Josephson Parametric Coupler

Abstract

A Josephson parametric device is presented, including an input port, an output port, and a signal path between the input port and the output port. The signal path includes a first section coupled to the input port and having a first passband, a second section coupled to the output port and having a second passband, and a Josephson junction coupling element for parametric coupling between the first section and the second section. The Josephson junction coupling element is coupled to and inserted between the first section and the second section. The Josephson junction coupling element is configured such that the input port receives a first signal at a first frequency within the first passband, and in response to the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal to a second signal at a second frequency within the second passband.

Description

[Technical field]

[0001] The present subject matter relates to Josephson parametric couplers. [Background technology]

[0002] Large-scale quantum computers have the potential to provide fast solutions to a class of different problems. Several challenges in designing and implementing quantum architectures to control, program, and maintain quantum hardware impede the realization of large-scale quantum computing. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] F. Lecocq, L. Ranzani, GA Peterson, K. Cicak, RW Simmonds, JD Teufel, and J. Aumentado, Phys. Rev. Applied 7, 024028 (2017) Summary of the Invention [Problem to be solved by the invention]

[0004] This disclosure relates, inter alia, to Josephson parametric couplers, including techniques for implementing amplification devices for measuring the state of a qubit. [Means for solving the problem]

[0005] In general, inventive aspects of the disclosed subject matter may be embodied in a Josephson parametric device including an input port, an output port, and a signal path between the input port and the output port. The signal path includes a first section coupled to the input port and having a first passband, a second section coupled to the output port and having a second passband, and a Josephson junction coupling element for parametric coupling between the first section and the second section. The Josephson junction coupling element is coupled to and interposed between the first section and the second section. The Josephson junction coupling element is configured such that the input port receives a first signal at a first frequency within the first passband, and in response to the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal to a second signal at a second frequency within the second passband.

[0006] Each of these and other implementations can optionally include one or more of the following features, alone or in combination.

[0007] In some implementations, the second frequency is the sum of the first frequency and the frequency of the pump tone.

[0008] In some implementations, the frequency of the pump tone is the sum of the first frequency and the second frequency.

[0009] In some implementations, the Josephson coupling element includes a Josephson junction, a first resonator having a first passband, and a second resonator having a second passband, and the Josephson junction is interposed between and connected to the first and second resonators.

[0010] In some implementations, the first resonator includes a first series inductor and a first shunt capacitor. The second resonator includes a second series inductor and a second shunt capacitor. The first series inductor and the Josephson junction are electrically connected in series with each other, and the second series inductor and the Josephson junction are electrically connected in series with each other.

[0011] In some implementations, the first resonator and the second resonator include resonator transmission line stubs.

[0012] In some implementations, the first resonator and the second resonator include transmission-line based resonators.

[0013] In some implementations, the first section includes at least one shunt resonator having a first passband disposed between an input port and the first resonator in the signal path, and the second section includes at least one shunt resonator having a second passband disposed between a second resonator and the output port in the signal path.

[0014] In some implementations, each of the at least one resonator includes a shunt capacitor and a shunt inductor.

[0015] In some implementations, each of the at least one resonator includes a resonator stub.

[0016] In some implementations, each of the at least one resonator includes a transmission-line based resonator.

[0017] In some implementations, the Josephson junction coupling element is an RF SQUID.

[0018] In some implementations, the RF SQUID is configured such that in response to a first external magnetic flux bias being applied to the RF SQUID, a Josephson inductance value of the RF SQUID diverges such that passive inductive coupling between the first resonator and the second resonator is reduced.

[0019] In general, another inventive aspect of the subject matter of this disclosure may be embodied in a method of designing a Josephson parametric device including an input port, an output port, and a signal path between the input port and the output port, the signal path including a first section coupled to the input port and having a first passband, a second section filter coupled to the output port and having a second passband, and a Josephson junction coupling element disposed between the first section and the second section. The method includes the steps of providing a first number of resonators j in the first section and a second number of resonators Nj in the second section, and coupling the resonators in the first section with a first resonant frequency ω A and providing the second section resonator with a second resonant frequency ω B providing an attenuation ratio γ between the input port and the first section and between the second section and the output port; providing a bandwidth δω of the first section and the second section; and providing an impedance Z 1 ~Z N and providing the normalized element value g 0 ~g N+1 and providing a 0 represents the normalized impedance at the input port, and g N+1 represents the normalized impedance at the output port and represents the normalized impedance of the N resonators. The normalized element value g 0 ~g N+1 is determined according to tabulated values ​​of the response functions of the first and second sections. This method 01 ~J N,N+1 Calculating the first admittance value J 01 represents the admittance of a first circuit element disposed between the input port and the first section resonator coupled adjacent to the input port, and the N+1th admittance value J N,N+1represents the admittance of the (N+1)th circuit element disposed between the output port and the Nth resonator of the second section connected adjacent to the output port, and the i-th admittance value J i-1,j The method further includes the step of calculating a first admittance value J, which represents the admittance of an (i)th circuit element disposed between the (i-1)th resonator and the i-th resonator. 01 teeth,

[0020]

number

[0021] The i-th admittance value J i-1i teeth,

[0022]

number

[0023] The N+1th admittance value J is given by N,N+1 teeth,

[0024]

number

[0025] is given by Z 0 is the impedance of the input port, and Z N+1 is the impedance of the output port, Z i is the impedance of the i-th resonator. This method uses a coupling coefficient β j,j+1 where j is a first number, Nj is a second number, and a coupling coefficient β j,j+1 teeth,

[0026]

number

[0027] The method further includes the step of calculating a coupling coefficient β j,j+1 Based on the AC magnetic flux Φ for application to the Josephson junction coupling element, AC The method further includes the step of calculating:

[0028] Each of these and other implementations can optionally include one or more of the following features, alone or in combination.

[0029] In some implementations, the coupling coefficient β j,j+1 Based on the AC magnetic flux Φ for application to the Josephson junction coupling element, AC The step of calculating

[0030]

number

[0031] Based on this, the DC magnetic flux Φ applied to the Josephson junction coupling element is DC teeth,

[0032]

number

[0033] L is the linear inductance of the Josephson junction coupling element, and I c is the critical current of the Josephson junction, and Φ 0 is the magnetic flux quantum,

[0034]

number

[0035] is the slope of the mutual inductive coupling between the jth and (j+1)th resonators with respect to the magnetic flux bias applied to the Josephson coupling element, and L j and L j+1are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively.

[0036] In some implementations, the Josephson junction coupling element includes an RF-SQUID.

[0037] In some implementations, the first number is equal to the second number, such that j=N / 2.

[0038] In general, another inventive aspect of the subject matter of this disclosure may be embodied in a method of using a Josephson parametric device, the method including the steps of determining a first frequency of a first signal and a second frequency of a second signal, determining a frequency of a pump tone such that when the pump tone is provided to the Josephson junction coupling element, the first signal is converted to the second signal, providing the pump tone to the Josephson junction coupling element, and providing the first signal at the first frequency to an input port.

[0039] The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will become apparent from the description and drawings, and from the claims. [Brief description of the drawings]

[0040] [Figure 1] FIG. 1 is a schematic diagram illustrating an exemplary Josephson parametric coupler. [Diagram 2] FIG. 1 is a schematic diagram illustrating an exemplary Josephson coupling element including a DC SQUID. [Diagram 3] FIG. 1 is a schematic diagram illustrating an exemplary Josephson parametric coupler. [Figure 4a] FIG. 4 is a diagram showing a simulation result of the Josephson parametric coupler shown in FIG. 3. [Figure 4b] FIG. 4 is a diagram showing a simulation result of the Josephson parametric coupler shown in FIG. 3. [Diagram 5] FIG. 2 is a schematic diagram illustrating an exemplary Josephson coupling element. [Figure 6] FIG. 1 is a diagram showing the design concept of a Josephson parametric coupler. [Figure 7] 1 is a flowchart illustrating an exemplary procedure for designing a Josephson parametric coupler. [Figure 8] 1 is a schematic diagram illustrating an exemplary Josephson parametric coupler in which coupling is provided by a Josephson parametric transducer. [Figure 9] FIG. 9 is a diagram showing a simulation result of the Josephson parametric coupler shown in FIG. 8. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041] Quantum computing involves the coherent processing of quantum information stored in quantum bits (qubits) in a quantum computer. Superconducting quantum computing is a promising implementation of solid-state quantum computing technology in which the quantum information processing system is formed in part from superconducting materials. To operate a quantum information processing system that uses solid-state quantum computing technology such as superconducting qubits, the system is maintained at extremely low temperatures, for example, tens of mK. Extreme cooling of the system helps to keep the superconducting material below its critical temperature and avoid undesirable state transitions. To maintain such low temperatures, the quantum information processing system may be operated within a cryostat, such as a dilution refrigerator.

[0042] In some implementations, the control signals are generated in a hotter environment and transmitted to the quantum information processing system using a shielded, impedance-controlled, GHz-compatible transmission line, such as a coaxial cable. The cryostat may ramp down from room temperature (e.g., about 300 K) to the operating temperature of the qubits in one or more intermediate cooling stages. For example, the cryostat may use a stage maintained in a temperature range that is one or two orders of magnitude lower than the room temperature stage, e.g., about 30-40 K or about 3-4 K, and warmer than the operating temperature of the qubits (e.g., about 10 mK or less).

[0043] In some implementations, state measurement of superconducting qubits is accomplished using a distributed detection scheme. To read out or detect the state of any qubit, a probing signal, e.g., a traveling microwave, can be excited along a readout transmission line coupled to the qubit via a respective readout resonator. The frequency of the probing signal can be in the vicinity of the resonant frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the intensity or phase of the probing signal transmitted along the readout transmission line can change, since the reflectivity of the readout resonator coupled to the qubit changes depending on the state of the qubit. This allows for state detection of the qubit.

[0044] For high fidelity state measurements of superconducting qubits with near quantum-limited noise performance, Josephson junction parametric amplifiers or Josephson junction converters can be constructed and used as preamplifiers of the probing signal. In a Josephson junction parametric amplifier or Josephson junction converter, the Josephson junction acts as a nonlinear inductor, with an inductance that depends on the intensity of the pump tone received at the Josephson junction. A portion of the energy of the pump tone is imparted to the probing signal, which leads to parametric amplification of the probing signal.

[0045] In an exemplary readout system, readout resonators for multiple sensed qubit signals are coupled to a single readout channel. The probing signals sensing the multiple readout resonators coupled to the single readout channel are amplified by a preamplifier. The preamplified signal on the single readout channel is amplified by a HEMT (High Electron Mobility Transistor) amplifier. When designing a readout system for more qubits, one of the conditions to be considered includes the saturation strength of the Josephson junction parametric amplifier or Josephson junction parametric converter, which limits the number of qubits in each readout channel. Josephson parametric frequency converters reported so far have been limited to a bandwidth of a few tens of MHz and a low saturation strength in the pW range.

[0046] The present disclosure relates to a circuit design of a parametric coupler including a Josephson junction that can be used as a preamplifier. In particular, the present disclosure relates to a circuit design that can provide a bandwidth of several hundreds of MHz with a defined transfer characteristic.

[0047] Such designs, referred to herein as Josephson parametric couplers, can be configured as bandpass filters that also function as Josephson parametric amplifiers or Josephson parametric transformers. In some implementations, the Josephson parametric coupler can include an RF SQUID embedded between two segments, each of which includes a series of shunt resonators connected by an admittance inverter.

[0048] The overall design of the Josephson parametric coupler can take the form of coupled resonators, where multiple shunt resonators are connected by admittance inverters, as described in detail herein. The parameters of the circuit, for example the flux bias applied to the RF SQUID, can be determined according to an RF filter synthesis method with prescribed transfer characteristics.

[0049] FIG. 1 is a schematic diagram illustrating an exemplary Josephson parametric coupler.

[0050] The Josephson parametric coupler 100 includes an input port 110 , a first section 120 , a Josephson junction coupling element 130 , a pump source 135 , a second section 140 , and an output port 150 .

[0051] An input signal is received at an input port 110. The signal is then transmitted through a first section 120, a Josephson junction coupling element 130, a second section 140, and then output at an output port 150.

[0052] The first section 120 has an overall response that is a first bandwidth Δf 1 A first center frequency f 1 The optical fiber may include a plurality of resonators so as to have a first passband having ....

[0053] The second section 140 has an overall response that is a second bandwidth Δf 2 A second center frequency f 2 Typically, the filter may include multiple resonators to have a second passband having Δf 1 is Δf 2 may be set to be equal to or similar to

[0054] The Josephson coupling element 130 is interposed between and electrically connected to the first section 120 and the second section 140. The first section 120 and the second section 140 are parametrically coupled through the Josephson coupling element 130. The reactance of the Josephson coupling element 130 is modulated by a pump tone provided by a pump source 135. The frequency of the signal input to the Josephson coupling element 130 is f 2 -f 1 For example, the frequency f 1 If a signal of +δf enters the Josephson coupling element 130, where δf is smaller than the bandwidth of the first section 120 and the second section 140, the frequency of the signal will be f 2 It changes to +δf.

[0055] In some implementations, the Josephson coupling element 130 includes an RF SQUID. At an operating point where the parametric coupling is at a maximum, the saturation power of the Josephson coupling element 130 may be higher than a circuit biased to a corresponding operating point, including a DC SQUID for a similar level of critical current. This is because, for an RF SQUID, the saturation strength is limited only by the critical current of the Josephson junction. For example, for a critical current of 1 μA, the pump power may be about −90 dBm. The probing signal saturation power is typically 1% or less of the pump power, so the probing signal saturation power may be about −110 dBm.

[0056] In some implementations, the operating point of the Josephson parametric coupler 100 may be determined such that the passive coupling between the first section 120 and the second section 140 is minimized. In the case of an RF SQUID as the Josephson coupling element 130, this operating point also corresponds to the point of maximum parametric coupling.

[0057] In contrast, if a DC SQUID is used for the Josephson coupling element 130, since it is shunted to ground, in order to achieve a similar suppression of passive coupling between the first section 120 and the second section 140, the inductance of the DC SQUID must be set relatively low, which leads to a correspondingly lower parametric coupling between the first section 120 and the second section 140. In terms of saturation power, the point of maximum parametric coupling for the DC SQUID is I c cos(πΦ / Φ 0 ) corresponds to an operating point where it is nearly zero. For DC SQUID coupling elements, the bias point of maximum parametric coupling does not coincide with the bias point of minimum stray passive coupling. The maximum possible bandwidth of a DC SQUID depends, like that of an RF SQUID, on the maximum achievable parametric coupling strength.

[0058] Thus, the RF SQUID can be configured to provide purely parametric coupling and little to no passive coupling since it is not shunted to ground. This aspect enables the design of the Josephson coupling element 130 described herein.

[0059] However, the Josephson parametric coupler 100 described herein is not limited to RF SQUIDs. The design concepts, as described herein, relate to modifying the driving point impedance and apply to both RF and DC SQUIDs. In other words, the Josephson parametric coupler 130 is designed such that when an admittance Y2 is connected to the output port of the Josephson parametric coupler 130, the impedance presented to the input port of the Josephson parametric coupler 130 is Y 1 =J 2 / Y 2 where J is related to the strength of the parametric coupling, and Y1 and Y2 are evaluated at the respective frequencies f1 and f2 of the circuits to which they are connected, assuming that the parametric process is frequency transformation. Thus, Josephson parametric coupler 130 may be viewed as an impedance or admittance transformer, as will be described in more detail below.

[0060] In some implementations, the Josephson coupling element 130 may be configured as a Josephson parametric frequency converter, in which case the frequency of the pump tone is f p =f 2 -f 1 It becomes.

[0061] In some implementations, the Josephson coupling element 130 may be configured as a Josephson parametric amplifier, in which case the frequency of the pump tone is f p =f 1 +f 2In comparison with the case where the Josephson coupling element 130 is configured as a Josephson parametric frequency converter, the number of effective poles in the circuit can be reduced.

[0062] In some implementations, the overall design of the Josephson parametric coupler 100 can take the form of coupled resonators, with multiple shunt resonators connected by admittance inverters, and the parameters of the circuit can thus be determined according to RF filter synthesis methods with prescribed transfer characteristics, as described herein.

[0063] In particular, for the application of the RF filter synthesis method, the Josephson coupling element 130 can be considered as a "parametric" admittance inverter, which is similar to an admittance inverter, but operates between two resonators with different resonant frequencies. For example, a desired coupling value of the Josephson coupling element 130 can be determined from an appropriate value of a filter coefficient corresponding to the position of the Josephson coupling element in a network of shunt resonators included in the Josephson parametric coupler 100. The determined coupling value determines the strength of the parametric coupling in the Josephson coupling element 130, which can be translated into the strength of the pump tone provided by the pump source 135 and the magnetic flux bias applied to the Josephson coupling element 130.

[0064] In some implementations, the first section 120 may be configured such that the overall response of the first section is within a first bandwidth Δf 1 A first center frequency f 1 The optical filter may include a plurality of shunt resonators implemented with lumped elements electrically connected to each other by an admittance inverter so as to have a first passband having a first passband having

[0065] In some implementations, the first section 120 may be configured such that the overall response of the first section is within a first bandwidth Δf 1 A first center frequency f 1The optical amplifier may include a plurality of shunt resonators implemented with transmission line based resonators connected to each other by admittance inverters so as to have a first passband having a first passband having

[0066] In some implementations, the first section 120 may be configured such that the overall response of the first section is within a first bandwidth Δf 1 A first center frequency f 1 The optical fiber may include a plurality of transmission line stubs so as to have a first passband having ....

[0067] In some implementations, the second section 140 may be configured such that the overall response of the second section 140 has a second bandwidth Δf 2 A second center frequency f 2 The optical filter may include a plurality of shunt resonators implemented with lumped elements electrically connected to each other by an admittance inverter so as to have a second passband having a first passband having a first passband having a second ...

[0068] In some implementations, the second section 140 may be configured such that the overall response of the second section 140 has a second bandwidth Δf 2 A second center frequency f 2 The optical filter may include a plurality of shunt resonators implemented with transmission line based resonators connected together by admittance inverters so as to have a second passband having a first passband having ...

[0069] In some implementations, the second section 140 may be configured such that the overall response of the second section 140 has a second bandwidth Δf 2 A second center frequency f 2 The optical fiber may include a plurality of transmission line stubs to have a second passband having a first passband having ...

[0070] In some implementations, the number of resonators included in the first section 120, the second section 140 may be the same. In the remainder of this specification, the number of resonators in the first section 120 and the second section 140 is assumed to be the same for simplicity. However, the same concept applies to designs where the number of resonators in the first section 120 and the second section 140 is different. The same concept also applies to designs where there are three sections 120, 140 or more and the parametric conversion process is provided by at least one Josephson coupling element 130 between two adjacent sections 120, 140.

[0071] In some implementations, the first bandwidth Δf 1 and the second bandwidth Δf 2 may be the same. In this case, the common bandwidth is Δf. In the remaining examples of this disclosure, the first bandwidth Δf 1 and the second bandwidth Δf 2 are assumed to be the same Δf for simplicity.

[0072] FIG. 2 is a schematic diagram illustrating an exemplary Josephson coupling element including a DC SQUID.

[0073] The Josephson coupling element 200 is an example of the Josephson coupling element 130 described in Figure 1 and includes a first port 201 and a second port 202 with a signal line defined therebetween. This configuration of the Josephson coupling element 200 using a DC SQUID has been previously described.

[0074] The Josephson coupling element 200 can be connected to other parts of the Josephson parametric coupler 100, namely the first section 120 and the second section 140, via a first port 201 and a second port 202, respectively.

[0075] The Josephson coupling element 200 includes a DC-SQUID 210 disposed between a first port 201 and a second port 202 .

[0076] The DC-SQUID 210 includes a first Josephson junction 211, labeled B1, and a second Josephson junction 212, labeled B2, sandwiched by a first inductor 213, labeled L1, and a second inductor 214, labeled L2. The first Josephson junction 211, the first inductor 213, the second Josephson junction 212, and the second inductor 214 are connected together to form a loop. The order of the components in the loop may not be limited to the example of FIG. 2. For example, the positions of the first Josephson junction 211, labeled B1, and the first inductor 213, labeled L1, may be swapped. The positions of the second Josephson junction 212, labeled B2, and the second inductor 214, labeled L2, may be swapped.

[0077] The Josephson coupling elements 130, 200 can be configured to operate at some cryogenic temperature below the critical temperature of the material forming at least a portion of the Josephson junctions 211, 212. For example, for Josephson junctions formed using an aluminum-aluminum oxide-aluminum structure, the Josephson junctions operate as described herein when the Josephson coupling elements 130, 200 are placed in an environment at a temperature below the superconducting temperature of aluminum. The Josephson parametric coupler 100 or Josephson coupling elements 130, 200 are configured to operate as described herein when placed at the appropriate cryogenic temperature.

[0078] In the loop, the port between the first Josephson junction 211 and the second inductor 214 is connected to the signal line. The port between the second Josephson junction 212 and the first inductor 213 is connected to ground. In other words, the DC SQUID 210 is shunted to ground.

[0079] The example shown in FIG. 2 shows a Josephson coupling element 200 implemented with lumped elements.

[0080] The Josephson junction element 200 further includes a first series inductor 221 and a second series inductor 231 connected in series to the signal line on either side of the port between the first Josephson junction 211 and the second inductor 214 .

[0081] The Josephson junction element 200 further includes a first shunt capacitor 222 and a second shunt capacitor 232 connected to the signal line and shunted to ground.

[0082] The first series inductor 221 is inserted between the first port 201 and the DC-SQUID 210 .

[0083] The second series inductor 231 is inserted between the DC-SQUID 210 and the second port 202 .

[0084] The first shunt capacitor 222 is inserted between the first port 201 and the first series inductor 221 .

[0085] The second shunt capacitor 232 is inserted between the second series inductor 231 and the second port 202 .

[0086] In some implementations, the DC-SQUID 210 transmits a DC magnetic flux Φ through a superconducting transformer of which the first inductor 213 (having a value L1) is a secondary winding, although the primary winding of the superconducting transformer is not shown in FIG. 2 . DC Alternatively, a second inductor 214 (having a value L2) may be used as a secondary winding.

[0087] In some implementations, the DC-SQUID 210 transmits a frequency f through a superconducting transformer in which the first inductor 213 is a secondary winding. p AC magnetic flux Φ AC Alternatively, the second inductor 214 may be used as a secondary winding. Alternatively, the DC-SQUID 210 may be pumped at frequency f through a superconducting transformer in which the additional inductor is a secondary winding.p AC magnetic flux Φ AC An additional inductor may be placed in the superconducting loop of DC-SQUID 210 so that it can be pumped by pump source 135 at .

[0088] DC magnetic flux Φ DC and AC magnetic flux Φ AC When flux-biased with , the DC-SQUID 210 appears as an inductor to the connected circuit elements. It has a corresponding inductance L, called the residual inductance. SQ is shunted to ground as explained above and is therefore shared between the first resonator 220 and the second resonator 230 formed within the Josephson coupling element 200.

[0089] In the example of FIG. 2, the first resonator 220 includes a first series inductor 221 (of value L A ) and residual inductance L SQ , i.e. L A +L SQ The first resonator 220 may be formed by a first shunt capacitor 222 connected in parallel with an inductance corresponding to the sum of 1 The gyro may be formed to have the following structure:

[0090] The second resonator 230 includes a second series inductor 231 (L B ) and residual inductance L SQ , i.e., L B +L SQ The second resonator 230 may be formed by a second shunt capacitor 232 connected in parallel with an inductance corresponding to the sum of 2 The gyro may be formed to have the following structure:

[0091] In some implementations, to design a Josephson coupling element 200 including a DC SQUID 210, a first series inductor L A 221, a second series inductor 231, a first shunt capacitor 222, a second shunt capacitor 232, and a residual inductance L SQThe value of is set when the resonant frequency of the first resonator 220 is f 1 and the resonant frequency of the first resonator is f 2 It can be selected to be:

[0092] In designs where the DC-SQUID 210 is shunted to ground, the DC-SQUID loads other components in the Josephson parametric coupler 100 or Josephson coupling element 130, 200, so the other components may be designed with the inductance of the DC-SQUID 210 in mind. While this may be possible, the inductance of the DC-SQUID 210 may be affected by the magnetic flux bias applied to the DC-SQUID 210, i.e., the frequency f p DC magnetic flux Φ DC and AC magnetic flux Φ AC The design procedure requires iteration since the parametric interactions provided by the Josephson coupling elements 130, 200 also depend on the components connected to the DC-SQUID 210.

[0093] In some implementations, after the Josephson coupling element 200 is designed, the Josephson coupling element 200 may be inserted between the first section 120 and the second section 140. For example, in a four-pole bandpass network, two of the poles are represented by the first resonator 220 and the second resonator 230 included in the Josephson coupling element 200 described herein, and additional resonators can be added to the first port 201 and the second port 202 on each side of the Josephson coupling element 200 via admittance inverters. The additional resonator connected to the first port 201 has a resonant frequency f 1 and an additional resonator connected to the second port 202 may be configured to have a resonant frequency f 2 The signal processing device may be configured to have the following configuration:

[0094] FIG. 3 is a schematic diagram illustrating an exemplary Josephson parametric coupler.

[0095] The Josephson parametric coupler 300 includes an input port 310 , a first section 320 , a Josephson coupling element 330 , a pump source 335 , a second section 340 , and an output port 350 .

[0096] In the example of FIG. 3, Josephson parametric coupler 300 is implemented with lumped elements.

[0097] In FIG. 3, the first section 320, the Josephson coupling element 330, the pump source 335, and the second section 340 are separated by dotted lines.

[0098] The Josephson coupling element 330 is interposed between and electrically connected to the first section 320 and the second section 340. The Josephson coupling element 330 may be designed and operated similarly to the Josephson coupling element 200 described in FIG.

[0099] The first section 320 and the second section 340 are parametrically inductively coupled via a Josephson coupling element 330. The reactance of the Josephson coupling element 330 is modulated by a pump tone provided by a pump source 335.

[0100] Each of the first section 320 and the second section 340 includes a shunt LC resonator with an admittance inverter on each side of the shunt LC resonator.

[0101] The first section 320 includes a shunt LC resonator formed by a capacitor labeled C7 and an inductor labeled L3. The shunt LC resonator of the first section 320 has a first center frequency f 1 The electrodes are arranged so as to have

[0102] The second section 340 includes a shunt LC resonator formed by a capacitor labeled C8 and an inductor labeled L4. The shunt LC resonator of the second section 340 has a second center frequency f2 The electrodes are arranged so as to have

[0103] In the example of FIG. 3, the Josephson parametric coupler 300 has a frequency of f 1 = 5GHz, f 2 = 7 GHz, Δf = 400 MHz. The first section 320 is designed to have a passband with a center frequency of 5 GHz, and the second section 340 is designed to have a center frequency of 7 GHz. Thus, a first frequency f 1 = 5 GHz signal is input, this signal is amplified at a second frequency f 2 = 7 GHz signal and output to the second port 350.

[0104] The Josephson coupling element 330 can be operated such that a 5 GHz signal is converted to a 7 GHz signal in the Josephson coupling element 330 when an appropriate pump tone is provided by the pump source 335 .

[0105] 4a and 4b show simulation results of the Josephson parametric coupler described in FIG. 3 with reference to FIGS. 1 to 3. In FIG.

[0106] FIG. 4a shows a panel 400 containing the results of a simulation performed in the Harmonic Balance simulation package within the Keysight ADS program, where the SQUID is simulated as a symbolically defined device.

[0107] The x-axis 401 of panel 400 represents frequency detuning in GHz. The y-axis 402 of panel 400 represents relative magnitude in dB.

[0108] In this example, the component values ​​of the first section 320 and the second section 340 were selected so that the Josephson parametric coupler 300 has an overall response of a four-pole Chebyshev response with a 400 MHz bandwidth. When the DC-SQUID 210 operates as a parametric frequency converter, the corresponding flux bias applied to the DC-SQUID 210 contained within the Josephson coupling element 200, 330 is a DC magnetic flux Φ DC =0.224Φ 0 and AC magnetic flux Φ AC =0.2Φ 0 It is evaluated to be.

[0109] The first curve 410 represents the relative magnitude of the power reflected at the input port 310. In the first curve 410, the x-axis 401 relates to f1=5 GHz.

[0110] A second curve 420 represents the relative magnitude of the power output at the output port 350. In the second curve 420, the x-axis 401 relates to f2=7 GHz.

[0111] The first curve 410 shows that over a bandwidth of approximately 400 MHz around the 0 GHz detuning, the reflection of power at the input port 310 is reduced by more than 20 dB, indicating that the input matching of the Josephson parametric coupler 300 is better than 20 dB.

[0112] The second curve 420 shows a similar width of bandwidth to that shown by the first curve 410, over a bandwidth of about 350 MHz, where the Josephson parametric coupler 300 outputs power with a conversion gain of about 1 dB, which is approximately 10×log 10 This is consistent with the results of the Manley-Rowe relationship, which predicts a conversion gain of (7 / 5)=1.46 dB.

[0113] Considering the first curve 410, the second curve 420 is between the two bands, namely, f 1 = 5GHz, f 2= 7 GHz, Δf = 350 MHz, with a flat response over the bandwidth 1 Surrounding Δf to f 2 The complete frequency transformation of the surrounding Δf is shown.

[0114] 4b shows a panel 430 containing the results of a simulation performed using the WRSpice program, which includes a model for simulating a Josephson junction. The simulation was run in transient mode, and the time domain output was numerically demodulated to obtain the magnitude of the signal at the device output port 350.

[0115] The x-axis 431 of panel 430 represents frequency detuning in GHz. The y-axis 432 of panel 400 represents relative magnitude in dB.

[0116] Curve 440 represents the relative magnitude of power output at output port 350. For curve 440, x-axis 401 is f 2 =7GHz.

[0117] Curve 440 shows that over a bandwidth of about 350 MHz, which is similar to the bandwidth shown by the simulation results shown in FIG. 4a, Josephson parametric coupler 300 outputs power with a flat response with a conversion gain of about 1 dB. Both simulation techniques, shown in FIGS. 4a and 4b, show good agreement and meet the circuit design goal f 1 = 5GHz, f 2 = 7 GHz, which coincides with Δf = 400 MHz.

[0118] 2 and 3, since the DC-SQUID 210 is shunted to ground, the DC-SQUID loads the other components in the Josephson parametric coupler 100 or Josephson coupling element 130, 200. Therefore, the other components may be designed taking into account the inductance of the DC-SQUID 210. While this may be possible, the inductance of the DC-SQUID 210 may be affected by the magnetic flux bias applied to the DC-SQUID 210, i.e., at frequency fp DC magnetic flux Φ DC and AC magnetic flux Φ AC The design procedure may not be straightforward since the parametric interactions provided by the Josephson coupling elements 130, 200 also depend on the components connected to the DC-SQUID 210.

[0119] For this reason, designing a Josephson parametric coupler 300 as shown in FIG. 3 can be difficult, since within the Josephson coupling elements 130, 200, 330, the first resonator 220 and the second resonator 230 are passively coupled via the first Josephson junction 211 and the second Josephson junction 212 in addition to the parametric coupling provided by the Josephson junction coupling elements 210, 330. In other words, since the DC-SQUID 210 is shunted to ground, the second resonator 230 does not present an open circuit impedance in the passband of the first resonator 220, and vice versa, and the first resonator 220 and the second resonator 230 effectively load each other. Furthermore, the interdependencies between all the components here can reduce design and operating margins.

[0120] Thus, in the designs depicted in FIGS. 2 and 3, where the Josephson junction coupling element 200, 330 includes a DC-SQUID 210, the first inductance L SQ , an approximation was used for the load inductance of DC-SQUID 210. Once a design that is close enough to the target is obtained using the approximation for the load inductance of DC-SQUID 210, further tuning of the element values ​​may be required to optimize the response of Josephson parametric coupler 300.

[0121] The following disclosure is directed to designs of Josephson parametric couplers 100, 300 that address these issues. In particular, the Josephson coupling elements 130, 200, 330 are designed to include RF-SQUIDs.

[0122] FIG. 5 is a schematic diagram illustrating an exemplary Josephson coupling element with reference to FIG.

[0123] The Josephson junction element 500 includes a first port 501 and a second port 502, with a signal line defined therebetween.

[0124] The Josephson coupling element 500 can be connected to other portions of the Josephson parametric coupler 100 via a first port 501 and a second port 502, respectively.

[0125] The Josephson coupling element 500 includes an RF-SQUID 510 disposed between a first port 501 and a second port 502. The RF-SQUID 510 is delimited by a dotted line in FIG.

[0126] RF-SQUID 510 includes a Josephson junction 511, labeled B3, sandwiched between a first inductor 513, labeled L3, and a second inductor 514, labeled L4.

[0127] The port between the Josephson junction 511 and the first inductor 513 is connected to a signal line toward the first port 501. The port between the Josephson junction 511 and the second inductor 514 is connected to a signal line toward the second port 502. The first inductor 513 and the second inductor 514 are connected to ground. The Josephson junction 511, the first inductor 513, the ground, and the second inductor 514 form a loop in this order.

[0128] The example shown in FIG. 5 shows a Josephson coupling element 500 implemented with lumped elements.

[0129] The Josephson coupling element 500 further includes a first series inductor 521 and a second series inductor 531 connected in series to the signal line.

[0130] The Josephson junction element 500 further includes a first shunt capacitor 522 and a second shunt capacitor 532 connected to the signal line and shunted to ground.

[0131] The first series inductor 521 is inserted between the first port 501 and the RF-SQUID 510 .

[0132] A second series inductor 531 is inserted between the RF-SQUID 510 and the second port 502 .

[0133] The first shunt capacitor 522 is inserted between the first port 501 and the first series inductor 521 .

[0134] The second shunt capacitor 532 is inserted between the second series inductor 531 and the second port 502 .

[0135] 5, the first resonator 520 may be formed by a first shunt capacitor 522, a first series inductor 521, and a first inductor 513. The first resonator 520 has a first center frequency f 1 The gyro may be formed to have the following structure:

[0136] The second resonator 530 may be formed by a second shunt capacitor 532, a second series inductor 531, and a second inductor 514. The second resonator 530 may have a second center frequency f 2 The gyro may be formed to have the following structure:

[0137] In some implementations, the RF-SQUID 510 is coupled to a reduced inductance β L is less than 1, β L < 1. The reduced inductance β L where L is the loop inductance and Φ 0 If is a flux quantum, then

[0138]

number

[0139] L, i.e., the loop inductance, corresponds to the sum of the inductance values ​​of the first inductor 513 and the second inductor 514, i.e., L3+L4.

[0140] This condition corresponds to a flux quantum state of n=0, where no stable flux quantum state is found in the loop of the RF-SQUID 510. This state can be achieved by adjusting the inductance values ​​of the first inductor 513 and the second inductor 514, i.e., L3 and L4, or by adjusting the critical current I c This can be achieved by varying the shape of the Josephson junction 511 to control

[0141] In some implementations, the RF-SQUID 510 transmits a frequency f through a superconducting transformer in which the first inductor 513 (having a value of L3) is the secondary winding. p AC magnetic flux Φ AC can be pumped by pump source 135 at

[0142] Alternatively, in some implementations, the RF-SQUID 510 transmits a frequency f through a superconducting transformer in which the second inductor 514 (having a value of L4) is the secondary winding. p AC magnetic flux Φ AC can be pumped by pump source 135 at

[0143] Alternatively, in some implementations, the RF-SQUID 510 is coupled to a superconducting transformer with an additional inductor as a secondary winding at a frequency f p AC magnetic flux Φ AC An additional inductor may be placed in the superconducting loop of the RF-SQUID 510 so that it can be pumped by the pump source 135 at .

[0144] In some implementations, the RF-SQUID 510 transmits a DC flux bias Φ through a superconducting transformer of which the first inductor 513 (having a value of L3) or the second inductor 514 (having a value of L4) is the secondary winding, although the primary winding of the superconducting transformer is not shown in FIG. 5 . DC The resistor may be flux biased with

[0145] Alternatively, in some implementations, the RF-SQUID 510 may be configured to generate a DC magnetic flux bias Φ by applying a magnetic field across the RF-SQUID 510. DC It can be flux biased with

[0146] The inductance of the Josephson junction 511 is determined by the DC magnetic flux bias Φ DC The RF-SQUID 510 detects the equilibrium phase δ across the junction. 0 DC magnetic flux bias Φ DC When biased at , the effective inductance of the Josephson junction 511 diverges. This condition depends on the reduced inductance of the RF-SQUID 510,

[0147]

number

[0148] It is defined as

[0149]

number

[0150] It is defined by the relationship:

[0151] As discussed above, in some implementations, the RF-SQUID 510 may be configured such that the reduced inductance of the RF-SQUID 510 is less than 1, β L < 1. For example, β L If Φ = 0.9, the effective inductance of the Josephson junction 511 isDC =0.39Φ 0 When the effective inductance of the Josephson junction 511 diverges, the passive inductive coupling between the first resonator 520 and the second resonator 530 vanishes, and the coupling provided by the Josephson coupling element 500 diverges at a frequency f p In the presence of an AC flux provided by the sine wave coupling, the coupling becomes purely parametric. In the case of a DC flux, the coupling vanishes.

[0152] In this case, the first and second resonators 520, 530 appear as open circuit impedances in the frequency band of the other resonator, and there is no parasitic interaction between the first section 120 and the second section 140. This allows the two segments of the bandpass filter 120, 140 and the RF SQUID 510 to be treated as separate elements when designing the filter. Thus, the design process can be greatly simplified, since all circuit elements can be calculated without trial and error or iteration. At the same DC flux at which the effective inductance of the Josephson junction 511 diverges, the slope of the curve representing inductance versus flux is maximized. Thus, parametric pumping is also most efficient at this operating point.

[0153] In some implementations, after the Josephson coupling element 500 is designed, the Josephson coupling element 500 may be inserted between the first section 120 and the second section 140. For example, in a four-pole bandpass network, two of the poles are represented by the first resonator 520 and the second resonator 530 included in the Josephson coupling element 500 described above, and one more resonator may be added to the first port 501 and the second port 502 on each side of the Josephson coupling element 500 via an admittance inverter, as described in more detail below. The additional resonator connected to the first port 501 via the first admittance inverter may have a resonant frequency f 1 and an additional resonator connected to the second port 502 via a second admittance inverter can be configured to have a resonant frequency f 2The signal processing device may be configured to have the following configuration:

[0154] Taking the construction of a four-pole bandpass network as an example, a method for designing the Josephson parametric coupler 100, 300 is described below.

[0155] FIG. 6 is a diagram showing the design concept of a Josephson parametric coupler.

[0156] The Josephson parametric coupler 100, 300 can be designed by finding a correspondence between passive filter synthesis methods and the coupled-mode theory approach that describes parametric coupled-mode systems. Coupled-mode theory originates from quantum optics and has been successful in designing non-reciprocal parametric devices. Passive bandpass filter design theory has been engineering practice for decades. Using both of these descriptions to address any system of coupled resonators, whether the coupling is passive or parametric, makes it possible to use established engineering techniques to design wideband parametric devices such as the Josephson parametric coupler 100, 300.

[0157] In particular, the method described below may provide a way to calculate the S-parameters for any system of coupled resonators where the ports are at different frequencies and the coupling coefficients may be complex, as is the case for the Josephson parametric couplers 100, 300. The method is illustrated using the example of a four-pole bandpass filter formed with coupled resonators.

[0158] The first diagram 610 is a graph showing a coupled mode theory representation of a four-pole bandpass filter network. The first diagram 610 shows a first resonator 611, a second resonator 612, a third resonator 613, and a fourth resonator 614 connected in series in that order. Each resonator 611, 612, 613, 614 is represented by a node in the graph. An input port 610, labeled Port A, is connected to the first resonator 611, and an output port 602, labeled Port B, is connected to the fourth resonator 614. In this example, four modes are shown, namely, frequencies ω ... A and the modes A1 and A2 at frequencies ω B Modes B3 and B4 at 611, 612, 613, 614 are considered. These four modes 611, 612, 613, 614 are coupled and the configuration is assumed to have a bandwidth Δω as a design requirement to determine the coupling strength. Mode A1 has a rate γ A and mode B4 is coupled to the external port of input port 601 at rate γ B 613. For the internal modes not connected to a port, i.e. the modes of resonators 612, 613, we set the damping factor γ=0. Similarly, the modes of resonators 611, 614 have no internal loss and their associated damping factors γ A and γ B is assumed to be solely due to their coupling to the ports 601, 602. This is an approximation that reflects the fact that the resonators 611, 612, 613, 614 are superconducting and have very low internal losses. Also, for the Chebyshev and Butterworth prototypes usable in this embodiment, γ A =γ B For example, the frequency of the mode is ω A =5GHz and ω B = 7 GHz. The bandwidth of the configuration, Δω, is 350 MHz. B It can be set to be a fractional bandwidth of around 5%.

[0159] The coupling coefficient representing the coupling between the resonators 611, 612, 613, and 614 is β ij , and resonators 611, 612, 613, 614 are each connected to an adjacent resonator or input / output port 601, 602. For example, the coupling coefficient between the first resonator 611 and the second resonator 612 is β 12 In the examples of Josephson parametric couplers 100 and 300, β 23 The coupling between the second resonator 612 and the third resonator 613, represented by 23 =β * 32 When β 23 corresponds to the parametric coupling provided by the Josephson parametric transducer. In particular, the real positive β 23 corresponds to passive binding. β 23 =-β * 32 When β 23 corresponds to the parametric coupling provided by a Josephson parametric amplifier. These rules are consistent with the parametric converter, where f p =f 2 -f 1 , and f for parametric amplifiers. p =f 1 +f 2 These rules are outlined in F. Lecocq, L. Ranzani, GA Peterson, K. Cicak, RW Simmonds, JD Teufel, and J. Aumentado, Phys. Rev. Applied 7, 024028 (2017).

[0160] A second diagram 620 illustrates how to design a bandpass filter network. Bandpass filter design begins with selecting the required transmission profile, from which the desired number of filter sections, N, the center frequency of the filter, ω 0 , fractional bandwidth

[0161]

number

[0162] and a response type such as a Chebyshev or Butterworth response function. In the example of the Josephson parametric coupler 100, 300, the number of filter sections N=4. The corresponding normalized filter coefficients, or normalized element values ​​g 0 ~g N+1 ,g 0 ~g 5 can be found from tables available as a matter of practice in the field of microwave engineering. The factor g 0 is usually omitted from the table and is usually, by definition, g 0 = 1, which represents the conductance of the source at the input port 601. The final coefficient g 5 represents the conductance of the load at the output port 602. The normalized filter coefficient g 0 ~g 5 is specified, four resonators are designed, corresponding to N=4. As in the example in Figure 5, the resonators are lumped-element LC resonators, i.e., with characteristic impedance Z 1 ~Z 4 The first shunt resonators 611, 621, the second shunt resonators 612, 622, the third shunt resonators 613, 623, and the fourth shunt resonators 614, 624 may be designed to have a resonant frequency of f1, and the third shunt resonators 613, 623, and the fourth shunt resonators 614, 624 may be designed to have a resonant frequency of f2. Only if all couplings are passive, then f1=f2, which is the center frequency of the filter, ω 0 Then, the shunt resonators 611, 621, 612, 622, 613, 623, 614, and 624 are connected to form a composite admittance inverter J, as shown in the second diagram 620. ijFor example, the second shunt resonator 622 and the third shunt resonator 623 are connected to an admittance inverter J 23 The input port 601 and the first shunt resonator 621 are connected via an admittance inverter J 01 are connected via.

[0163] Admittance Inverter J 01 As shown in panel 630 of FIG. 6, which refers to the admittance inverters, the admittance inverters may be configured as a network of capacitors or inductors. However, the implementation of the admittance inverters is not limited to these examples. The admittance inverters may be implemented as quarter-wave transformers, transmission lines, and reactive elements. The admittance value of each admittance inverter is determined by the characteristic impedances and normalized filter coefficients of the shunt resonators and / or input / output ports 601, 602 connected by the admittance inverter, and is given by the following equation:

[0164]

number

[0165] For example, the admittance of the admittance inverter connecting the input port 601 and the first shunt resonator 621 is

[0166]

number

[0167] and the admittance inverter J 12 To configure the .DELTA..times ...

[0168] In the design method for bandpass filter networks, the procedure described above provides fully specified S-parameters, which are the elements of the scattering matrix S, for a system of coupled resonators. However, in contrast to the coupled mode theory representation shown in the first diagram 610, only a single center frequency ω 0 Note that only the admittance inverter J can be used for the design. 23 Although the positions of the Josephson coupling elements 130, 200, 330, 500 in the Josephson parametric couplers 100, 300 correspond to the positions of the Josephson coupling elements 130, 200, 330, 500, the design method is unable to describe the parametric coupling associated with the conversion between the two frequencies. In other words, the admittance inverters are all passive and therefore unable to provide coupling between resonators with different frequencies.

[0169] To address this issue, we present a method by establishing a correspondence between the coupled mode description and the filter theory description.

[0170] The correspondence between the coupled mode theory description and the filter theory description as shown in FIG.

[0171]

number

[0172] ,

[0173]

number

[0174] and

[0175]

number

[0176] Wherein, γ=γ A =γ BIn other words, the coupling coefficient β from the coupled mode theory ij are the normalized filter coefficients g from filter design theory. i The inverter value J ij is associated with.

[0177] The procedure described so far can be applied to the design of, for example, a Josephson parametric coupler 100, 300 built with a 4-pole Chebyshev network with 0.01 dB ripple. Since N=4, the normalized filter coefficients found from the design table are g 0 = 1.0, g 1 =0.7128, g 2 = 1.2003, g 3 = 1.3212, g 4 = 0.6476, and g 5 In the first diagram 610, which shows a graph of the coupled mode theory, the frequency of the mode is ω A =5GHz and ω B = 7 GHz. The network bandwidth, Δω, is chosen to be ω, about 350 MHz. B The fractional bandwidth is chosen to be around 5%. Then, γ = γ A =γ B =491MHz, β 12 =β 34 = 0.385 and β 23 = 0.283. Admittance inverter J ij The admittance of is the normalized filter coefficient g 0 ~g 5 directly from γ and β ij The value can be used to evaluate.

[0178] Once the resonators 621, 622, 623, 624 are designed and the coupling coefficients are determined, the operating condition of the Josephson coupling element 130, 200, 330, 500 is determined based on a prescribed coupling coefficient β between the second shunt resonator 622 and the third shunt resonator 623. 23 = 0.283.

[0179] As explained in FIG. 5, the DC flux operating point is, where L is the loop inductance, to diverge the inductance of the Josephson junction 511.

[0180]

number

[0181] The coupling coefficient β can be determined by 23 For i=2 and j=3,

[0182]

number

[0183] The mutual inductive coupling M between the second shunt resonator 622 and the third shunt resonator 623 is 23 We reconstruct the results given in F. Lecocq et al., Phys. Rev. Applied 7,024028 (2017), which describes the parametric interaction between the two resonators, relating the amplitude of the modulation of Φ ac is the pump amplitude of the AC magnetic flux induced in the RF SQUID by the pump current supplied by the pump source 135. j and L k ,The inductance values ​​of the resonators are selected when designing the resonant frequency, or can be calculated from the resonant frequency and impedance of each resonator if the resonators are not implemented with lumped elements.

[0184]

number

[0185] corresponds to the slope of the mutual inductive coupling between resonators j and k with respect to the flux bias applied to the Josephson coupling element 500.

[0186]

number

[0187] The calculation of the junction critical current I c and depends only on the linear inductance L of the RF-SQUID 510. The mutual coupling M is

[0188]

number

[0189] is given by L j is 1 / cosδ 0 corresponds to the junction inductance proportional to L g are the inductance values, L3, L4, of the first inductor 513 and the second inductor 514 when they are set to be the same. Since all other terms are known, Φ ac During the calculation, the desired β 23 Give

[0190]

number

[0191] It can be calculated by:

[0192] The procedure described above provides a method for synthesizing a bandpass network for a Josephson parametric coupler 100, 300. The procedure also provides a method for calculating the S-parameters of any system of coupled resonators without trial and error or iteration, where the ports may be at different frequencies and the couplings may be complex, as in the parametric process. The procedure has been illustrated using an example for the case N=4, but the concepts apply to any number of resonators or poles.

[0193] FIG. 7, with reference to FIG. 6, is a flow chart illustrating an exemplary procedure for designing a Josephson parametric coupler.

[0194] In step S710, a first number of resonators j is provided in the first section and a second number of resonators Nj is provided in the second section, where N=2 and j=2 in the example of FIG.

[0195] In step S720, the first resonant frequency ω A to the first section resonator, providing a second resonant frequency ω B to the second section resonator. In the example of FIG. 6, the frequency of the mode is ω A =5GHz and ω B =7GHz is selected.

[0196] In step S730, the bandwidth Δω of the first section and the second section is provided. In the example of FIG. 6, the bandwidth Δω is ω 1 , which is about 350 MHz. B The bandwidth is chosen to be a fractional bandwidth of about 5%.

[0197] In step S740, an impedance Z 1 ~Z N When the shunt resonators 621, 622, 623, 624 are configured as LC resonators with lumped elements, the impedance Z 1 ~Z N is determined when the inductance and capacitance values ​​are selected.

[0198] In practice, once the resonant frequencies of the parametrically coupled jth and (j+1)th resonators are selected in step S720, the capacitance and inductance values ​​can be selected, which also determine the impedances of these two resonators, as in step S740. The resonant frequencies of the first section resonators are determined to be the same as those corresponding to step S720, respectively.

[0199] In step S750, the normalized element value g 0 ~g N+1 is provided. 0represents the normalized impedance at the input port, and g N+1 represents the normalized impedance at the output port, and g 1 ~g N represents the normalized impedance of N resonators. In the example of FIG. 6, when N=4, the normalized filter coefficients found from the design table are, for a Chebyshev response, g 0 = 1.0, g 1 =1.7128, g 2 = 1.2003, g 3 = 1.3212, g 4 = 0.6476, and g 5 =1.1007.

[0200] In step S760, the admittance values ​​J between the input port and the first section and between the second section and the output port are calculated. 01 ~J N,N+1 and the decay rate γ is evaluated by:

[0201]

number

[0202] and

[0203]

number

[0204] ,

[0205]

number

[0206] In the formula, γ=Y A =Y B It is.

[0207] The admittance inverter can be configured accordingly, for example by selecting the inductance or capacitance values.

[0208] In step S770, a coupling coefficient β representing the degree of coupling between the j-th resonator included in the first section and the j+1-th resonator included in the second section is calculated. j,j+1 is calculated.

[0209]

number

[0210] In step S780, the coupling coefficient β j,j+1 Based on this, the AC magnetic flux Φ for application to the Josephson junction coupling element AC is calculated as follows:

[0211]

number

[0212] For example, a DC magnetic flux Φ applied to a Josephson junction coupling element, such as the Josephson junction coupling element 510 of the Josephson parametric coupler 500 described in FIG. DC is given by:

[0213]

number

[0214] L is the linear inductance of the Josephson junction coupling element, and I c is the critical current of the Josephson junction, and Φ 0 is the magnetic flux quantum,

[0215]

number

[0216] is the slope of the mutual inductive coupling between the jth and (j+1)th resonators with respect to the magnetic flux bias applied to the Josephson coupling element, and Lj and L j+1 are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively.

[0217] 8 is a schematic diagram illustrating an exemplary Josephson parametric coupler. In particular, FIG 8 illustrates a Josephson parametric coupler 800 constructed according to the procedure of FIG 7.

[0218] The Josephson parametric coupler 800 includes an input port 810 , a first section 820 , a Josephson junction coupling element 830 , a pump source 835 , a second section 840 , and an output port 850 .

[0219] In the example of FIG. 8, Josephson parametric coupler 800 is implemented with lumped elements.

[0220] In FIG. 8, the first section 820, the Josephson coupling element 830, the pump source 835, and the second section 840 are separated by dotted lines.

[0221] The Josephson coupling element 830 is interposed between and electrically connected to the first section 820 and the second section 840. The Josephson coupling element 830 is the Josephson coupling element 500 described in FIG.

[0222] The first section 820 and the second section 840 are parametrically coupled via a Josephson coupling element 830. The reactance of the Josephson coupling element 830 is modulated by a pump tone provided by a pump source 835.

[0223] First section 820 and second section 830 each include a shunt LC resonator with an admittance inverter on each side of the shunt LC resonator, as described in FIGS.

[0224] The input port 310, which is a matching terminal, is connected to the shunt LC resonator through a capacitor network, for example an admittance inverter formed by the combination of a series capacitor labeled C5 and a pair of shunt capacitors. Because the shunt capacitors of the admittance inverter connecting the input port 310, the shunt LC resonator in the first section 320, and the inductor labeled L3 are in parallel with the capacitors of the shunt LC resonator, their capacitance values ​​can be added to determine the capacitance of the capacitor labeled C7.

[0225] A Josephson coupling element 830 including an RF-SQUID as described in Figure 5 is connected to a shunt LC resonator of the first section 820 formed by a capacitor labeled C7 and an inductor labeled L3 through another admittance inverter including a series capacitor labeled C2. As described above in Figures 6 and 7, the capacitance value of the series capacitor labeled C2 is

[0226]

number

[0227] and the configuration of the admittance inverter shown in panel 630, i.e.

[0228]

number

[0229] The determination can be made based on the following:

[0230] The shunt capacitors of the admittance inverter, having value −C2, are not shown in FIG. 8. Since they are in parallel with the capacitor labeled C7 of the LC shunt resonator and the capacitor labeled C1 of the Josephson coupling element 830, the capacitance value −C2 of the shunt capacitors of the admittance inverter can be added to these capacitors labeled C7 and C1. Similarly, the shunt capacitors forming part of the admittance inverter connecting the input port 810 and the shunt LC resonator of the first section 820, together with the series capacitor labeled C5, can be incorporated by modifying the capacitance value of the capacitor labeled C7. Thus, the capacitance values ​​of the capacitors labeled C1 and C7 are initially adjusted to the center frequency ω of the resonator. A is determined and then modified to incorporate the shunt capacitors of the admittance inverter on each side of the resonator.

[0231] The second section 840 includes a shunt LC resonator formed by a capacitor labeled C8 and an inductor labeled L4. The shunt LC resonator of the second section 340 has a second center frequency ω B The series capacitors labeled C3 and C6 can be determined in a similar manner to the series capacitors C2 and C5.

[0232] In this example, the Josephson parametric coupler 800 has a A =5GHz, ω B = 7 GHz, and Δω = 350 MHz. The first section 820 is designed to have a passband with a center frequency of 5 GHz, and the second section 840 is designed to have a center frequency of 7 GHz. In this example, the component values ​​of the first section 820 and the second section 840 were selected such that the Josephson parametric coupler 800 has an overall response of a four-pole Chebyshev response with a 350 MHz bandwidth.

[0233] The Josephson coupling element 830 is coupled to a suitable pump tone Φ AC is provided by the pump source 835, and the RF-SQUID is driven at an appropriate Φ DC value, a 5 GHz signal is designed to be converted to a 7 GHz signal by the Josephson coupling element 830. Thus, a first frequency f 1 = 5 GHz signal is input, this signal is amplified at a second frequency f 2 = 7 GHz signal and output to the second port 850. Within the bandwidth, the frequency of the input signal is 2 -f 1 In this example, the DC magnetic flux Φ DC =0.39Φ 0 , AC magnetic flux Φ AC =0.05Φ 0 It is.

[0234] FIG. 9 shows the simulation results of the Josephson parametric coupler described with reference to FIG.

[0235] FIG. 9 shows a panel 930 containing the results of a simulation performed with the WRSpice program using the same specifications as the circuit of FIG. 8, including operating frequency and transfer characteristics. The simulation was run in transient mode, and the time domain output was numerically demodulated to obtain the magnitude of the signal at the device output port 850. The pump amplitude in this simulation is Φ AC =0.05Φ 0 It was.

[0236] The x-axis 931 of panel 930 represents frequency detuning in GHz. The y-axis 932 of panel 400 represents relative magnitude in dB.

[0237] Curve 940 represents the relative magnitude of power output at output port 850. For curve 940, the x-axis 931 is ω B =7GHz.

[0238] The first curve 940 is shown to have a flat response over a bandwidth of about 350 MHz with a conversion gain of about 1.4 dB, which is consistent with the expected conversion gain from the Manley Rowe relationship.

[0239] Thus, the simulation results indicate that the Josephson parametric coupler 800 shown in FIG. 8 performs according to design specifications.

[0240] There may be designs with more than one Josephson junction coupling element 130, 200, 330, 500, 830 in the circuit to operate at more than two separate frequencies, in which case more than one pump tones must be provided.

[0241] Implementations of the subject matter and operations described herein can be implemented in suitable circuits where the input power is sufficiently low, the operating temperature is below the superconducting temperature of the device, and low loss and low insertion loss are required. Examples of such circuits may include quantum computing systems, also referred to as quantum information processing systems, including the structures disclosed herein and their structural equivalents, or in one or more combinations thereof. The terms "quantum computing system" and "quantum information processing system" may include, but are not limited to, a quantum computer, a quantum cryptography system, a topological quantum computer, or a quantum simulator.

[0242] The terms quantum information and quantum data refer to information or data carried by, held, or stored in a quantum system, with the smallest non-trivial system being a qubit, e.g., a system that defines a unit of quantum information. The term "qubit" is understood to encompass all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems may include, for example, multi-level systems having more than two levels. By way of example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In some implementations, the computational basis states are identified with ground and a first excited state, although it is understood that other configurations are possible in which the computational states are identified with higher levels of excited states. A quantum memory is understood to be a device capable of storing quantum data with high fidelity and efficiency for long periods of time, e.g., where light is used for transmission and matter is a light-matter interface for storing and preserving quantum features of the quantum data, such as superposition or quantum coherence.

[0243] Quantum circuit elements (also called quantum computing circuit elements) include circuit elements for performing quantum processing operations. That is, quantum circuit elements are configured to exploit quantum mechanical phenomena such as superposition and entanglement to perform operations on data non-deterministically. Some quantum circuit elements, such as qubits, can be configured to represent and manipulate two or more states of information simultaneously. 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), among others.

[0244] In contrast, classical circuit elements generally process data in a deterministic manner. Classical circuit elements can be configured to collectively execute instructions of a computer program by performing basic arithmetic, logical, 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 circuit elements based on CMOS circuits, rapid single flux quantum (RSFQ) devices, inverse quantum logic (RQL) devices, and ERSFQ devices, which are energy-efficient versions of RSFQ that do not use bias resistors.

[0245] Fabrication of the quantum and classical circuit elements described herein may involve deposition of one or more materials, such as superconductors, dielectrics, and / or metals. Depending on the materials selected, these materials can be deposited using deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering), or epitaxial techniques, among other deposition processes. The process of fabricating the circuit elements described herein may involve removing 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 techniques, dry etching techniques, or lift-off processes. The materials forming the circuit elements described herein can be patterned using known lithography techniques (e.g., photolithography or electron beam lithography).

[0246] During operation of a quantum computing system using superconducting quantum circuit elements and / or superconducting classical circuit elements such as those described herein, the superconducting circuit elements are cooled in a cryostat to a temperature that allows the superconducting material to exhibit superconducting properties. A superconductor (or alternatively superconducting) material can be understood as a material that exhibits superconducting properties below its superconducting critical temperature. Examples of superconducting materials include aluminum (superconducting critical temperature of about 1.2 Kelvin), indium (superconducting critical temperature of about 3.4 Kelvin), NbTi (superconducting critical temperature of about 10 Kelvin), and niobium (superconducting critical temperature of about 9.3 Kelvin). Thus, superconducting structures such as superconducting traces and superconducting ground planes are formed from materials that exhibit superconducting properties below their superconducting critical temperature.

[0247] Although this specification includes many specific implementation details, these are not to be construed as limitations on the scope of the claims, but rather as descriptions of features that may be specific to a particular implementation. Some features described in the specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable subcombination. Furthermore, although features are described above as acting in some combinations and may initially be claimed as such, in some cases one or more features from the claimed combination can be deleted from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0248] Similarly, although operations are shown in the figures in a particular order, this should not be understood as requiring such operations to be performed in the particular order shown, or in a sequential order, or that all of the illustrated operations be performed to achieve desirable results. For example, actions recited in the claims can be performed in a different order and still achieve desirable results. In some situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various components in the implementations described above should not be understood as requiring such separation in all implementations.

[0249] Although several embodiments of the present invention have been described, it will be understood that various modifications can be made without departing from the scope and spirit of the invention. Accordingly, other embodiments are within the scope of the following claims. [Explanation of symbols]

[0250] 100 Josephson Parametric Coupler 110 Input Port 120 First Section 130 Josephson Junction Element 135 Pump Source 140 Second Section 150 output ports 200 Josephson coupling elements 201 First Port 202 Secondary Port 210 DC-SQUID 211 The first Josephson junction 212 Second Josephson Junction 213 First Inductor 214 Second Inductor 220 First Resonator 221 First series inductor 222 First Shunt Capacitor 230 Second Resonator 231 Second series inductor 232 Second Shunt Capacitor 300 Josephson Parametric Coupler 310 Input Port 320 First Section 330 Josephson coupling element 335 Pump Source 340 Second Section 350 output ports 400 Panels Panel 430 500 Josephson Junction Elements 501 Primary Port 502 Secondary Port 510 RF-SQUID 511 Josephson Junction 513 First Inductor 514 Second Inductor 520 First Resonator 521 First series inductor 522 First Shunt Capacitor 530 Second Resonator 531 Second series inductor 532 Second Shunt Capacitor 601 Input Port 602 Output Port 610 Input Port 611 First Resonator 612 Second Resonator 613 The third resonator 614 The Fourth Resonator 621 First Shunt Resonator 622 Second Shunt Resonator 623 Third Shunt Resonator 624 4th Shunt Resonator 800 Josephson Parametric Coupler 810 Input Port 820 First Section 830 Josephson Junction Coupling Elements 835 Pump Source 840 Second Section 850 output ports

Claims

1. An input port; an output port separate from the input port; A signal path between the input port and the output port, a first section coupled to the input port and having a first passband; a second section coupled to the output port, the second section having a second passband; and a Josephson junction coupling element for parametrically coupling between the first section and the second section, the Josephson junction coupling element being coupled to the first section and the second section and interposed between the first section and the second section; A signal path including Including, the Josephson junction coupling element is configured such that the input port receives a first signal at a first frequency within the first passband, and in response to the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal to a second signal at a second frequency within the second passband; The Josephson junction coupling element is Josephson junctions and a first resonator having the first passband; a second resonator having the second passband; Including, the Josephson junction is inserted between the first resonator and the second resonator and is connected to the first resonator and the second resonator; the first section includes at least one resonator having the first passband disposed between the input port and a first resonator in the signal path; the second section includes at least one resonator having the second passband disposed between a second resonator in the signal path and the output port. Josephson parametric device.

2. the second frequency being the sum of the first frequency and the frequency of the pump tone; 2. The Josephson parametric device of claim 1.

3. the frequency of the pump tone is the sum of the first frequency and the second frequency; 2. The Josephson parametric device of claim 1.

4. the first resonator includes a first series inductor and a first shunt capacitor; the second resonator includes a second series inductor and a second shunt capacitor; the first series inductor and the Josephson junction are electrically connected in series with each other; the second series inductor and the Josephson junction are electrically connected in series with each other.

2. The Josephson parametric device of claim 1.

5. the first resonator and the second resonator include transmission line stubs.

2. The Josephson parametric device of claim 1.

6. the first resonator and the second resonator comprise transmission line based resonators.

2. The Josephson parametric device of claim 1.

7. each of the at least one resonator having the first passband and the at least one resonator having the second passband is a shunt resonator; 2. The Josephson parametric device of claim 1.

8. each of the at least one resonator includes a shunt capacitor and a shunt inductor; 8. A Josephson parametric device as claimed in claim 7.

9. each of the at least one resonator includes a resonator stub; 8. A Josephson parametric device as claimed in claim 7.

10. each of the at least one resonator comprises a transmission line based resonator.

8. A Josephson parametric device as claimed in claim 7.

11. the Josephson junction coupling element is an RF SQUID; A Josephson parametric device according to any one of claims 1 to 10.

12. the RF SQUID is configured such that in response to a first external magnetic flux bias being applied to the RF SQUID, a Josephson inductance value of the RF SQUID diverges such that passive inductive coupling between a first resonator and a second resonator is reduced.

12. A Josephson parametric device as claimed in claim 11.

13. 1. A computer-implemented method for designing a Josephson parametric device, the device comprising: An input port; an output port separate from the input port; A signal path between the input port and the output port, a first section coupled to the input port and having a first passband; a second section coupled to the output port, the second section having a second passband; and A Josephson junction coupling element comprising: Josephson junctions and a first resonator having the first passband; a second resonator having the second passband; Including, the Josephson junction is inserted between the first resonator and the second resonator, and a signal path including a Josephson junction coupling element connected to the first resonator and the second resonator; Including, the Josephson junction coupling element is configured such that the input port receives a first signal at a first frequency within the first passband, and in response to the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal to a second signal at a second frequency within the second passband; The method further comprising: providing a first number of resonators j in the first section and a second number of resonators Nj in the second section; The resonator in the first section has a first resonant frequency ω A and providing the resonator of the second section with a second resonant frequency ω B and providing an attenuation factor γ between the input port and the first section and between the second section and the output port; providing a bandwidth δω of the first section and the second section; Each of the resonators has an impedance Z 1 ~Z N providing a The normalized element value g 0 ~g N+1 providing g 0 represents the normalized impedance at the input port, and g N+1 represents the normalized impedance at the output port, and g 1 ~g N represents the normalized impedance of N resonators, The normalized element value g 0 ~g N+1 is determined according to tabulated values ​​of response functions of the first section and the second section. Providing a step of: Admittance value J 01 ~J N,N+1 Calculating The first admittance value J 01 represents the admittance of a first circuit element disposed between the input port and the resonator of the first section coupled adjacent to the input port, and the N+1th admittance value J N,N+1 represents the admittance of the (N+1)th circuit element disposed between the output port and the Nth resonator of the second section connected adjacent to the output port, and the i-th admittance value J i-1,j represents the admittance of the (i)th circuit element disposed between the (i-1)th resonator and the i-th resonator, The first admittance value J 01 teeth, [0010] is given by The i-th admittance value J i-1i teeth, [0025] is given by The N+1 admittance value J N,N+1 teeth, [0030] is given by Z 0 is the impedance of the input port, and Z N+1 is the impedance of the output port, and Z i is the impedance of the i-th resonator, A calculating step; A coupling coefficient β representing the degree of coupling between the j-th resonator included in the first section and the j+1-th resonator included in the second section. j,j+1 Calculating j is the first number and Nj is the second number, The coupling coefficient β j,j+1 teeth, [0045] is given by, A calculating step; The coupling coefficient β j,j+1 Based on this, an AC magnetic flux Φ AC and calculating The method includes:

14. The coupling coefficient β j,j+1 Based on this, an AC magnetic flux Φ AC wherein the step of calculating [0050] Based on At this time, a DC magnetic flux Φ DC teeth, [006] is given by L is the linear inductance of the Josephson junction coupling element, and I c is the critical current of the Josephson junction, and Φ 0 is the magnetic flux quantum, [0070] is the slope of the mutual inductive coupling between the j-th resonator and the (j+1)-th resonator with respect to the magnetic flux bias applied to the Josephson junction coupling element, and L j and L j+1 are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively. The method of claim 13.

15. the Josephson junction coupling element comprises an RF-SQUID; 15. The method of claim 13 or 14.

16. the first number is equal to the second number, such that j=N / 2; 16. The method according to any one of claims 13 to 15.

17. determining the first frequency of the first signal and the second frequency of the second signal; determining a frequency of the pump tone such that, when the pump tone is provided to the Josephson junction coupling element, the first signal is converted to the second signal; providing the pump tone to the Josephson junction coupling element; providing the first signal at the first frequency to the input port; 13. A method of using a Josephson parametric device according to any one of claims 1 to 12, comprising:

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