0022] Figure 2 This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0023] Figure 3 This is a schematic diagram illustrating an exemplary directional multiplexer.

[0024] Figure 4A This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0025] Figure 4B Shown in Figure 4A Simulation results of the directional bandpass filter component described in [the document].

[0026] Figure 5A This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0027] Figure 5B It is shown Figure 5A A schematic diagram of the directional multiplexer component.

[0028] Figure 5C Showing includes Figure 5B Simulation results of the multiplexed qubit readout system of the directional bandpass filter component described in the paper. Detailed Implementation

[0029] Quantum computing requires the coherent processing of quantum information stored in qubits within a quantum computer. Superconducting quantum computing is a promising realization of solid-state quantum computing technology, in which the quantum information processing system is partly composed of superconducting materials. To operate quantum information processing systems employing solid-state quantum computing technology, such as superconducting qubits, the system is kept at extremely low temperatures, such as tens of mK. This extreme cooling keeps the superconducting material below its critical temperature and helps avoid unwanted state transitions. To maintain such low temperatures, the quantum information processing system can operate within a cryostat, such as a dilution refrigerator.

[0030] In some implementations, control signals are generated in a higher temperature environment and transmitted to the quantum information processing system using shielded, impedance-controlled GHz transmission lines (such as coaxial cables). Cryostats can progressively cool from room temperature (e.g., about 300 K) to the operating temperature of the qubit in one or more intermediate cooling stages. For example, a cryostat may employ stages that are one or two orders of magnitude colder than the room temperature stage, e.g., about 30-40 K or about 3-4 K, and hotter than the operating temperature of the qubit (e.g., about 10 mK or lower).

[0031] Even at extremely low qubit operating temperatures, qubits can still suffer from decoherence and gate errors. Therefore, large-scale quantum error correction algorithms can be deployed to compensate for gate errors and qubit decoherence. Error-correcting quantum processors utilize redundancy to synthesize protected logical qubits from a whole of error-prone qubits.

[0032] Therefore, current superconducting quantum systems may require a large number of qubits to implement error correction algorithms in the future. As the number of qubits increases, heat dissipation from peripheral devices (such as amplifiers on the readout system) also increases, which can cause problems given the limited cooling capacity of cryostats. In an exemplary readout system, a readout resonator from multiple qubits is coupled to a single readout channel and pre-amplified, for example, using a parametric amplifier. The pre-amplified signal on the single readout channel is then amplified by a microwave amplifier chain, which includes a HEMT (High Electron Mobility Transistor) amplifier arranged within the cryostat and one or more amplifiers at room temperature. The resonant frequencies of the qubit readout resonators can be arranged to be distributed within the bandwidth of the readout channel and not overlap with each other.

[0033] When designing a readout system with a larger number of qubits, the conditions to be considered include: the saturation intensity of the parametric amplifier, which limits the number of qubits per readout channel; and the bandwidth of each readout channel, which is set by the bandwidth of the parametric amplifier and the bandwidth of the Purcell filter within each readout channel.

[0034] Since the power dissipation of HEMT amplifiers can constitute a significant portion of the available cooling power in a 3K-level cryostat, using multiple readout channels and corresponding HEMT amplifiers may not be a viable option when designing readout systems for a large number of qubits, as this limits the number of individual readout lines that can operate simultaneously. However, considering that in some exemplary schemes currently in use, a large portion of the bandwidth and saturation power of the HEMT amplifier remains unused, each HEMT amplifier can read out more qubits. For example, the typical bandwidth of an HEMT amplifier is several GHz, while the typical bandwidth of each channel may be limited to less than GHz.

[0035] This disclosure proposes a directional multiplexer with low insertion loss to combine signals from multiple readout channels, each readout channel including multiple qubits, a readout resonator, and a preamplifier, such that the multiple readout channels can be passively frequency-multiplexed to cover most or the entire bandwidth of a HEMT amplifier.

[0036] Multiple readout channels spanning the full bandwidth of the HEMT amplifier are arranged, each occupying a dedicated, non-overlapping frequency band. This is achieved by operating the preamplifier in frequency-switching mode and / or configuring the resonant frequency of the qubit readout resonator in each such channel.

[0037] Figure 1 This is a schematic diagram illustrating an exemplary multiplexed qubit readout system. The multiplexed qubit readout system 100 includes multiple channels 110, 111, 112, and 113, in... Figure 1 The channels are also labeled Ch0, Ch1, Ch2, and Ch3. Each channel 110, 111, 112, and 113 includes multiple qubits 120, 121, 122, and 123. Figure 1 The upward arrows in the diagram indicate the frequency of the readout signal from each of the multiple qubits 120, 121, 122, and 123. In some implementations, the number of qubits 120, 121, 122, and 123 in each channel is the same for all channels. The number of qubits that each channel can include will be discussed in more detail later.

[0038] The multiplexed qubit readout system 100 also includes a plurality of directional multiplexers 130, 131, 132, and 133. The plurality of directional multiplexers 130, 131, 132, and 133 are arranged to couple signals from a plurality of qubits 120, 121, 122, and 123 to a bus transmission line 140, such that the signals from the plurality of qubits 120, 121, 122, and 123 are combined in the bus transmission line 140 and subsequently sent to a first amplifier 150. The first amplifier 150 may include a semiconductor low-noise amplifier capable of operating at low temperatures. Examples of the first amplifier 150 include HEMT (High Electron Mobility Transistor) amplifiers and silicon-germanium low-temperature low-noise amplifiers.

[0039] In some implementations, multiple channels 110, 111, 112, and 113 can have predetermined bandwidths. In some implementations, the bandwidths of multiple channels 110, 111, 112, and 113 can be the same or different. In some implementations, the frequency bands of multiple channels can occupy dedicated frequency bands 10, 11, 12, and 13 that do not overlap with each other. For example, in... Figure 1 In the middle, the bandwidth of frequency bands 10, 11, 12, and 13 is 250MHz. Figure 1They are also labeled as Band 0, Band 1, Band 2, and Band 3. Bands 10, 11, 12, 13, Band 0, Band 1, Band 2, and Band 3 can be arranged adjacent to each other in terms of frequency, but they do not overlap.

[0040] In some implementations, the fundamental resonant frequencies of qubits 120, 121, 122, and 123 can differ from the resonant frequencies of the readout resonators coupled to qubits 120, 121, 122, and 123 by approximately 1 GHz, and only the resonant frequencies of the readout resonators can be within the frequency bands of channels 10, 11, 12, and 13. The fundamental resonant frequencies of qubits 120, 121, 122, and 123 can be arranged outside the bandwidths of the corresponding channels 10, 11, 12, and 13 to avoid decoherence.

[0041] In some implementations, the resonant frequencies of the readout resonators coupled to multiple qubits 120, 121, 122, and 123 in each of channels 110, 111, 112, and 113 can be distributed across the bandwidths of channels 110, 111, 112, and 113. In other words, the resonant frequencies of the readout resonators coupled to the multiple qubits 120, 121, 122, and 123 are separated from each other by an interval greater than the respective linewidth of the multiple qubits 120, 121, 122, and 123 or the linewidth of the readout resonators, for passive frequency multiplexing of the multiple qubits 120, 121, 122, and 123.

[0042] In some implementations, the resonant frequencies of the readout resonators coupled to multiple qubits 120, 121, 122, and 123 can be spaced apart within the bandwidth of each channel 110, 111, 112, and 113. For example, if each channel 110, 111, 112, and 113 comprises 9 qubits, and the bandwidth of channels 110, 111, 112, and 113 is 250 MHz, then the qubit resonant frequencies of each channel can be spaced 25 MHz apart. Figure 1 In the example, channels 110, 111, 112, and 113 each contain 6 qubits. If the bandwidth of channels 110, 111, 112, and 113 is 250 MHz, then the resonant frequencies of the qubits in each channel can be spaced 50 MHz apart. The frequency bands of multiple channels 110, 111, 112, and 113 can be frequency-unoverlapping. In other words, the frequency bands 10, 11, 12, and 13 occupied by the outputs of each channel 110, 111, 112, and 113 do not overlap with the frequency bands occupied by the outputs of another channel 110, 111, 112, and 113. Therefore, multiple channels 110, 111, 112, and 113 are frequency-multiplexed. For example, in... Figure 1In the example, the center frequencies of the bands of multiple channels 110, 111, 112, and 113, each with a bandwidth of 250 MHz, are spaced apart by at least 250 MHz.

[0043] In some implementations, the resonant frequencies of the readout resonators coupled to multiple qubits 120, 121, 122, and 123 can be spaced apart from each other in an unequal or irregular manner. For example, some qubits 120, 121, 122, and 123 that are coupled to each other can be more closely spaced in frequency than other qubits.

[0044] The outputs of multiple channels 110, 111, 112, and 113 are passively frequency-multiplexed and sent to the first amplifier 150.

[0045] In some implementations, the frequency bands of the outputs of channels 110, 111, 112, and 113 are frequency-multiplexed because the resonant frequencies of the readout resonators of qubits 120, 121, 122, and 123 coupled to one of channels 110, 111, 112, and 113 are configured not to overlap with the resonant frequencies of qubits 120, 121, 122, and 123 of the other channel 110, 111, 112, and 113. In other words, the resonant frequencies of the readout resonators of qubits 120, 121, 122, and 123 coupled to one of channels 110, 111, 112, and 113 are configured to occupy the corresponding non-overlapping frequency bands 10, 11, 12, and 13.

[0046] In some implementations, the multiple channels 110, 111, 112, and 113 may additionally include preamplifiers, such as parametric amplifiers, used as frequency converters, which shift the frequencies of the signals from qubits 120, 121, 122, and 123 in channels 110, 111, 112, and 113 such that the frequency bands of the outputs of channels 110, 111, 112, and 113 do not overlap in frequency, thereby frequency multiplexing of the output signals of multiple channels 110, 111, 112, and 113. For example, in Figure 1 In the example, the resonant frequencies of the readout resonators of qubits 120, 121, 122, and 123 coupled to all channels 110, 111, 112, and 113 can initially all be within Band 0 and 10, which is one of the available frequency bands within the bandwidth of the first amplifier 150. Before the signals from the multiple qubits 120, 121, 122, and 123 are sent to the corresponding directional multiplexers 130, 131, 132, and 133, the frequencies of the signals from the multiple qubits 120, 121, 122, and 123 are frequency-converted so that channels Ch0, Ch1, Ch2, and Ch3 occupy the frequency bands Band 0, Band 1, Band 2, and Band 3, respectively. These preamplifiers, used as frequency converters, will... Figure 2 The discussion is ongoing.

[0047] In some implementations, the multiple channels 110, 111, 112, 113 may include a combination of the two implementations described above. In other words, the frequency bands of the outputs of channels 110, 111, 112, 113 are frequency multiplexed because the resonant frequencies of the readout resonators of qubits 120, 121, 122, 123, respectively coupled to one of channels 110, 111, 112, 113, are configured to occupy the corresponding non-overlapping frequency bands 10, 11, 12, 13, and because the preamplifiers included in each of the multiple channels 110, 111, 112, 113 shift the frequencies of the signals from qubits 120, 121, 122, 123 in channels 110, 111, 112, 113.

[0048] The frequency bands 10, 11, 12, and 13 of multiple channels 110, 111, 112, and 113 are included within the bandwidth of the first amplifier 150. For example, in Figure 1 In the example, since the bandwidth of multiple channels 110, 111, 112, 113 is 250MHz, and there are four such channels 110, 111, 112, 113, the bandwidth of the first amplifier 150 is at least 1GHz.

[0049] Directional multiplexers 130, 131, 132, and 133 can be arranged to transmit signals from multiple qubits 120, 121, 122, and 123 of channels 110, 111, 112, and 113 to bus transmission line 140. For example, in Figure 1 In the example, if the resonant frequencies of the readout resonators coupled to qubits 120, 121, 122, and 123 are distributed across the full bandwidth of 250 MHz in each channel 110, 111, 112, and 113, then the bandwidth of the directional multiplexer should be at least 250 MHz, such that signals from all qubits 120, 121, 122, and 123 in each channel 110, 111, 112, and 113 are transmitted to bus transmission line 140 via directional multiplexers 130, 131, 132, and 133.

[0050] Directional multiplexers 130, 131, 132, and 133 are coupled to bus transmission line 140, such that signals output from directional multiplexers 130, 131, 132, and 133 are coupled to the bus transmission line. In some implementations, directional multiplexers 130, 131, 132, and 133 may be resonant devices including one or more resonators, which will be described in more detail later.

[0051] The multiplexed qubit readout system 100 also includes multiple receiver-oriented demultiplexers 160, 161, 162, and 163, arranged to demultiplex the amplified signal output from the HEMT amplifier 150. In other words, since the signals output from channels 110, 111, 112, and 113 (which occupy different frequency bands 10, 11, 12, and 13) are combined in the bus transmission line 140 before being amplified by the first amplifier 150, the amplified signal is divided into the corresponding frequency bands 10, 11, 12, and 13 after amplification and before being processed, such as being demodulated at multiple mixers 170, 171, 172, and 173.

[0052] In some implementations, receiver-directed demultiplexers 160, 161, 162, and 163 can be designed to be identical to directional multiplexers 130, 131, 132, and 133.

[0053] Alternatively, in some implementations, receiver-oriented demultiplexers 160, 161, 162, and 163 can be implemented using commercially available off-the-shelf components because the requirements for insertion loss and power consumption of the demultiplexing are far less stringent, since the demultiplexing can operate at room temperature and the HEMT amplifier 150 dominates the system noise portion.

[0054] In some implementations, if the full bandwidth of the HEMT amplifier 150 can be directly digitized, then receiver-oriented demultiplexers 160, 161, 162, and 163 are not required.

[0055] The total number of qubits 120, 121, 122, and 123 in each of the channels 110, 111, 112, and 113 can be limited by the parameters of the preamplifier used as the frequency converter, such as the saturation strength of the Josephson junction parametric frequency converter, and also by the bandwidth of each readout channel, set by the bandwidth of the preamplifier and the bandwidth of the readout resonator of the qubits 120, 121, 122, and 123 within each readout channel. This will be discussed in more detail below.

[0056] The total number of channels can be determined by the bandwidths of channels 110, 111, 112, and 113 and the bandwidth of the first amplifier 150. For example, in Figure 1 In the example, each channel 110, 111, 112, 113 has a bandwidth of 250MHz. If the bandwidth of the first amplifier is 4GHz, as is available in commercial HEMT amplifiers, then there can be up to 16 channels.

[0057] Therefore, by increasing the number of channels 110, 111, 112, and 113, a larger number of qubits 120, 121, 122, and 123 can be used for most of the bandwidth of the HEMT amplifier.

[0058] Figure 2 This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0059] As mentioned above Figure 1 The qubit readout system 200 includes multiple channels 210, 211, and 212. Figure 2 The components are labeled Channel 0, Channel 1, ..., Channel N, and include a bus transmission line 240 connected to the input of the first amplifier 250. Figure 2 The Chinese label is HEMT (High Electron Mobility Transistor).

[0060] In some implementations, the first amplifier 250 includes a HEMT amplifier. However, the type of the first amplifier 250 is not limited to a HEMT amplifier. The first amplifier 250 may include any semiconductor low-noise amplifier capable of operating at low temperatures, such as a silicon-germanium low-temperature low-noise amplifier.

[0061] In some implementations, bus transmission line 240 can be a 50 Ohm transmission line.

[0062] As described above, the number of channels 210, 211, and 212, N+1, is determined by considering the bandwidth of each of channels 210, 211, and 212 and the bandwidth of the first amplifier 250. For example, if each channel 210, 211, and 212 has a bandwidth of 250 MHz and the bandwidth of the first amplifier 250 is 4 GHz, then the number of channels N+1 can be as high as 16.

[0063] Multiple channels 210, 211, 212 are coupled to bus transmission line 240 via multiple directional multiplexers 230, 231, 232 included in the respective multiple channels 210, 211, 212.

[0064] Each channel 210, 211, 212 includes multiple readout resonators 280, 281, 282 for reading signals from corresponding multiple qubits 220, 221, 222. Since the multiple readout resonators 280, 281, 282 are coupled to the multiple qubits 220, 221, 222, the resonant frequencies of the corresponding multiple readout resonators 280, 281, 282 change depending on the state of the multiple qubits 220, 221, 222.

[0065] Each channel 210, 211, 212 includes readout transmission lines 290, 291, 292. Multiple readout resonators 280, 281, 282 are coupled to readout transmission lines 290, 291, 292. Multiple readout resonators 280, 281, 282 are coupled to readout transmission lines 290, 291, 292 either inductively or capacitively. In some implementations, readout transmission lines 290, 291, 292 themselves can be configured as Purcell filters.

[0066] In some implementations, to read out or detect the state of any one of the multiple qubits 220, 221, 222, a probe signal or traveling wave can be excited along the readout transmission lines 290, 291, 292. The frequency of the probe signal can be the resonant frequency of or near the resonant frequency of one or more of the readout resonators of the multiple qubits.

[0067] In some implementations, the resonant frequencies of the readout resonators 280, 281, and 282 can be correspondingly distributed across the frequency band of Channel 0210, because the readout resonators 280, 281, and 282 are tuned to couple to the corresponding plurality of qubits 220, 221, and 222. The frequency of the probe signal can be at or near the resonant frequency of one or more of the readout resonators 280, 281, and 282 coupled to the plurality of qubits 220, 221, and 222.

[0068] Depending on the internal quantum mechanical states of qubits 220, 221, and 222, the strength or phase of the probe signals transmitted along readout transmission lines 290, 291, and 292 can change because the reflectivity of the readout resonators 280, 281, and 282 coupled to qubits 220, 221, and 222 varies depending on the states of qubits 220, 221, and 222. This allows for state detection of qubits 220, 221, and 222.

[0069] In some implementations, the probe signals sent to the readout transmission lines 290, 291, 292 may include multiple tones or frequencies, such that readouts are performed simultaneously and in parallel on all qubits 220, 221, 222 coupled to the readout transmission lines 290, 291, 292.

[0070] In some implementations, the probe signals sent to readout transmission lines 290, 291, 292 may include a tone or a frequency. In this case, by changing the frequency of the probe signals sent along readout transmission lines 290, 291, 292, the states of multiple qubits 220, 221, 222 can be read out one at a time.

[0071] In some implementations, qubits 220, 221, and 222 in multiple channels 210, 211, and 212 can be arranged on a substrate separate from some other features included in the qubit readout system 200. For example, qubits 220, 221, and 222 of all channels 210, 211, and 212 can be arranged on a first surface of a first substrate, and readout resonators 280, 281, and 282 of all channels 210, 211, and 212 can be arranged on a first surface of a second substrate. The first and second substrates can be aligned such that the first surfaces of the first and second substrates face each other, and the readout resonators 280, 281, and 282 on the second substrate are aligned and very close to the corresponding qubit 220, 221, and 222.

[0072] In some implementations, the resonant frequencies of qubits 220, 221, and 222 within each channel 210, 211, and 212 can be different from those of other qubits 220, 221, and 222 within the same channel 210, 211, and 212. For example, in Figure 2 In the example, the resonant frequencies of the readout resonators 280-1, 280-2, 280-3, and 280-4 coupled to qubits 220-1, 220-2, 220-3, and 220-4 respectively in Channel 0 210 can be uniformly distributed within the bandwidth of Channel 0 210, such that none of the resonant frequencies of the readout resonators 280-1, 280-2, 280-3, and 280-4 coupled to qubits 220-1, 220-2, 220-3, and 220-4 overlap with each other. The resonant frequencies of qubits 220-1, 220-2, 220-3, and 220-4 can be approximately 1 GHz away from the resonant frequencies of the readout resonators 280-1, 280-2, 280-3, and 280-4 coupled to them, and can be located outside the bandwidth of Channel 0 210 to avoid decoherence.

[0073] Each channel 210, 211, 212 also includes preamplifiers 260, 261, 262.

[0074] Each channel 210, 211, 212 also includes at least one circulator 270, 271, 272.

[0075] In some implementations, preamplifiers 260, 261, and 262 may include parametric frequency converters.

[0076] A parametric frequency converter is a nonlinear device in which the reactance in the circuit is modulated by a pump tone of frequency fp to facilitate a frequency conversion from a first frequency band Δf centered around f1 to a second frequency band Δf centered around f2, such that f2 = f1 + fp.

[0077] In some implementations, preamplifiers 260, 261, and 262 may include parametric amplifiers.

[0078] In some implementations, preamplifiers 260, 261, and 262 may include Josephson junction frequency converters, wherein the nonlinear medium of the Josephson junction parametric amplifier is provided by a Josephson junction.

[0079] A parametric amplifier is a nonlinear device in which the reactance in the circuit is pumped by a frequency fp to facilitate amplification and frequency conversion from a first frequency band Δf centered around f1 to a second frequency band Δf centered around f2, such that fp = f1 + f2.

[0080] In some implementations, preamplifiers 260, 261, and 262 may include Josephson junction parametric amplifiers, wherein the nonlinear medium of the Josephson junction parametric amplifier is provided by a Josephson junction.

[0081] In some implementations, preamplifiers 260, 261, and 262 can be arranged to amplify the intensity of the probe signal.

[0082] exist Figure 2 In the examples, unless otherwise stated, it is assumed that preamplifiers 260, 261, and 262 include Josephson junction parametric frequency converters. For frequency conversion, pump tones are provided to Josephson junction parametric frequency converters 260, 261, and 262.

[0083] In some implementations, pump sounds are provided to Josephson junction parametric frequency converters 260, 261, and 262. Figure 2 The terminals through which pump tones are supplied to Josephson junction parametric frequency converters 260, 261, and 262 are not shown. Circulators 270, 271, and 272 may be arranged between Josephson junction parametric frequency converters 260, 261, and 262 and multiple readout resonators 280, 281, and 282, such that pump tones or signal tones reflected from preamplifiers 260, 261, and 262 are terminated without proceeding back to qubits 220, 221, and 222.

[0084] The detection signal can be provided to the terminals of circulators 270, 271, and 272. Figure 2The diagram shows a horizontal line that is not directly connected to Josephson junction parametric frequency converters 260, 261, and 262, nor is it directly connected to readout transmission lines 290, 291, and 292. The probe signal is sent to readout transmission lines 290, 291, and 292 via circulators 270, 271, and 272. The probe signal reflected from readout resonators 280, 281, and 282 is sent back to circulators 270, 271, and 272, and then guided to Josephson junction parametric frequency converters 260, 261, and 262. Figure 2 In the example, Josephson junction parametric frequency converters 260, 261, and 262 are configured as transmit types, where the probe signals amplified by Josephson junction parametric frequency converters 260, 261, and 262 are primarily transmitted, rather than reflected back to circulators 270, 271, and 272. If Josephson junction parametric frequency converters 260, 261, and 262 were configured as reflective types, each channel might require an additional circulator to redirect the amplified probe signals.

[0085] In some implementations, preamplifiers 260, 261, and 262 may be arranged to upconvert the probe signal. For example, preamplifiers 260, 261, and 262 may include Josephson junction parametric frequency converters 260, 261, and 262, which are configured to change the frequency of the probe signal to a higher frequency.

[0086] Various implementations of upconversion parametric frequency converters are well known in this field. For example, an upconversion parametric frequency converter can be implemented using a JPC amplifier, a traveling wave amplifier, or a non-degenerate parametric amplifier, naturally achieving frequency conversion by generating idle tones.

[0087] In some implementations, the intensity of the probe signal can be kept below a certain level so that the electric field from the probe signal within the readout resonator does not cause decoherence of qubits 220, 221, and 222.

[0088] In some implementations, the probe signals sent to readout transmission lines 290, 291, 292 may include multiple tones or multiple frequencies, enabling the simultaneous readout of the states of multiple qubits 220, 221, 222. Probe signals with multiple tones can be sent simultaneously to preamplifier 260. Therefore, the number of qubits 220, 221, 222 that can be probed simultaneously can be limited by the saturation intensity of preamplifiers 260, 261, 262 (e.g., Josephson junction parametric frequency converters).

[0089] For example, the strength of the probe signal can be between -130 dBm and -120 dBm per frequency tone. Depending on the architecture of the preamplifiers 260, 261, and 262, the saturation power of the preamplifiers 260, 261, and 262 can be between -110 dBm and -90 dBm. Therefore, more than 10 qubits 220, 221, and 222 can be included in a single channel 210, 211, and 212. By increasing the saturation power of the preamplifiers 260, 261, and 262, for example by using a traveling-wave parametric amplifier (TWPA) configuration, each channel 210, 211, and 212 can include an even greater number of qubits 220, 221, and 222.

[0090] Regarding bandwidth, an exemplary bandwidth allocated to each readout resonator could be 20 to 50 MHz. An exemplary bandwidth for preamplifiers 260, 261, and 262 could be approximately 500 MHz. Therefore, 10 or more qubits 220, 221, and 222 could be included in a single channel 210, 211, and 212. For a traveling-wave parametric amplifier (TWPA), an exemplary bandwidth could be approximately 2 to 3 GHz, allowing for the inclusion of a larger number of qubits 220, 221, and 222. In this case, the number of qubits 220, 221, and 222 that could be included in each channel 210, 211, and 212 could also be limited by the saturation power of the TWPA. Furthermore, the directional multiplexer, as described below, can be designed to match the desired bandwidth.

[0091] Each channel 210, 211, 212 also includes directional multiplexers 230, 231, 232.

[0092] In some implementations, directional multiplexers 230, 231, and 232 can be designed as resonator structures, such that a probe signal containing information about the state of multiple qubits is coupled unidirectionally to bus transmission line 240 and subsequently to the input port of first amplifier 250.

[0093] In some implementations, directional multiplexers 230, 231, and 232 can be configured as multiple 2-pole ring resonator directional filters, such that signals from multiple readout resonators 280, 281, and 282 that resonate in the passband of directional multiplexers 230, 231, and 232 or resonate within the passband of directional multiplexers 230, 231, and 232 are unidirectionally coupled to bus transmission line 240 and further coupled to the input port of first amplifier 250.

[0094] In some implementations, directional multiplexers 230, 231, and 232 can be configured as multiple 2-pole ring resonator directional filters, such that signals from multiple readout resonators 280, 281, and 282 within the respective channels 210, 211, and 212 that are detuned from or outside the passband of directional multiplexers 230, 231, and 232 are terminated at terminating resistors 236, 237, and 238, preventing coupling to bus transmission line 240.

[0095] In some implementations, directional multiplexers 230, 231, and 232 may include four ports: first ports 230-1, 231-1, and 232-1; second ports 230-2, 231-2, and 232-2; third ports 230-3, 231-3, and 232-3; and fourth ports 230-4, 231-4, and 232-4. The third ports 230-3, 231-3, and 232-3, and the fourth ports 230-4, 231-4, and 232-4 are coupled to bus transmission line 240. It is assumed that the first amplifier 250 is located on one side of the fourth ports 230-4, 231-4, and 232-4 of the directional multiplexers 230, 231, and 232.

[0096] In some implementations, the directed multiplexers 230, 231, and 232 can be further configured as follows.

[0097] The outputs from preamplifiers 260, 261, 262, such as Josephson parametric frequency converters, are coupled to the first ports 230-1, 231-1, 232-1 of directional multiplexers 230, 231, 232. If the outputs of preamplifiers 260, 261, 262 resonate with or within the passband of directional multiplexers 230, 231, 232, the signal exits the directional multiplexers 230, 231, 232 at the fourth ports 230-4, 231-4, 232-4 and enters the bus transmission line 240 toward the first amplifier 250.

[0098] If the outputs of parametric frequency converters 260, 261, 262 are detuned from or outside the passband of directional multiplexers 230, 231, 232, then after the outputs from preamplifiers 260, 261, 262 are coupled to the first ports 230-1, 231-1, 232-1 of directional multiplexers 230, 231, 232, the signal leaves directional multiplexers 230, 231, 232 at the second ports 230-2, 231-2, 232-2. The signal is terminated by terminating resistors 236, 237, 238 and dissipates at terminating resistors 236, 237, 238.

[0099] If the signal does not resonate with the passband of directional multiplexers 230, 231, and 232 or is outside their passband, the signal entering the third ports 230-3, 231-3, and 232-3 of directional multiplexers 230, 231, and 232 from the bus transmission line 240 is coupled to the fourth ports 230-4, 231-4, and 232-4.

[0100] If a signal resonates with or within the passband of directional multiplexers 230, 231, and 232, the signal entering the third ports 230-3, 231-3, and 232-3 of directional multiplexers 230, 231, and 232 from bus transmission line 240 terminates at the terminating resistors 236, 237, and 238 at the second ports 230-2, 231-2, and 232-2 of directional multiplexers 230, 231, and 232.

[0101] In some implementations, when the preamplifiers 260, 261, and 262 are Josephson junction parametric frequency converters, the frequency of the pump tone sent to the Josephson junction parametric frequency converter can be determined such that, after up-conversion, the signals from the multiple readout resonators 280, 281, and 282 resonate with the passband of the directional multiplexers 230, 231, and 232 or within their passband, thereby coupling them to the bus transmission line 240.

[0102] In some implementations, the resonant frequencies of the readout resonators 281, 282, and 283 of all qubits 220, 221, and 222 in the multiple channels 210, 211, and 212 can be arranged to be different from each other, such that the resonant frequencies of all qubits 220, 221, and 222 do not overlap in frequency. In this case, the preamplifier 260 can be configured to amplify the intensity of the probe signal without changing the frequency of the probe signal. For example, the preamplifier 260 can be a Josephson junction parametric amplifier, and the pump frequency supplied to the Josephson junction parametric amplifier can be configured such that the frequency of the probe signal remains unchanged. In this case, passive frequency multiplexing of the multiple qubits 220, 221, and 222 can be achieved by configuring the resonant frequencies of the readout resonators coupled to the qubits 220, 221, and 222 to be different from each other.

[0103] In some implementations, the resonant frequencies of the readout resonators coupled to qubits 220, 221, and 222 in at least two of the multiple channels 210, 211, and 212 can be configured such that they occupy the same frequency band. In other words, the frequency band occupied by qubits 220, 221, and 222 in one of the channels 210, 211, and 212 can also be occupied by the other channel 211 or 212. In this case, the preamplifiers 260, 261, and 262 of at least two channels 210, 211, and 212 can be configured such that the frequency of the probe signal is changed by the preamplifiers 260, 261, and 262, so that the frequency bands occupied by at least two channels 210, 211, and 212 are different in the bus transmission line 240.

[0104] For example, Channel 0 210 and Channel 1 211 can occupy the same frequency band from 5.00 GHz to 5.25 GHz, with a bandwidth of 250 MHz, and each channel includes six qubits 220, 221, coupled to six readout resonators 280, 281, which are spaced 50 MHz apart in frequency. In this case, preamplifiers 260, 261 can be Josephson junction parametric frequency converters, and the pump frequency supplied to the Josephson junction parametric amplifiers can be configured such that the output signal band of Channel 0 210 remains unchanged, i.e., from 5.00 GHz to 5.25 GHz, and the output signal band of Channel 1 211 is up-converted from 5.50 GHz to 5.75 GHz. The pump frequency of Channel 0 is 10 GHz, and the pump frequency in Channel 1 is 10.5 GHz. Alternatively, if the preamplifier is a degenerate amplifier (phase-sensitive or non-phase-sensitive) and followed by a unity-gain parametric frequency converter, the frequency band of the output signal of Channel 1 211 will be up-converted from 5.50 GHz to 5.75 GHz, and the pump frequency of the converter in Channel 1 is 500 MHz.

[0105] The bandwidth of each channel 210, 211, 212 can be determined by a combination of the following parameters: the bandwidth of preamplifiers 260, 261, 262; the bandwidth of directional multiplexers 210, 211, 212; and the bandwidth of the Purcell filter. Figure 2 Not shown, it can be placed between the readout resonator 280 and the readout transmission lines 290, 291, 292.

[0106] Figure 3 This is a schematic diagram illustrating an exemplary directional multiplexer.

[0107] In some implementations, the directional multiplexer 300 may include a first directional coupler 310, a second directional coupler 320, a first quarter-wavelength transmission line 330, and a second quarter-wavelength transmission line 340.

[0108] The first directional coupler 310 includes a first input port 311, a first transmission port 312, a first isolation port 313, and a first coupling port 314.

[0109] The second directional coupler 320 includes a second input port 321, a second transmission port 322, a second isolation port 323, and a second coupling port 324.

[0110] The first directional coupler 310 and the second directional coupler 320 can be quarter-wave or quarter-wavelength directional couplers, such that they form a closed path with a circumference of one wavelength with the first directional coupler 310, the second directional coupler 320, the first quarter-wavelength transmission line 330 and the second quarter-wavelength transmission line 340.

[0111] In some implementations, the first directional coupler 310 and the second directional coupler 320 may be made of stripline waveguides or coplanar waveguides.

[0112] The first quarter-wavelength transmission line 330 connects the first coupling port 314 and the second coupling port 324.

[0113] The second quarter-wavelength transmission line 340 connects the first isolation port 313 and the second isolation port 323.

[0114] The second transmission port 322 is terminated with terminating resistor 350.

[0115] In some implementations, when the first directional coupler 310, the second directional coupler 320, the first quarter-wavelength transmission line 330, and the second quarter-wavelength transmission line 340 are connected to each other as described above, the second input port 321 is the first port 300-1 of the directional multiplexer 300, the second transmission port 322 is the second port 300-2 of the directional multiplexer 300, the first transmission port 312 is the third port 300-3 of the directional multiplexer 300, and the first input port 311 is the fourth port 300-4 of the directional multiplexer 300.

[0116] In some implementations, the directed multiplexer 300 can be further arranged as follows.

[0117] If the signal entering the first port 300-1 of the directional multiplexer 300 resonates with or within the passband of the directional multiplexer 300, the signal exits the directional multiplexer 300 at the fourth port 300-4.

[0118] If a signal entering the first port 300-1 of the directional multiplexer 300 is detuned to or outside the passband of the directional multiplexer 300, the signal leaves the directional multiplexer 300 at the second port 300-2, is terminated by the termination resistor 350, and dissipates at the termination resistor 350.

[0119] If a signal entering the third port 300-3 of the directional multiplexer 300 is detuned to or outside the passband of the directional multiplexer 300, the signal is coupled to the fourth port 300-4.

[0120] If the signal entering the third port 300-3 of the directional multiplexer 300 resonates with or within the passband of the directional multiplexer 300, the signal terminates at the terminating resistor 350 at the second port 300-2 of the directional multiplexer 300.

[0121] If the signal entering the fourth port 300-4 of the directional multiplexer 300 is detuned to or outside the passband of the directional multiplexer 300, then the signal is coupled to the third port 300-3. This will be discussed in more detail below. Figure 2 In the configuration shown and in the further examples below, the signal entering the fourth port 300-4 corresponds to a reflection from the first amplifiers 150 and 250. To dissipate this signal, a termination resistor can be placed at the third port 300-3 of one of the directional multiplexers 210, 211, and 212. For example, in Figure 2 In the middle, a terminating resistor is connected to the third port 232-3 of the directional multiplexer 232 of Channel N 212 to dissipate reflections from the first amplifier 250.

[0122] If a signal entering the fourth port 300-4 of the directional multiplexer 300 resonates with or within the passband of the directional multiplexer 300, then the signal is coupled to the first port 300-1 of the directional multiplexer 300. Figure 2 In the configuration shown and in the further examples below, the signal entering the fourth port 300-4 corresponds to a reflection from the first amplifiers 150, 250. Isolators 270, 271, 272 protect qubits 220, 221, 222 from this reflected signal, and additional isolators can be arranged in each channel 210, 211, 212 to further suppress the reflected signal.

[0123] exist Figure 2 In the multiplexed qubit readout system described above, the third port 300-3 and the fourth port 300-4 can be coupled to the above-mentioned... Figure 2 Bus transmission line 240. The directional multiplexer 300 can be arranged such that the fourth port 300-4 faces the first amplifier 250. (Source: [Original Source Name]) Figure 2 The outputs of the preamplifiers 260, 261, and 262 described herein are coupled to the first port 300-1 of the directional multiplexer 300 via readout transmission lines 290, 291, and 292.

[0124] The directional multiplexer 300 can be used as a channelization filter, which combines multiple signals from multiple channels 210, 211, 212 in the bus transmission line 240 toward the first amplifier 250.

[0125] The directional multiplexer 300 can be implemented in the form of a superconducting coplanar waveguide, making it suitable for integration with superconducting quantum computing systems.

[0126] In some implementations, when the superconducting coplanar waveguide is constructed to have a 50 Ohm impedance, the termination resistor 350 can be a 50 Ohm resistor.

[0127] The directional multiplexer 300 includes a single resonator whose perimeter is a wavelength at a frequency in the middle of the passband or at the resonant point of the resonator. The resonator can be a loop for traveling waves. The perimeter of the resonator includes two quarter-wavelengths of the first quarter-wavelength transmission line 330 and the second quarter-wavelength transmission line 340, as well as two quarter-wavelengths of the coupling length of the first directional coupler 310 and the second directional coupler 320.

[0128] The above and Figure 3 The design of the directional multiplexer 300 shown is from the field of microwave engineering. Implementations of directional multiplexers 130, 131, 132, 133, 230, 231, and 232 are not limited to... Figure 3 The configuration described below. A directional multiplexer can be designed to include any number of resonators, which are traveling wave loops, with a perimeter that is a multiple of the wavelength at the mid-passband frequency or the resonant frequency of the resonator. Coupling between loops can be achieved by using directional couplers with a quarter-wavelength coupling region. A directional filter obtained with n resonators has four ports. If the directional filter is excited at the port of the first resonator, the traveling wave is excited in one direction (clockwise or counterclockwise) in all resonators, and the nth resonator excites a unidirectional signal at its other port. The following... Figure 5B The design of a directional multiplexer including two resonators for a 2-pole response will be shown.

[0129] The bandwidth of a directional multiplexer can be determined by the coupling strength of the directional coupler. The multipole response can be used to adjust the bandwidth of the directional multiplexer.

[0130] Examples of directional multiplexers 130, 131, 132, 133, 230, 231, and 232 may also include so-called cochlear filters or any kind of microwave multiplexer.

[0131] Figure 4A This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0132] Specifically, Figure 4A A portion of a multiplexed qubit readout system 400 is shown, including a bus transmission line 440, a first amplifier 450, and a directional multiplexer assembly comprising a first directional multiplexer 430, a second directional multiplexer 431, and a third directional multiplexer 432.

[0133] Figure 4A It is a layout drawn as a schematic diagram in ADS (Advanced Design System) software. Based on Figure 4A The ADS schematic diagram shown illustrates the channelization simulation of the filter components as follows: Figure 4B As shown.

[0134] exist Figure 4A In the example, the first directional multiplexer 430, the second directional multiplexer 431, and the third directional multiplexer 432 are connected in series to the bus transmission line 440. Specifically, the third ports 430-3, 431-3, 432-3 and the fourth ports 430-4, 431-4, 432-4 of the first to third directional multiplexers 430, 431, and 432 are connected to the bus transmission line 440. The fourth port 432-4 of the third directional multiplexer 432 is connected to the third port 431-3 of the second directional multiplexer 431. The fourth port 431-4 of the second directional multiplexer 431 is connected to the third port 430-3 of the second directional multiplexer 430. The fourth port 430-4 of the first directional multiplexer 430 is connected to the first amplifier 450. Therefore, the first directional filter 430 is arranged closest to the first amplifier 450, and the third directional filter 450 is arranged furthest from the first amplifier.

[0135] The first directional multiplexer 430, the second directional multiplexer 431, and the third directional multiplexer 432 are respectively parts of channels 210, 211, and 212. Channels 210, 211, and 212 include corresponding multiple qubits 220, 221, and 222, such as... Figure 2 As shown.

[0136] The first directional multiplexer 430, the second directional multiplexer 431, and the third directional multiplexer 432 are as described above. Figure 3 A single-pole directional multiplexer configured in the middle. Each of the first directional multiplexer 430, the second directional multiplexer 431, and the third directional multiplexer 432 is in Figure 4A The middle part is marked with a dashed line.

[0137] Each directional multiplexer includes two directional couplers with a quarter-wavelength coupling length, labeled X1 and X2 in the first directional coupler 430, X3 and X4 in the second directional coupler 431, and X5 and X6 in the third directional coupler 432. The two directional couplers are connected to two quarter-wavelength transmission lines, labeled TL1 and TL2 in the first directional coupler 430, TL3 and TL4 in the second directional coupler 431, and TL5 and TL6 in the third directional coupler 432.

[0138] Each directional multiplexer includes four ports: ports 430-1, 431-1, and 432-1; ports 430-2, 431-2, and 432-2; ports 430-3, 431-3, and 432-3; and ports 430-4, 431-4, and 432-4. Ports 430-2, 431-2, and 432-2 are connected to terminating resistors 436, 437, and 438, respectively.

[0139] like Figure 2 The first ports 430-1, 431-1, and 432-1 of each directional multiplexer 430, 431, and 432 are connected to the outputs of the corresponding preamplifiers 260, 261, 262, 460, 461, and 462.

[0140] exist Figure 4A In the ADS schematic shown, since only the channelization aspect of the directional multiplexer components is considered in the simulation by measuring the frequency response, the first ports 430-1, 431-1, and 432-1 of each directional multiplexer 430, 431, and 432 are connected to 50 Ohm resistors for termination. For similar reasons, each end of the bus transmission line 440 (including the terminals of the first amplifier 450) is replaced with 50 Ohm resistors for termination.

[0141] Each of the directional multiplexers 430, 431, and 432 can have a different resonant frequency, or a passband centered at a different frequency. For example, for Figure 4B The simulation assumes that the first directional multiplexer 430 resonates at 5 GHz, the second directional multiplexer 431 resonates at 5.05 GHz, and the third directional multiplexer 432 resonates at 5.1 GHz.

[0142] Despite Figure 4AIn the example, the multiplexed qubit readout system 400 includes three directional multiplexers 430, 431, and 432, but the number of directional multiplexers 430, 431, and 432 is not limited to three. As mentioned above, given the bandwidth of each channel connected to the directional multiplexers 430, 431, and 432, more channels can be added using the corresponding number of directional multiplexers 430, 431, and 432, provided that the bandwidth of the first amplifier 450 allows.

[0143] Figure 4B Show Figure 4A Simulation results of the directional bandpass filter component described in [the document].

[0144] based on Figure 4A The layout of the multiplexed qubit readout system 400, shown in the ADS (Advanced Design System) software schematic, is simulated, simulating the channelization of the filter components. The results are as follows... Figure 4B As shown.

[0145] The first curve 490 shows the S-parameter S21, which represents the frequency response of the linear gain from terminal 1 of the output signal connected to the first port 430-1 of the first preamplifier 450 and the first directional multiplexer 430 via the bus transmission line 440 to terminal 2 of the output signal connected to the first amplifier 450 and the fourth port 430-4.

[0146] The first curve 490 exhibits a single resonance at a frequency of 5 GHz, where the gain is maximized. Since the first directional multiplexer 430 is positioned closest to the first amplifier 450, the first curve 490 corresponds to the frequency response of the first directional multiplexer 430. This is because, as described above, the signal entering the first port 430-1 of the first directional multiplexer 430 exits at the fourth port 430-4 of the first directional multiplexer 430, heading towards the first amplifier 450.

[0147] The second curve 491 shows the S-parameter S23, which represents the frequency response of the linear gain from terminal 3 of the output signal connected to the first port 431-1 of the second preamplifier 461 and the second directional multiplexer 431 to terminal 2 of the fourth port 430-4 of the first amplifier 450 and the first directional multiplexer 430.

[0148] The second curve 491 shows a resonance at 5.05 GHz, where the gain is maximized, and another resonance at 5 GHz, where notch rejection or suppression of the gain is shown.

[0149] The resonance at 5.05 GHz is caused by the resonant frequency of the second directional multiplexer 431. Since the first directional multiplexer 430 is positioned between the first amplifier 450 and the second directional multiplexer 431, it receives a signal from the fourth port 431-4 of the second directional multiplexer 431 at its third port 430-3. When this signal resonates with the first directional multiplexer 430, i.e., at 5 GHz, the signal is terminated at its second port 430-2 and prevented from being transmitted to the first amplifier 450.

[0150] The third curve 492 shows the S-parameter S25, which represents the frequency response of the linear gain from terminal 5 of the output signal connected to the first port 432-1 of the third preamplifier 462 and the third directional multiplexer 432 to terminal 2 of the fourth port 430-4 of the first amplifier 450 and the first directional multiplexer 430.

[0151] The third curve 492 shows the resonance at 5.1 GHz, where the gain is maximized, and also shows two other resonances at 5 GHz and 5.05 GHz, where notch filtering or suppression of the gain is observed.

[0152] The resonance at 5.1 GHz is caused by the resonant frequency of the third directional multiplexer 432. Since the first directional multiplexer 430 and the second directional multiplexer 431 are arranged between the first amplifier 450 and the third directional multiplexer 432, the signal originating from the fourth port 432-4 of the third directional multiplexer 431 is received at the third port 431-3 of the second directional multiplexer 431. If this signal resonates with the second directional multiplexer 431, i.e., at 5.05 GHz, the signal is terminated at the second port 431-2 of the second directional multiplexer 431 and is prevented from being transmitted to the first amplifier 450.

[0153] Signals that do not resonate with the second directional multiplexer 431 exit from the fourth port 431-4 of the second directional multiplexer 431 and enter the third port 430-3 of the first directional multiplexer 430. If the signal resonates with the first directional multiplexer 430, i.e. at 5.0 GHz, the signal is terminated at the second port 430-2 of the first directional multiplexer 430 and is prevented from being sent to the first amplifier 450.

[0154] Therefore, according to Figure 4BThe simulation results shown indicate that the directional multiplexer components are configured such that signals resonating with and emanating from a corresponding one of the directional multiplexers 430, 431, and 432 are sent to the first amplifier 450. Frequency multiplexing is achieved because any signals entering from the third ports 430-3, 431-3, and 432 of the directional multiplexers 430, 431, and 432, resonating with the directional filters 430, 431, and 432, are rejected by terminating at the second ports 430-2, 431-2, and 432-2, and are prevented from being sent to the first amplifier 450.

[0155] Figure 5A This is a schematic diagram illustrating an exemplary multiplexed qubit readout system.

[0156] Specifically, Figure 5A A portion of multiplexed qubit readout systems 200, 400, and 500 is shown, including two channels (first channel 510 and second channel 511), a directional multiplexer assembly 532, a bus transmission line 540, and a first amplifier 550. Each channel 510 includes a first preamplifier 560 and a second preamplifier 561, which are configured as Josephson parametric amplifiers.

[0157] Figure 5A This is a layout drawn as a schematic diagram for the ADS (Advanced Design System) software. Based on the ADS schematic diagram shown in Figure 5a, the two readout channels 510 and 511 and the directional multiplexer component 532 can be simulated using harmonic balance simulator software, such as... Figure 5C As shown.

[0158] To simulate the detection signals of qubits 220, 221, 222 and corresponding readout resonators 280, 281, 282 in each channel 210, 211, 212, 510, 511, a first signal source 510-1 and a second signal source 511-1 are respectively included in the first channel 510 and the second channel 511. Figures 5A to 5C In the example, it is assumed that the first signal source 510-1 and the second signal source 511-1 generate a first signal and a second signal, respectively, where both the first signal and the second signal are single tones that can sweep across approximately 5 GHz. The first signal source 510-1 and the second signal source 511-1 simulate the following situation: it is assumed that the resonant frequencies of the readout resonators 280 and 281, respectively coupled to the qubits 220 and 221 included in the first channels 210 and 510 and the second channels 211 and 511, occupy the same or similar frequency bands, therefore the first preamplifier 560 and the second preamplifier 561 are required to perform frequency conversion on the signals for frequency multiplexing.

[0159] exist Figures 5A to 5CIn the example, it is assumed that both the first preamplifier 560 and the second preamplifier 561 are Josephson junction parametric amplifiers. As described above, a parametric amplifier is a nonlinear device in which the reactance in the circuit is modulated by a pump tone of frequency fp to facilitate amplification and frequency conversion from a first frequency band Δf centered near f1 to a second frequency band Δf centered near f2, such that fp = f1 + f2. A pump tone at 11 GHz is provided to the first preamplifier 560, and a pump tone at 11.5 GHz is provided to the second preamplifier 561. When the frequency of the first signal is 5 GHz, the first preamplifier 561 upconverts the frequency of the first signal to 6 GHz. When the frequency of the second signal is 5 GHz, the second preamplifier 562 upconverts the 5 GHz frequency of the second signal to 6.5 GHz.

[0160] Directional multiplexer assembly 532 is configured to combine signals output from first preamplifier 560 and second preamplifier 561 into bus transmission line 540, directed toward first amplifier 550. Directional multiplexer assembly 532 includes a first directional multiplexer 530 and a second directional multiplexer 531, each including first ports 530-1, 531-1, second ports 530-2, 531-2, third ports 530-3, 531-3, and fourth ports 530-4, 531-4. Figure 5B As shown, although in Figure 5A The schematic diagram does not show the second directional multiplexer, but the fourth port 531-4 of the second directional multiplexer and the third port 530-3 of the first directional multiplexer are internally interconnected.

[0161] The outputs of the first preamplifier 560 and the second preamplifier 561 are respectively connected to the first port 530-1 of the first directional multiplexer 530 and the first port 531-1 of the second directional multiplexer 531.

[0162] The second ports 530-2 and 531-2 of the first directional multiplexer 530 and the second directional multiplexer 531 are connected to terminating resistors 536 and 537.

[0163] In this example, assume that the first directional multiplexer 530 is positioned closer to the first amplifier 550. Therefore, the fourth port 530-4 of the first directional multiplexer 530 is connected to the first amplifier 550.

[0164] Since the channelization aspect of the directional multiplexer component 532 is considered only by analog frequency response, the first amplifier 550 is replaced by a 50 Ohm resistor for termination, and the output is monitored at the location of the first amplifier 550. To terminate the signal reflected from the first amplifier 550, the end of the bus transmission line 540 connected to the third terminal 531-3 of the second directional coupler 531 is connected to a 50 Ohm resistor for termination.

[0165] In Figure 5B The structure of the directional multiplexer component 532 is described in more detail below.

[0166] Figure 5B It is shown Figure 5A A schematic diagram of the directional multiplexer assembly 532. The directional multiplexer assembly 532 includes a first directional multiplexer 530 and a second directional multiplexer 531. The first directional multiplexer 530 and the second directional multiplexer 531 are indicated by dashed lines.

[0167] The first directional multiplexer 530 and the second directional multiplexer 531 are configured as two-pole resonators, and each includes three directional couplers with a quarter-wavelength coupling length, labeled X2, X1, X7 and X3, X9, X8, respectively, connected to quarter-wavelength transmission lines labeled TL1, TL2, TL7, TL8 and TL4, TL3, TL9, TL10, respectively.

[0168] The first directional multiplexer 530 is configured as follows.

[0169] Directional couplers X2 and X1 are connected via quarter transmission lines TL1 and TL2. Figure 3 They are connected to each other in the manner described herein. Specifically, the first port of directional coupler X2 is connected to the first port of directional coupler X1 via a quarter-wavelength transmission line TL1, and the second port of directional coupler X2 is connected to the second port of directional coupler X1 via a quarter-wavelength transmission line TL2.

[0170] Directional couplers X1 and X7 are connected via quarter-wavelength transmission lines TL7 and TL8. Figure 3 They are connected to each other in the manner described herein. Specifically, the third port of directional coupler X1 is connected to the third port of directional coupler X7 via a quarter-wavelength transmission line TL7, and the fourth port of directional coupler X1 is connected to the fourth port of directional coupler X7 via a quarter-wavelength transmission line TL8.

[0171] The first directional multiplexer 530 includes a first port 530-1, a second port 530-2, a third port 530-3, and a fourth port 530-4.

[0172] The first port 530-1 of the first directional multiplexer 530 is the first port of the directional coupler X7.

[0173] The second port 530-2 of the first directional multiplexer 530 is the second port of the directional coupler X7.

[0174] The third port 530-3 of the first directional multiplexer 530 is the fourth port of the directional coupler X2.

[0175] The fourth port 530-4 of the first directional multiplexer 530 is the third port of the directional coupler X2.

[0176] The second directional multiplexer 531 is configured as follows.

[0177] Directional couplers X3 and X9 are connected via quarter-wavelength transmission lines TL4 and TL3. Figure 3 They are connected to each other in the manner described herein. Specifically, the first port of directional coupler X3 is connected to the first port of directional coupler X9 via a quarter-wavelength transmission line TL4, and the second port of directional coupler X3 is connected to the second port of directional coupler X9 via a quarter-wavelength transmission line TL3.

[0178] Directional couplers X9 and X8 are connected via quarter-wavelength transmission lines TL10 and TL9. Figure 3 They are connected to each other in the manner described herein. Specifically, the third port of directional coupler X9 is connected to the third port of directional coupler X8 via a quarter-wavelength transmission line TL10, and the fourth port of directional coupler X9 is connected to the fourth port of directional coupler X8 via a quarter-wavelength transmission line TL9.

[0179] The second directional multiplexer 531 includes a first port 531-1, a second port 531-2, a third port 531-3, and a fourth port 531-4.

[0180] The first port 531-1 of the second directional multiplexer 531 is the first port of the directional coupler X8.

[0181] The second port 531-2 of the second directional multiplexer 531 is the second port of the directional coupler X8.

[0182] The third port 531-3 of the second directional multiplexer 531 is the fourth port of the directional coupler X3.

[0183] The fourth port 531-4 of the second directional multiplexer 531 is the third port of the directional coupler X3.

[0184] As described above, directional multiplexers can be designed to include any number of resonators, which are traveling-wave loops, with a perimeter that is a multiple of the wavelength at the mid-passband frequency or the resonant frequency of the resonator. The first directional multiplexer 530 and the second directional multiplexer 531 each include two resonators. For example, in the first directional multiplexer 530, the first resonator is formed by a loop passing through directional couplers X1, X2 and quarter-wavelength transmission lines TL1, TL2, and the second resonator is formed by a loop passing through directional couplers X1, X7 and quarter-wavelength transmission lines TL7, TL8. The first and second resonators are coupled via directional coupler X1. Each loop has a perimeter of one wavelength at the frequency resonating with the passband of the resonator formed by the loop, or in the middle of that passband.

[0185] The first directional multiplexer 530 and the second directional multiplexer 531 provide a 2-pole response because each includes three directional couplers.

[0186] At the second port 530-2 of the first directional multiplexer 530, a terminating resistor 536 is connected.

[0187] At the second port 531-2 of the second directional multiplexer 531, a terminating resistor 537 is connected.

[0188] The third port 530-3 of the first directional multiplexer 530 is connected to the fourth port 531-4 of the second directional multiplexer 531. The fourth port 530-4 of the first directional multiplexer 530 is connected to the first amplifier 550, which is replaced with a 50 Ohm resistor for analog operation.

[0189] The output of the first preamplifier 560 is connected to the first port 530-1 of the second directional multiplexer 530.

[0190] The output of the second preamplifier 561 is connected to the first port 531-1 of the second directional multiplexer 531.

[0191] Figure 5C Showing includes Figure 5B Simulation results of the multiplexed qubit readout system 500 of the directional bandpass filter component 530 described in the figure.

[0192] The simulation was performed in ADS software with the harmonic balance simulator package.

[0193] The first curve 590 represents the power of the first signal from the first signal source 510-1, measured at terminal 550 corresponding to the location of the first amplifier 550, when the frequency of the first signal sweeps across the vicinity of 5 GHz and the pump tone of the first preamplifier 560 is fixed at 11 GHz. Since the first preamplifier 560 is configured to convert the 5 GHz frequency to 6 GHz, the first curve 590 is centered at 6 GHz. Assume the gain of the first preamplifier 560 is 20 dB. Before reaching terminal 550 of the first amplifier, the first signal travels through the first directional multiplexer 530.

[0194] The shape of the first curve 590 is given by the response of the first preamplifier 560, which in this example is a Josephson parametric amplifier. The bandwidth of the first directional multiplexer 530 is set to be wider than that of the first preamplifier 560.

[0195] The second curve 591 represents the power of the second signal from the second signal source 511-1, measured at terminal 550 corresponding to the position of the first amplifier 550, when the frequency of the second signal sweeps around 5 GHz and the pump tone entering the second preamplifier 561 is fixed at 11.5 GHz. Since the second preamplifier 561 is configured to convert the 5 GHz frequency to 6.5 GHz, the second curve 591 is centered at 6.5 GHz. Assume the gain of the second preamplifier 561 is 20 dB. The second signal travels through the second directional multiplexer 531 before the first signal reaches the first directional multiplexer 530 and subsequently the terminal 550 of the first amplifier.

[0196] The shape of the second curve 591 is given by the response of the second preamplifier 561, which in this example is a Josephson parametric amplifier. The bandwidth of the second directional multiplexer 531 is set to be wider than that of the first preamplifier 561. Since the frequency band of the signal output from the second directional multiplexer 531 at port 431-4 is outside the passband of the first directional multiplexer 530, the second signal is not attenuated by the first directional multiplexer 530 to a large extent.

[0197] like Figure 5C The simulation results shown demonstrate that the multiplexed qubit readout system 500 can frequency multiplex two channels 510 and 511 containing multiple qubits 120 and 220, wherein the resonant frequencies coupled to the qubits occupy the same frequency band.

[0198] The implementation of the quantum topics and quantum operations described in this specification can be realized in suitable quantum circuits or, more generally, in quantum computing systems, also known as quantum information processing systems, including the structures disclosed in this specification and their structural equivalents, or combinations thereof. The terms "quantum computing system" and "quantum information processing system" may include, but are not limited to, quantum computers, quantum cryptography systems, topological quantum computers, or quantum simulators.

[0199] The terms quantum information and quantum data refer to information or data carried, stored, or preserved by quantum systems, where the smallest nontrivial system is a qubit, i.e., a system that defines a unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems can include, for example, multi-level systems with two or more levels. For example, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In some implementations, the computational ground state is identified as both the ground state and the first excited state; however, it should be understood that other settings where the computational state is identified as a higher-level excited state are also possible. Quantum memory is understood to be a device capable of storing quantum data for long periods, with high fidelity and high efficiency, such as an optical-matter interface, where light is used for transmission and matter is used for storage and preservation of quantum characteristics of the quantum data, such as superposition or quantum coherence.

[0200] Quantum circuit elements (also known as quantum computing circuit elements) include circuit elements used to perform quantum processing operations. That is, quantum circuit elements are configured to utilize quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data in a nondeterministic manner. Some quantum circuit elements, such as qubits, can be configured to simultaneously represent and manipulate information from multiple states. Examples of superconducting quantum circuit elements include circuit elements such as quantum LC oscillators, qubits (e.g., flux qubits, phase qubits, or charge qubits), and superconducting quantum interference devices (SQUIDs) (e.g., RF-SQUIDs or DC-SQUIDs).

[0201] In contrast, classical circuit elements typically process data in a deterministic manner. Classical circuit elements can be configured to collectively execute the instructions of a computer program by performing basic arithmetic, logic, and / or input / output operations on data, where the data is represented in analog or digital form. In some implementations, classical circuit elements can be used to transmit data to and / or receive data from quantum circuit elements via electrical or electromagnetic connections. Examples of classical circuit elements include CMOS-based circuit elements, fast single-throughput quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices, and ERSFQ devices, which are energy-efficient versions of RSFQs that do not use bias resistors.

[0202] The fabrication of the quantum and classical circuit elements described herein may require the deposition of one or more materials, such as superconductors, dielectrics, and / or metals. Depending on the chosen materials, these materials may be deposited using deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering), or epitaxy, as well as other deposition processes. The processes described herein for fabricating circuit elements may require the removal of one or more materials from the device during fabrication. Depending on the material to be removed, the removal process may include, for example, wet etching, dry etching, or stripping processes. The materials forming the circuit elements described herein can be patterned using known photolithography techniques (e.g., photolithography or electron beam lithography).

[0203] During the operation of quantum computing systems using superconducting quantum circuit elements and / or superconducting classical circuit elements (such as those described herein), the superconducting circuit elements are cooled within a cryostat to a temperature that allows the superconducting material to exhibit superconducting properties. A superconducting (or superconducting) material can be understood as a material that exhibits superconducting properties at or below its superconducting critical temperature. Examples of superconducting materials include aluminum (superconducting critical temperature of approximately 1.2 Kelvin), indium (superconducting critical temperature of approximately 3.4 Kelvin), NbTi (superconducting critical temperature of approximately 10 Kelvin), and niobium (superconducting critical temperature of approximately 9.3 Kelvin). Therefore, superconducting structures such as superconducting traces and superconducting ground planes are formed from materials that exhibit superconducting properties at or below their superconducting critical temperature.

[0204] Although this specification contains many implementation-specific details, these details should not be construed as limiting the scope of possible claims, but rather as descriptions of features specific to a particular implementation. Specific features described in the context of a single implementation may also be implemented in combination within a single implementation. Conversely, various features described in the context of a single implementation may also be implemented separately in multiple implementations or in any suitable sub-combination. Furthermore, although features may be described above as functioning in a particular combination, and even initially claimed to be so, in some cases, one or more features from the claimed combination may be removed, and the claimed combination may be used for sub-combinations or variations thereof.

[0205] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring that such operations be performed in the specific order shown or in a sequential order, or that all the operations shown be performed to achieve the desired result. For example, the actions described in the claims can be performed in different orders and the desired result can still be achieved. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of the various components in the above implementation should not be construed as requiring such separation in all implementations.

[0206] Many embodiments have been described. However, it should be understood that various modifications can be made without departing from the spirit and scope of the invention. Therefore, other embodiments are within the scope of the appended claims.

Claims

1. A readout circuit comprising: a first amplifier having an input; a transmission line having a first end and a second end, wherein the first end of the transmission line is coupled to the input of the first amplifier; and a plurality of channels, each channel comprising: a plurality of resonators arranged to read out a plurality of qubits, respectively; and a readout line arranged to receive readout signals from the plurality of resonators, wherein the readout line of each channel is coupled to the transmission line, and wherein each channel is configured to output a respective signal in a respective frequency band that is different from the frequency bands of the other channels in the plurality of channels, wherein the transmission line is a first transmission line and the readout line comprised by each channel is a second transmission line, wherein each channel in the plurality of channels further comprises: a second amplifier connected to the second transmission line configured to amplify the readout signals from the plurality of readout resonators before the readout signals are coupled to the first transmission line, and wherein each second amplifier is configured to shift the frequency of the readout signals to a different corresponding frequency band.

2. The readout circuit of claim 1, wherein the second amplifier is a Josephson junction parametric amplifier.

3. The readout circuit of claim 2, wherein the Josephson junction parametric amplifier is any one of a JPC amplifier, a non- degenerate parametric amplifier, or a traveling wave amplifier.

4. The readout circuit of claim 2 or 3, wherein each channel in the plurality of channels further comprises: a circulator disposed between an output of the second transmission line and the Josephson junction parametric amplifier arranged to receive the readout signals and direct the readout signals to the second transmission line towards the plurality of resonators and direct the readout signals reflected from the plurality of resonators to the Josephson junction parametric amplifier.

5. The readout circuit of any one of claims 1 to 3, wherein the first amplifier has a first frequency bandwidth and each of the plurality of channels has a different corresponding second frequency bandwidth, wherein each second frequency bandwidth is smaller than the first frequency bandwidth, does not overlap with another second frequency bandwidth, and spans a range of frequencies within the first frequency bandwidth.

6. The readout circuit of claim 1, wherein each channel in the plurality of channels further comprises: a directional multiplexer configured to couple the readout signals from the readout line or the second transmission line to the first transmission line towards the first amplifier.

7. The readout circuit of claim 6, wherein, the directional multiplexer is arranged such that the readout signals travel unidirectionally in the first transmission line towards the first amplifier.

8. The readout circuit of claim 7, wherein the directional multiplexer comprises at least one ring resonator, wherein the directional multiplexer further comprises: a first port arranged to receive the signals from the plurality of readout resonators via the second transmission line; a second port connected to a terminating resistor; a third port coupled to the first transmission line; and a fourth port coupled to the first transmission line.

9. The readout circuit of claim 8, wherein the directional multiplexer is arranged such that: in response to receiving a readout signal at the first port and resonating with the at least one ring resonator, the readout signal is directed to the fourth port and subsequently into the first transmission towards the first amplifier, in response to receiving a readout signal at the first port and being detuned from the at least one ring resonator, the readout signal is directed to the second port and terminated at the terminating resistor, in response to receiving a signal at the third port from the first transmission line and being detuned from the at least one ring resonator, the received signal is directed to the first transmission line via the fourth port to be directed towards the first amplifier, in response to receiving a signal at the third port from the first transmission line and being resonant with the at least one ring resonator, the received signal is directed to the second port and terminated at the terminating resistor.

10. The readout circuit according to any one of claims 8 or 9, wherein The directional multiplexer comprises: a first directional coupler; a second directional coupler; a first quarter wavelength connector; and a second quarter wavelength connector, wherein the first directional coupler comprises a first port, a second port, a third port and a fourth port, wherein the second directional coupler comprises a first port, a second port, a third port and a fourth port, wherein the first port of the directional multiplexer comprises the first port of the second directional coupler, the second port of the directional multiplexer comprises the second port of the second directional coupler, the third port of the directional multiplexer comprises the second port of the first directional coupler, and the fourth port of the directional multiplexer comprises the first port of the first directional coupler, wherein the fourth port of the first directional coupler is connected to the fourth port of the second directional coupler via the first quarter wavelength connector, and wherein the third port of the first directional coupler is connected to the third port of the second directional coupler via the second quarter wavelength connector.

11. The readout circuit according to any one of claims 8 or 9, wherein, The directional multiplexer comprises: a first directional coupler; a second directional coupler; a third directional coupler; a first quarter wavelength connector; a second quarter wavelength connector; a third quarter wavelength connector; and a fourth quarter wavelength connector, wherein the first directional coupler comprises a first port, a second port, a third port and a fourth port, wherein the second directional coupler comprises a first port, a second port, a third port and a fourth port, wherein the third directional coupler comprises a first port, a second port, a third port and a fourth port, wherein the first port of the directional multiplexer comprises the first port of the third directional coupler, the second port of the directional multiplexer comprises the second port of the third directional coupler, the third port of the directional multiplexer comprises the fourth port of the first directional coupler, and the fourth port of the directional multiplexer comprises the third port of the first directional coupler, wherein the first port of the first directional coupler is connected to the first port of the second directional coupler via the first quarter wavelength connector, wherein the second port of the first directional coupler is connected to the second port of the second directional coupler via the second quarter wavelength connector, wherein the third port of the second directional coupler is connected to the third port of the third directional coupler via the third quarter wavelength connector, and wherein the fourth port of the second directional coupler is connected to the fourth port of the third directional coupler via the fourth quarter wavelength connector.

12. The readout circuit according to any one of claims 1 to 3 and 6 to 9, wherein The first amplifier is a HEMT (High Electron Mobility Transistor) amplifier or a silicon-germanium amplifier.

13. The readout circuit according to any one of claims 1 to 3 and 6 to 9, wherein, The first transmission line is impedance matched at 50 Ohms.

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