Josephson parameter coupler

Abstract

A Josephson parametric device is presented that includes 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 and second sections. 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, in response to the input port receiving a first signal at a first frequency within the first passband and the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal to a second signal having a second frequency within the second passband.

Description

Technical Field

[0001] This topic relates to Josephson parametric couplers. Background Technology

[0002] Large-scale quantum computers have the potential to provide rapid solutions to certain classes of difficult problems. Several 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 disclosure relates to Josephson parameter couplers, including techniques for implementing amplification devices for state measurement of qubits, etc.

[0004] Typically, the innovative aspects of the subject matter of this disclosure can be embodied in a Josephson parametric device comprising an input port, an output port, and a signal path between the input port and the output port. The signal path includes: a first segment coupled to the input port and having a first passband; a second segment coupled to the output port and having a second passband; and a Josephson junction coupling element for parametric coupling between the first segment and the second segment. The Josephson junction coupling element is coupled to the first segment and the second segment and is interposed between the first segment and the second segment. The Josephson junction coupling element is configured such that, in response to the input port receiving a first signal at a first frequency within the first passband and the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal into a second signal having a second frequency within the second passband.

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

[0006] In some implementations, the second frequency is the sum of the first frequency and the pump tone frequency.

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

[0008] In some implementations, the Josephson junction coupling element includes a Josephson junction, a first resonator having a first passband, and a second resonator having a second passband. The Josephson junction is inserted between and connected to the first and second resonators.

[0009] 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 connected in series with each other, and the second series inductor and the Josephson junction are also connected in series with each other.

[0010] In some implementations, the first and second resonators include stubs of the resonator transmission lines.

[0011] In some implementations, the first and second resonators include transmission line-based resonators.

[0012] In some implementations, the first segment includes at least one shunt resonator between an input port having a first passband and arranged in the signal path and a first resonator, and the second segment includes at least one shunt resonator between a second resonator having a second passband and arranged in the signal path and an output port.

[0013] In some implementations, each of at least one resonator includes a shunt capacitor and a shunt inductor.

[0014] In some implementations, each of at least one resonator includes a resonator truncated section.

[0015] In some implementations, each of at least one resonator includes a transmission line-based resonator.

[0016] In some implementations, the Josephson junction coupling element is an RF SQUID.

[0017] In some implementations, the RF SQUID is arranged such that, in response to a first external flux bias applied to the RF SQUID, the Josephson inductance value of the RF SQUID diverges, thereby reducing the passive inductive coupling between the first resonator and the second resonator.

[0018] Typically, another innovative aspect of the subject matter of this disclosure can be embodied in a method for designing a Josephson parametric device, the Josephson parametric device including an input port, an output port, and a signal path between the input port and the output port, wherein the signal path includes a first segment coupled to the input port and having a first passband, a second segment coupled to the output port and having a second passband, and a Josephson junction coupling element interposed between the first segment and the second segment. The method includes: providing a first number j resonators in the first segment and a second number Nj resonators in the second segment; providing a first resonant frequency to the resonators in the first segment. And provide a second resonant frequency to the resonator in the second section. And provides attenuation rate between the input port and the first section and between the second section and the output port. Provide bandwidth for the first and second segments. Provide impedance for each resonator arrive Provides normalized element values arrive . This represents the normalized impedance at the input port. This represents the normalized impedance at the output port, and arrive This represents the normalized impedance of N resonators. The normalized element values ​​g0 to g' are determined based on the tabulated values ​​of the response functions of the first and second segments. N+1 The method also includes: calculating the admittance value. to Among them, the first admittance value This represents the admittance of the first circuit element to be placed between the input port and the resonator in the first segment adjacent to and coupled to the input port, the (N+1)th admittance value. Let represent the admittance of the (N+1)th circuit element to be arranged between the output port and the Nth resonator in the second segment adjacent to and connected to the output port, and let represent the admittance value of the i-th circuit element. This represents the admittance of the i-th circuit element to be placed between the (i-1)-th resonator and the i-th resonator. The first admittance value... Depend on Given the i-th admittance value. Depend on Given, and the (N+1)th admittance value Depend on Given, among which, It is the impedance of the input port. It is the impedance of the output port, and It is the impedance of the i-th resonator. The method further includes: calculating a coupling coefficient representing the coupling degree between the j-th resonator included in the first segment and the (j+1)-th resonator included in the second segment. Where j is the first quantity and Nj is the second quantity, where the coupling coefficient is... Depend on The method is given. It also includes methods based on coupling coefficients. Calculate the AC flux applied to the Josephson junction coupling element. .

[0019] The foregoing and other implementations can optionally include one or more of the following features, either individually or in combination.

[0020] In some implementations, when the DC flux applied to the Josephson junction coupling element Depend on When given, based on the coupling coefficient Calculate the AC flux applied to the Josephson junction coupling element. based on L is the linear inductance of the Josephson junction coupling element, and I... CIt is the critical current of the Josephson junction. It is a magnetic flux quantum. It is the slope of the mutual inductance coupling between the j-th resonator and the (j+1)-th resonator relative to the flux bias applied to the Josephson junction coupling element, and and These are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively.

[0021] In some implementations, the Josephson junction coupling element includes an RF-SQUID.

[0022] In some implementations, the first quantity equals the second quantity, such that j = N / 2.

[0023] Typically, another innovative aspect of the subject matter of this disclosure can be embodied in a method using a Josephson parameter device, the method comprising: determining a first frequency of a first signal and a second frequency of a second signal; determining a pump tone frequency such that when the pump tone is provided to a Josephson junction coupling element, the first signal is converted into the second signal; providing the pump tone to the Josephson junction coupling element and providing the first signal of the first frequency to an input port.

[0024] Details of one or more embodiments are set forth in the accompanying drawings and the following description. Other features and advantages will become apparent from the specification, drawings, and claims. Attached Figure Description

[0025] Figure 1 This is a schematic diagram illustrating an exemplary Josephson parameter coupler.

[0026] Figure 2 This is a schematic diagram illustrating an exemplary Josephson junction coupling element including a DC SQUID.

[0027] Figure 3 This is a schematic diagram illustrating an exemplary Josephson parameter coupler.

[0028] Figure 4A and Figure 4B It shows Figure 3 Simulation results of the Josephson parametric coupler described in [the text].

[0029] Figure 5 This is a schematic diagram illustrating an exemplary Josephson junction coupling element.

[0030] Figure 6 This is a diagram illustrating the design concept of the Josephson parametric coupler.

[0031] Figure 7 This is a flowchart illustrating an exemplary process for designing a Josephson parametric coupler.

[0032] Figure 8 This is a schematic diagram illustrating an exemplary Josephson parameter coupler in which coupling is provided by a Josephson parameter converter.

[0033] Figure 9 Shown in Figure 8 Simulation results of the Josephson parametric coupler described in [the text]. Detailed Implementation

[0034] Quantum computing requires the coherent processing of quantum information stored in qubits within a quantum computer. Superconducting quantum computing is a promising approach to solid-state quantum computing, in which the quantum information processing system is partially formed from superconducting materials. To operate a quantum information processing system employing solid-state quantum computing techniques such as superconducting qubits, the system is kept at extremely low temperatures, for example, within 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.

[0035] 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-capacity transmission lines (such as coaxial cables). The cryostat can gradually reduce from room temperature (e.g., about 300 K) to the operating temperature of the qubit in one or more intermediate cooling stages. For example, the cryostat can employ stages maintained at a temperature range that is one or two orders of magnitude colder than the room temperature stage (e.g., about 30-40 K or about 3-4 K) and warmer than the operating temperature of the qubit (e.g., about 10 mK or lower).

[0036] In some implementations, a dispersive detection scheme is used to measure the state of a superconducting qubit. To read out or detect the state of any qubit, a probe signal, such as a traveling microwave, can be excited along a readout transmission line coupled to the qubit via a corresponding readout resonator. The frequency of the probe signal can be near the resonant frequency of the readout resonator. Depending on the internal quantum mechanical state of the qubit, the intensity or phase of the probe signal propagating along the readout transmission line can be altered because the reflectivity of the readout resonator coupled to the qubit changes according to the qubit's state. This allows for the detection of the qubit's state.

[0037] For high-fidelity state measurements of superconducting qubits with near-quantum confinement noise performance, a Josephson junction parametric amplifier or Josephson junction transducer can be constructed and used as a preamplifier for the probe signal. Within the Josephson junction parametric amplifier or Josephson junction transducer, the Josephson junction acts as a nonlinear inductor, where the inductance depends on the intensity of the pump tone received at the Josephson junction. A portion of the energy of the pump tone is assigned to the probe signal, resulting in parametric amplification of the probe signal.

[0038] In an exemplary readout system, readout resonators for multiple sensed qubit signals are coupled to a single readout channel. The probe signals sensed by the multiple readout resonators coupled to the single readout channel are amplified by a preamplifier. The pre-amplified signal on the single readout channel is then amplified by a HEMT (High Electron Mobility Transistor) amplifier. One of the conditions to consider when designing readout systems for a larger number of qubits is the saturation intensity of the Josephson junction-parameter amplifier or Josephson junction-parameter converter, which limits the number of qubits in each readout channel. Josephson junction-parameter frequency converters reported to date have been limited to bandwidths of tens of MHz and low saturation intensity in the pW range.

[0039] This disclosure relates to a circuit design for a parametric coupler including a Josephson junction, which can be used as a preamplifier. In particular, this disclosure relates to a circuit design that can provide a bandwidth of several hundred MHz with specified transfer characteristics.

[0040] This design, referred to herein as a Josephson parametric coupler, can be constructed as a bandpass filter, which also functions as a Josephson parametric amplifier or Josephson parametric converter. In some implementations, the Josephson parametric coupler may include an RF SQUID. The RF SQUID is embedded between two segments, each segment comprising a series of shunt resonators connected by an admittance inverter.

[0041] As discussed in detail in this paper, the overall design of the Josephson parametric coupler can take the form of a coupled resonator, in which multiple shunt resonators are connected via an admittance inverter. The circuit parameters, such as the flux bias to be applied to the RF SQUID, can be determined by following an RF filter synthesis method with specified transfer characteristics.

[0042] Figure 1 This is a schematic diagram illustrating an exemplary Josephson parameter coupler.

[0043] 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.

[0044] The input signal is received at input port 110. The signal is then transmitted sequentially to the first segment 120, the Josephson junction coupling element 130, and the second segment 140, and then output at output port 150.

[0045] The first segment 120 may include multiple resonators, such that the total response of the first segment has a first passband, the first passband having a first center frequency f1 and a first bandwidth. f1.

[0046] The second segment 140 may include multiple resonators, such that the overall response of the second segment 140 has a second passband, the second passband having a second center frequency f2 and a second bandwidth. f2. Typically, f1 can be arranged to be equal to or similar to f2.

[0047] A Josephson junction coupling element 130 is inserted between and electrically connected to the first segment 120 and the second segment 140. The first segment 120 and the second segment 140 are parametrically coupled via the Josephson junction coupling element 130. The reactance of the Josephson junction coupling element 130 is modulated by a pump tone provided by a pump source 135. The frequency of the signal input to the Josephson junction coupling element 130 changes from f2 to f1. For example, if the frequency from the first segment 120 is f1 + f2, then the frequency of the signal input to the Josephson junction coupling element 130 is f2 - f1. If the signal f enters the Josephson junction coupling element 130, then if When f is less than the bandwidth of the first segment 120 and the second segment 140, the signal frequency becomes f2 + when the signal leaves the Josephson junction coupling element 130. f.

[0048] In some implementations, the Josephson junction coupling element 130 includes an RF SQUID. At the operating point where the parametric coupling is at its maximum, the saturation power of the Josephson junction coupling element 130 can be higher than that of a circuit including a DC SQUID, which is used for a similar level of critical current and biased to the corresponding operating point. 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 can be approximately -90 dBm. Since the saturation power of the probe signal typically does not exceed 1% of the pump power, the saturation power of the probe signal can be approximately -110 dBm.

[0049] In some implementations, the operating point of the Josephson parametric coupler 100 can be determined such that the passive coupling between the first segment 120 and the second segment 140 is minimized. This operating point also corresponds to the point of maximum parametric coupling for the RFSQUID, which serves as the Josephson junction coupling element 130.

[0050] Conversely, if a DC SQUID is used for Josephson junction coupling element 130, since it is shunt to ground, the inductance of the DC SQUID may have to be set relatively low to achieve similar suppression of passive coupling between the first segment 120 and the second segment 140. This results in a correspondingly low parametric coupling between the first segment 120 and the second segment 140. Regarding saturation power, since the maximum parametric coupling point of the DC SQUID corresponds to... With an operating point close to zero, the power level of a DC SQUID must be relatively low. For DC SQUID coupled elements, the bias point for maximum parametric coupling does not coincide with the bias point for minimum stray passive coupling. The maximum possible bandwidth of a DC SQUID depends on the maximum achievable parametric coupling strength for the RF SQUID case.

[0051] Therefore, the RF SQUID can be configured to provide purely parametric coupling and minimal passive coupling because it is not shunt to ground. This aspect allows for the design of the Josephson junction coupled element 130 described herein.

[0052] However, the Josephson parametric coupler 100 described herein is not limited to RF SQUIDs. As described herein, the design concept involves modifying the drive point impedance and is applied to both RF SQUIDs and DC SQUIDs. In other words, the Josephson parametric coupler 130 can be considered as an admittance inverter such that if admittance Y2 is connected to the output port of the Josephson parametric coupler 130, the impedance presented at the input port of the Josephson parametric coupler 130 is Y1 = J. 2 / Y2, where J is related to the strength of the parametric coupling, and assuming the parametric process is a frequency conversion, Y1 and Y2 are estimated at the corresponding frequencies f1 and f2 of the circuits to which they are connected. Therefore, the Josephson parametric coupler 130 can be considered as an impedance or admittance transformer, as will be discussed in more detail later.

[0053] In some implementations, the Josephson junction coupling element 130 can be configured as a Josephson parameter frequency converter. In this case, the pump tone frequency is f. p = f2 - f1.

[0054] In some implementations, the Josephson junction coupling element 130 can be configured as a Josephson parametric amplifier. In this case, the pump tone frequency is f. p = f1 + f2. Compared to the case where the Josephson junction coupling element 130 is configured as a Josephson parameter frequency converter, the effective number of poles in the circuit can be lower.

[0055] In some implementations, the overall design of the Josephson parametric coupler 100 can take the form of a coupled resonator, where multiple shunt resonators are connected via an admittance inverter. Therefore, the circuit parameters can be determined by following an RF filter synthesis method with specified transfer characteristics, as described herein.

[0056] Specifically, for the purpose of applying RF filter synthesis methods, the Josephson junction coupling element 130 can be considered a "parametric" admittance inverter, which is similar to an admittance inverter but operates between two resonators with different resonant frequencies. For example, the desired coupling value of the Josephson junction coupling element 130 can be determined based on appropriate values ​​of filter coefficients corresponding to the position of the Josephson junction coupling element in the network of shunt resonators included in the Josephson parametric coupler 100. The determined coupling value determines the strength of the parametric coupling at the Josephson junction coupling element 130, which can be converted into the strength of the pump tone provided by the pump source 135 and the flux bias applied to the Josephson junction coupling element 130.

[0057] In some implementations, the first segment 120 may include a plurality of shunt resonators implemented using lumped elements electrically connected to each other via admittance inverters, such that the overall response of the first segment has a first passband having a first center frequency f1 and a first bandwidth. f1.

[0058] In some implementations, the first segment 120 may include a plurality of shunt resonators implemented using transmission line-based resonators interconnected via admittance inverters, such that the overall response of the first segment has a first passband having a first center frequency f1 and a first bandwidth. f1.

[0059] In some implementations, the first segment 120 may include multiple transmission line stubs, such that the overall response of the first segment has a first passband, which has a first center frequency f1 and a first bandwidth. f1.

[0060] In some implementations, the second segment 140 may include a plurality of shunt resonators implemented using lumped elements electrically connected to each other via admittance inverters, such that the overall response of the second segment 140 has a second passband having a second center frequency f2 and a second bandwidth. f2.

[0061] In some implementations, the second segment 140 may include a plurality of shunt resonators implemented using transmission line-based resonators interconnected via admittance inverters, such that the overall response of the second segment 140 has a second passband having a second center frequency f2 and a second bandwidth. f2.

[0062] In some implementations, the second segment 140 may include multiple transmission line stubs such that the overall response of the second segment 140 has a second passband having a second center frequency f2 and a second bandwidth. f2.

[0063] In some implementations, the number of resonators included in the first segment 120 and the second segment 140 may be the same. For the remainder of this specification, for simplicity, it will be assumed that the number of resonators in the first segment 120 and the second segment 140 is the same. However, the same concept applies to designs in which the number of resonators in the first segment 120 and the second segment 140 is different. The same concept also applies to designs with three or more segments 120, 140, and the parameter transformation process is provided by at least one Josephson junction coupling element 130 between two adjacent segments 120, 140.

[0064] In some implementations, the first bandwidth f1 and second bandwidth f2 can be the same. In this case, the common bandwidth will be f. For the remaining examples in this disclosure, for simplicity, a first bandwidth is assumed. f1 and second bandwidth f2 is the same.

[0065] Figure 2 This is a schematic diagram illustrating an exemplary Josephson junction coupling element including a DC SQUID.

[0066] Josephson junction coupling element 200 is Figure 1 An example of the Josephson junction coupling element 130 described herein includes a first port 201 and a second port 202, defining a signal line between the first port 201 and the second port 202. This configuration of the Josephson junction coupling element 200 using a DC SQUID has previously been described.

[0067] The Josephson junction coupling element 200 can be connected to other parts of the Josephson parametric coupler 100, namely the first segment 120 and the second segment 140, via the first port 201 and the second port 202, respectively.

[0068] The Josephson junction coupling element 200 includes a DC-SQUID 210 disposed between a first port 201 and a second port 202.

[0069] The DC-SQUID 210 includes a first Josephson junction 211, labeled B1, and a second Josephson junction 212, labeled B2. The first Josephson junction 211 and the second Josephson junction 212 are interposed 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 to each other to form a loop. The order of the components in the loop is not limited to... Figure 2 Examples. For instance, the positions of the first Josephson junction 211, labeled B1, and the first inductor 213, labeled L1, can be interchanged. The positions of the second Josephson junction 212, labeled B2, and the second inductor 214, labeled L2, can also be interchanged.

[0070] Josephson junction coupling elements 130, 200 can be arranged to operate at a specific cryogenic temperature below the critical temperature of the material forming at least a portion of the Josephson junctions 211, 212. For example, for a Josephson junction formed using an aluminum-alumina-alumina structure, once the Josephson junction coupling elements 130, 200 are arranged in an environment at a temperature below the superconducting temperature of aluminum, the Josephson junction operates as described herein. The Josephson parametric coupler 100 or the Josephson junction coupling elements 130, 200 are configured to operate as described herein once arranged at a suitable cryogenic temperature.

[0071] Within 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 shunt to ground.

[0072] Figure 2 The example shown illustrates a Josephson junction coupling element 200 implemented using lumped elements.

[0073] The Josephson junction coupling element 200 also includes a first series inductor 221 and a second series inductor 231 connected in series to the signal line on each side of the port between the first Josephson junction 211 and the second inductor 214.

[0074] The Josephson junction coupling element 200 also includes a first shunt capacitor 222 and a second shunt capacitor 232 connected to the signal line and shunted to ground.

[0075] The first series inductor 221 is inserted between the first port 201 and the DC-SQUID 210.

[0076] The second series inductor 231 is inserted between the DC-SQUID 210 and the second port 202.

[0077] The first shunt capacitor 222 is inserted between the first port 201 and the first series inductor 221.

[0078] The second shunt capacitor 232 is inserted between the second series inductor 231 and the second port 202.

[0079] In some implementations, the DC-SQUID 210 can utilize DC flux via a superconducting transformer. Flux biased, wherein the first inductor 213 (with value L1) is the secondary coil, although in Figure 2 The primary coil of the superconducting transformer is not shown. Alternatively, a second inductor 214 (with a value L2) can be used as the secondary coil.

[0080] In some implementations, the DC-SQUID 210 can be powered by a pump source 135 via a superconducting transformer at a frequency f. p AC flux Pumping is performed, wherein the first inductor 213 is a secondary coil. Alternatively, a second inductor 214 can be used as a secondary coil. Alternatively, an additional inductor can be arranged in the superconducting circuit of the DC-SQUID 210, such that the DC-SQUID 210 can be pumped from the pump source 135 via a superconducting transformer at a frequency f. p AC flux Pumping, wherein the additional inductor is the secondary coil.

[0081] When using DC flux and AC flux When biased by flux, the DC-SQUID 210 behaves as an inductor for the connected circuit elements. The corresponding inductance L... SQ (We refer to this as residual inductance) is shared between the first resonator 220 and the second resonator 230 formed within the Josephson junction coupling element 200, because it is shunt to ground, as described above.

[0082] exist Figure 2 In the example, the first resonator 220 can be formed by connecting a first shunt capacitor 222 in parallel with an inductor, the inductor corresponding to a first series inductor 221 (having a value L). A ) and residual inductance L SQ The sum, i.e. L A + L SQ The first resonator 220 can be configured to have a first center frequency f1.

[0083] The second resonator 230 can be formed by connecting a second shunt capacitor 232 in parallel with an inductor, which corresponds to the second series inductor 231 (having L... B(value) and residual inductance L SQ The sum, i.e. L B + L SQ The second resonator 230 can be configured to have a second center frequency f2.

[0084] In some implementations, to design a Josephson junction coupling element 200 including a DC SQUID 210, a first series inductor L can be selected. A 221, second series inductor 231, first shunt capacitor 222, second shunt capacitor 232, and residual inductance L SQ The value of f1 is such that the resonant frequency of the first resonator 220 is f1 and the resonant frequency of the second resonator is f2.

[0085] In designs where the DC-SQUID 210 is shunt to ground, since the DC-SQUID loads other components in the Josephson parametric coupler 100 or Josephson junction coupling elements 130, 200, the inductance of the DC-SQUID 210 can be considered in designing these other components. While this may be feasible, the design process requires iteration because the inductance of the DC-SQUID 210 depends on the flux bias applied to the DC-SQUID 210, i.e., the frequency f. p DC flux at the location and AC flux Furthermore, the parameter interactions provided by the Josephson junction coupling elements 130 and 200 depend on the components connected to the DC-SQUID 210.

[0086] In some implementations, after designing the Josephson junction coupling element 200, it can be inserted between the first segment 120 and the second segment 140. For example, in a 4-pole bandpass network, two of the poles are represented by a first resonator 220 and a second resonator 230 included in the Josephson junction coupling element 200 described herein, and additional resonators can be added to each side of the Josephson junction coupling element 200 via an admittance inverter at the first port 201 and the second port 202. The additional resonator connected to the first port 201 can also be configured to have a resonant frequency f1, and the additional resonator connected to the second port 202 can be configured to have a resonant frequency f2.

[0087] Figure 3 This is a schematic diagram illustrating an exemplary Josephson parameter coupler.

[0088] The Josephson parametric coupler 300 includes an input port 310, a first section 320, a Josephson junction coupling element 330, a pump source 335, a second section 340, and an output port 350.

[0089] exist Figure 3 In the example, the Josephson parametric coupler 300 is implemented using lumped elements.

[0090] exist Figure 3 In the middle section, the first section 320, the Josephson junction coupling element 330, the pump source 335, and the second section 340 are demarcated by dashed lines.

[0091] Josephson junction coupling element 330 is inserted between and electrically connected to the first segment 320 and the second segment 340. Josephson junction coupling element 330 can be coupled with... Figure 2 The Josephson junction coupling element 200 described herein is designed and operated in a similar manner.

[0092] The first segment 320 and the second segment 340 are parametrically and inductively coupled via a Josephson junction coupling element 330. The reactance of the Josephson junction coupling element 330 is modulated by a pump tone provided by a pump source 335.

[0093] Each of the first segment 320 and the second segment 340 includes a shunt LC resonator, with an admittance inverter on each side of the shunt LC resonator.

[0094] The first segment 320 includes a shunt LC resonator formed by a capacitor labeled C7 and an inductor labeled L3. The shunt LC resonator of the first segment 320 is arranged to have a first center frequency f1.

[0095] 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 is arranged to have a second center frequency f2.

[0096] exist Figure 3 In the example, the Josephson parametric coupler 300 is designed such that f1 = 5 GHz, f2 = 7 GHz. f = 400MHz. The first segment 320 is designed as a passband with a center frequency of 5GHz, and the second segment 340 is designed as a center frequency of 7GHz. Therefore, when a signal with the first frequency f1 = 5GHz is input to the first port 310, the signal is converted into a signal with the second frequency f2 = 7GHz and output at the second port 350.

[0097] The Josephson junction coupling element 330 is operable such that when an appropriate pump tone is provided from the pump source 335, a 5 GHz signal is converted to a 7 GHz signal at the Josephson junction coupling element 330.

[0098] Figure 4A and Figure 4B References are shown Figures 1 to 3 exist Figure 3 Simulation results of the Josephson parametric coupler described in [the text].

[0099] Figure 4A Panel 400 is shown, which includes the results of a simulation performed using the harmonic balance simulation package within the Keysight ADS program, wherein SQUID is simulated as a symbolically defined device.

[0100] The x-axis 401 of panel 400 represents frequency detuning in GHz. The y-axis 402 of panel 400 represents relative amplitude in dB.

[0101] In this example, the values ​​of the components in the first segment 320 and the second segment 340 are selected such that the Josephson parametric coupler 300 has a total response of a 4-pole Chebyshev response with a bandwidth of 400 MHz. When the DC-SQUID 210 operates as a parametric frequency converter, the corresponding flux bias applied to the DC-SQUID 210, included in the Josephson junction coupling elements 200, 330, is estimated as the DC flux. = 0.224 and AC flux = 0.2 .

[0102] The first curve 410 represents the relative magnitude of the power reflected at input port 310. For the first curve 410, the x-axis 401 is relative to f1 = 5 GHz.

[0103] The second curve 420 represents the relative magnitude of the power output at output port 350. For the second curve 420, the x-axis 401 is relative to f2 = 7 GHz.

[0104] The first curve 410 shows that, over a roughly 400MHz bandwidth with approximately 0GHz detuning, power reflection at input port 310 is reduced by more than 20dB. This demonstrates that the input matching of the Josephson parametric coupler 300 is better than 20dB.

[0105] The second curve 420 shows that, over a bandwidth similar to that shown by the first curve 410, the Josephson parametric coupler 300 outputs power with a conversion gain of approximately 1 dB over a bandwidth of approximately 350 MHz. This value is consistent with the predicted conversion gain of 10 × log₂. 10 The results for the Manley-Rowe relationship (7 / 5) = 1.46 dB are consistent.

[0106] Considering the first curve 410, the second curve 420 shows the complete frequency transition between the two bands, i.e., Δf around f1 to Δf around f2, where f1 = 5 GHz, f2 = 7 GHz, Δf = 350 MHz, with a flat response across the bandwidth.

[0107] Figure 4B Panel 430 is shown, which includes the results of a simulation performed using the WRSpice program, which includes a model for simulating a Josephson junction. The simulation is performed in transient mode, where the time-domain output is digitally demodulated to obtain the signal amplitude at device output port 350.

[0108] The x-axis 431 of panel 430 represents frequency detuning in GHz. The y-axis 432 of panel 400 represents relative amplitude in dB.

[0109] Curve 440 represents the relative magnitude of the power output at output port 350. For curve 440, the x-axis 401 is relative to f2 = 7 GHz.

[0110] Curve 440 shows the bandwidth at approximately 350MHz ( Figure 4A On a bandwidth similar to that shown in the simulation results, the Josephson parametric coupler 300 outputs a power with a flat response and a conversion gain of approximately 1 dB. Figure 4A and 4B The two analog techniques shown are in good agreement and meet the circuit design goals: f1 = 5GHz, f2 = 7GHz, ∆f = 400MHz.

[0111] exist Figure 2 and Figure 3 In the design shown, since the DC-SQUID 210 is shunt to ground, it loads other components in the Josephson parametric coupler 100 or Josephson junction coupling elements 130, 200. Therefore, the inductance of the DC-SQUID 210 can be considered in designing these other components. While this may be feasible, the design process may not be straightforward because the inductance of the DC-SQUID 210 depends on the flux bias applied to it, i.e., at frequency f. p DC flux at the location and AC flux Furthermore, the parameter interactions provided by the Josephson junction coupling elements 130 and 200 depend on the components connected to the DC-SQUID 210.

[0112] Therefore, as Figure 3The design of the Josephson parametric coupler 300 shown can be challenging because, within the Josephson junction coupling elements 130, 200, and 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 and 330. In other words, since the DC-SQUID 210 is shunt to ground, the second resonator 230 does not present open-circuit impedance in the passband of the first resonator 220, and vice versa, and the first resonator 220 and the second resonator 230 are effectively loaded onto each other. Furthermore, the interdependence among all components here can reduce design and operational margins.

[0113] Therefore, in Figure 2 and Figure 3 In the described design, the Josephson junction coupling elements 200 and 330 include a DC-SQUID 210, which is coupled to the first inductor L. SQ The load inductance of the DC-SQUID 210 is used as an approximation for ease of design. Once a design is obtained close enough to the target using the approximation of the load inductance of the DC-SQUID 210, further tuning of the element values ​​may be required to optimize the response of the Josephson parametric coupler 300.

[0114] The following disclosure relates to the design of Josephson parametric couplers 100 and 300, which address these issues. In particular, Josephson junction coupling elements 130, 200, and 330 are designed to include RF-SQUIDs.

[0115] Figure 5 It is a reference. Figure 1 A schematic diagram of an exemplary Josephson junction coupling element.

[0116] The Josephson junction coupling element 500 includes a first port 501 and a second port 502, defining a signal line between the first port 501 and the second port 502.

[0117] The Josephson junction coupling element 500 can be connected to other parts of the Josephson parametric coupler 100 via the first port 501 and the second port 502, respectively.

[0118] The Josephson junction coupling element 500 includes an RF-SQUID 510 disposed between a first port 501 and a second port 502. The RF-SQUID 510 in... Figure 5 The boundary is drawn with a dashed line.

[0119] The RF-SQUID 510 includes a Josephson junction 511, labeled B3, inserted via a first inductor 513 labeled L3 and a second inductor 514 labeled L4.

[0120] The port between Josephson junction 511 and the first inductor 513 is connected to the signal line via the first port 501. The port between Josephson junction 511 and the second inductor 514 is connected to the signal line via the second port 502. The first inductor 513 and the second inductor 514 are connected to ground. Josephson junction 511, the first inductor 513, ground, and the second inductor 514 form a loop in this sequence.

[0121] Figure 5 The example shown illustrates a Josephson junction coupling element 500 implemented using lumped elements.

[0122] The Josephson junction coupling element 500 also includes a first series inductor 521 and a second series inductor 531 connected in series to the signal line.

[0123] The Josephson junction coupling element 500 also includes a first shunt capacitor 522 and a second shunt capacitor 532 connected to the signal line and shunted to ground.

[0124] The first series inductor 521 is inserted between the first port 501 and the RF-SQUID 510.

[0125] The second series inductor 531 is inserted between the RF-SQUID 510 and the second port 502.

[0126] The first shunt capacitor 522 is inserted between the first port 501 and the first series inductor 521.

[0127] The second shunt capacitor 532 is inserted between the second series inductor 531 and the second port 502.

[0128] exist Figure 5 In the example, 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 may be configured to have a first center frequency f1.

[0129] The second resonator 530 can be formed by a second shunt capacitor 532, a second series inductor 531, and a second inductor 514. The second resonator 530 can be configured to have a second center frequency f2.

[0130] In some implementations, the RF-SQUID 510 can be arranged to reduce the inductance of the RF-SQUID 510. Less than 1, that is, Reduced inductance Defined as Where L is the loop inductance, and It is a magnetic flux quantum. The loop inductance L corresponds to the sum of the inductance values ​​of the first inductor 513 and the second inductor 514, i.e., L3 + L4.

[0131] This condition corresponds to Flux quantum states were not found to be stable in the loop of the RF-SQUID 510. The critical current I can be controlled by adjusting the inductance values ​​of the first inductor 513 and the second inductor 514 (i.e., L3 and L4) or by changing the geometry of the Josephson junction 511. C To achieve this condition.

[0132] In some implementations, the RF-SQUID 510 can be powered by a pump source 135 via a superconducting transformer at a frequency f. p AC flux Pumping, wherein the first inductor 513 (with value L3) is the secondary coil.

[0133] Alternatively, in some implementations, the RF-SQUID 510 can be powered by a pump source 135 via a superconducting transformer at a frequency fp of AC flux. Pumping, wherein the second inductor 514 (with value L4) is the secondary coil.

[0134] Alternatively, in some implementations, an additional inductor can be arranged in the superconducting circuit of the RF-SQUID 510, enabling the RF-SQUID 510 to be pumped from the pump source 135 via a superconducting transformer at a frequency f. p AC flux Pumping, wherein the additional inductor is the secondary coil.

[0135] In some implementations, the RF-SQUID 510 can be DC flux biased via a superconducting transformer. Flux bias is applied, wherein either the first inductor 513 (with value L3) or the second inductor 514 (with value L4) is a secondary coil, although Figure 5 The primary coil of the superconducting transformer is not shown.

[0136] Alternatively, in some implementations, the DC flux bias can be achieved by applying a magnetic field through the RF-SQUID 510. Flux bias is applied to the RF-SQUID 510.

[0137] The inductance of the Josephson junction 511 depends on the DC flux bias applied to the RF-SQUID 510. When the RF-SQUID510 is biased with DC flux... The biasing makes the equilibrium phase at both ends of the junction for At this point, the effective inductance of the Josephson junction 511 diverges. This condition depends on the reduced inductance of the RF-SQUID 510, which is defined as... And by relation definition.

[0138] As discussed here, in some implementations, the RF-SQUID 510 can be arranged such that the reduced inductance of the RF-SQUID 510 is less than 1, i.e., <1. For example, if The effective inductance of the Josephson junction 511 is... The effective inductance of the Josephson junction 511 diverges at a frequency f. p With the provided AC flux, the passive inductive coupling between the first resonator 520 and the second resonator 530 disappears, and the coupling provided by the Josephson junction coupling element 500 becomes purely parametric. For DC flux, the coupling disappears.

[0139] In this configuration, the first resonator 520 and the second resonator 530 appear as open-circuit impedances in the frequency band of the other resonator, and there are no parasitic interactions between the first segment 120 and the second segment 140. This allows the bandpass filters 120 and 140 and the two segments of the RF SQUID 510 to be treated as separate components when designing the filter. Therefore, the design process can be significantly simplified, as all circuit elements can be calculated without trial and error or iteration. At the same DC flux where the effective inductance of the Josephson junction 511 diverges, the slope of the curve representing the inductance versus flux is maximized. Therefore, the parametric pump is also most efficient at this operating point.

[0140] In some implementations, after designing the Josephson junction coupling element 500, it can be inserted between the first segment 120 and the second segment 140. For example, in a 4-pole bandpass network, two of the poles are represented by the first resonator 520 and the second resonator 530 included in the aforementioned Josephson junction coupling element 500, and another resonator can be added to each side of the Josephson junction coupling element 500 via an admittance inverter, as will be described in more detail later. The additional resonator connected to the first port 501 via the first admittance inverter can be configured to have a resonant frequency f1, and the additional resonator connected to the second port 502 via the second admittance inverter can be configured to have a resonant frequency f2.

[0141] The following section will use the construction of a 4-pole bandpass network as an example to describe the method for designing Josephson parametric couplers 100 and 300.

[0142] Figure 6 This is a diagram illustrating the design concept of the Josephson parametric coupler.

[0143] Josephson parametric couplers 100 and 300 can be designed by finding the correspondence between passive filter synthesis methods and coupling mode theory methods describing parametric coupled-mode systems. Coupled-mode theory originates from quantum optics and has been successfully used to design non-reciprocal parametric devices. Passive bandpass filter design theory has been practiced in engineering for decades. Using these two descriptions to solve any system of coupled resonators, whether the coupling is passive or parametric, allows us to design broadband parametric devices such as Josephson parametric couplers 100 and 300 using established engineering techniques.

[0144] In particular, the method described below provides a means of calculating the S-parameters of arbitrary systems with coupled resonators, such as Josephson parameter couplers 100 and 300, where the ports can be at different frequencies and the coupling coefficients can be complex. This method will be described using an example of a 4-pole bandpass filter formed by coupled resonators.

[0145] The first diagram 610 is a graph illustrating the coupled-mode theoretical representation of a 4-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. Each resonator 611, 612, 613, and 614 is represented by a node in the diagram. Input port 610, labeled port A, is connected to the first resonator 611, and output port 602, labeled port B, is connected to the fourth resonator 614. In this example, four modes are considered: at the first resonator 611 and the second resonator 612, respectively, at frequencies... Modes A1 and A2 at the location; and frequencies at the third resonator 613 and the fourth resonator 614, respectively. Modes B3 and B4 are located at [location]. These four modes 611, 612, 613, and 614 are coupled, and it is assumed that this arrangement has bandwidth [value missing]. As a design requirement for determining coupling strength, Mode A1 at a rate Coupled to the external port of input port 601, and mode B4 at rate Coupled to output port 602. For the internal modes not connected to the port, i.e., the modes of resonators 612 and 613, we set the attenuation rate to γ=0. Similarly, we assume that the modes of resonators 611 and 614 have no internal losses, and their associated attenuation rates... and This is solely due to their coupling to ports 601 and 602. This is an approximation reflecting the fact that resonators 611, 612, 613, and 614 are superconducting and have very low internal losses. Furthermore, for the Chebychev and Butterworth prototypes that can be used in this embodiment, the following settings are provided... For example, the frequency of the mode can be selected as... = 5GHz and = 7GHz. The bandwidth of this arrangement. It can be set to approximately It has a very small bandwidth of 5%, which is 350MHz.

[0146] The coupling coefficients representing the coupling between resonators 611, 612, 613, and 614 are denoted as... Furthermore, each of resonators 611, 612, 613, and 614 is 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... In our example of Josephson parametric couplers 100 and 300, the coupling between the second resonator 612 and the third resonator 613—is determined by… This indicates—corresponding to the parameter interactions provided by Josephson junction coupling elements 130, 200, 330, and 500. If ,but This corresponds to the parameter coupling provided by the Josephson parameter converter. Specifically, the actual... This corresponds to passive coupling. If... ,but This corresponds to the parameter coupling provided by the Josephson parametric amplifier. These rules are f for the parameter converter. p = f2 - f1 is the result of the pump flux, and for the parametric amplifier it is f p = f1 + f2 is the result of the pump flux. These rules are outlined in Phys. Chem. Rev. Applied 7, 024028 (2017) by F. Lecocq, L. Ranzani, G.A. Peterson, K. Cicak, R.W. Simmonds, JD. Deufel, and J. Aumentado.

[0147] Figure 620 illustrates the design method for a bandpass filter network. Bandpass filter design begins with selecting the desired transmission profile, from which we can choose the desired number N of filter segments and the filter's center frequency. Fractional bandwidth And the response type, such as the Chebyshev or Butterworth response function. In our Josephson parametric coupler 100, 300 example, the number of filter segments N=4. Then, the corresponding normalized filter coefficients or normalized element values ​​can be found in the table. to , to This table can be used as a practical guide in the field of microwave engineering. Coefficients It is usually omitted from the table and is usually defined as =1, indicating the conductance of the source at input port 601. The last coefficient... This represents the conductance of the load at output port 602. Once the normalized filter coefficients are specified... to Therefore, four resonators were designed corresponding to N=4. For example, in... Figure 5 In the examples, the resonator can be constructed as a lumped-element LC resonator, i.e., with a characteristic impedance. to The filter consists of four shunt resonators: 611, 621; 612, 622; 613, 623; and 614, 624. The first shunt resonators 611, 621 and the second shunt resonators 612, 622 can be designed to have a resonant frequency at f1, and the third shunt resonators 613, 623 and the fourth shunt resonators 614, 624 can be designed to have a resonant frequency at f2. f1 = f2 only when all couplings are passive, and this frequency can be the center frequency of the filter. Then, the shunt resonators 611, 621, 612, 622, 613, 623, 614, and 624 are connected via a synthesis admittance inverter. The connections form a one-dimensional network as shown in the second figure 620. For example, the second shunt resonator 622 and the third shunt resonator 623 are connected via an admittance inverter. The connection is made between the input port 601 and the first shunt resonator 621 via the admittance inverter. connect.

[0148] like Figure 6 Directional admittance inverter As shown in section 630, the admittance inverter can be constructed as a network of capacitors or inductors. However, the implementation of the admittance inverter is not limited to these examples. The admittance inverter can be implemented as a quarter-wavelength transformer, transmission line, and reactive element. The admittance value of each admittance inverter is determined by the characteristic impedance and normalized filter coefficients of the shunt resonator and / or input and output ports 601, 602 connected through the admittance inverter, and is given by the following equation:

[0149] .

[0150] For example, the admittance of the inverter that connects input port 601 and the first shunt resonator 621 is Furthermore, it is possible to select capacitors or inductors accordingly to construct admittance inverters. .

[0151] In the design methodology of bandpass filter networks, the above process provides fully defined S-parameters for the coupled resonator system, i.e., the elements of the scattering matrix S. However, it should be noted that, compared to the theoretical representation of the coupled modes shown in the first illustration 610, only the single center frequency... It can be used for design. In other words, despite the location of admittance inverter 23 The locations of the Josephson junction coupling elements 130, 200, 330, and 500 within the Josephson parametric couplers 100 and 300 correspond to these locations, but the design methodology cannot describe the parametric coupling related to the transition between two frequencies. In other words, since the admittance inverter is entirely passive, it cannot provide coupling between resonators with different frequencies.

[0152] To address this problem, this specification provides a method for establishing a correspondence between coupled-mode descriptions and filter theory descriptions.

[0153] like Figure 6 The correspondence between the theoretical description of the coupling mode and the theoretical description of the filter shown can be realized as follows:

[0154] , , and , in, .

[0155] In other words, the coupling coefficients from coupled-mode theory Able to use normalized filter coefficients from filter design theory To estimate, and with inverter value J ij Related.

[0156] The process described so far can be applied to the design of Josephson parametric couplers 100 and 300, for example, constructed using a 4-pole Chebyshev network with 0.01 dB ripple. Given N=4, the normalized filter coefficients found in the design table are: =1.0, =0.7128, =1.2003, =1.3212, =0.6476, and =1.1007. In the first diagram 610 representing the curves of coupled-mode theory, the mode frequency is chosen as . = 5GHz and = 7GHz. Network bandwidth. Selected as approximately A very small bandwidth of 5%, which is 350MHz. So, MHz, = = 0.385 and = 0.283. Admittance inverter The admittance can be directly derived from the normalized filter coefficients. to Or use and The value is used to estimate.

[0157] Once the resonators 621, 622, 623, and 624 are designed and the coupling coefficients are determined, it is possible to determine the coupling coefficients between the second shunt resonator 622 and the third shunt resonators 623 and 624 based on the specified coupling coefficients. = 0.283 to determine the operating conditions of Josephson junction coupling elements 130, 200, 330, and 500.

[0158] like Figure 5 As discussed in the article, the DC flux operating point can be determined by... Determine that L is the loop inductance, so that the inductance of the Josephson junction 511 diverges. Coupling coefficient. Mutual inductance coupling between the second shunt resonator 622 and the third shunt resonator 623 The relationship between the modulation amplitudes is as follows , where i=2, j=3, is a rearrangement of the results given by F. Lecocq et al. in Phys. Rev. Applied 7, 024028 (2017), which describes the parametric interaction between two resonators. The pump amplitude is the AC flux induced in the RF SQUID by the pump current supplied by pump source 135. and Alternatively, in cases where the resonators are not implemented using lumped elements, the impedance can be calculated from the resonant frequency and the impedance of each resonator. This corresponds to the slope of the mutual inductive coupling between resonators j and k relative to the magnetic flux bias applied to the Josephson junction coupling element 500. Calculation Depends only on the junction critical current I C And the linear inductor L of the RF-SQUID 510. Mutual coupling M is formed by... Given, among which, Corresponding to Proportional junction inductance, and These are the inductance values ​​of the first inductor 513 and the second inductor 514, L3 and L4, when they are set to the same value. Since all other terms are known, it is possible to... To calculate During operation, it provides the expected result from the above relationship. .

[0159] The above process provides a method for synthesizing bandpass networks for Josephson parametric couplers 100 and 300. This process also provides a method for calculating the S-parameters of arbitrary systems of coupled resonators without trial and error or iteration, where the ports can be at different frequencies, as is the case for parametric processes, and the coupling can be complex. Although the process is explained using an example with N=4, the concept is applicable to any arbitrary number of resonators or poles.

[0160] Figure 7 It is a reference. Figure 6 A flowchart illustrating an exemplary process for designing a Josephson parametric coupler.

[0161] In step S710, a first number j of resonators are provided in the first segment, and a second number N-j resonators are provided in the second segment. Figure 6 In the example, N=2 and j=2.

[0162] In step S720, a first resonant frequency is provided to the resonator in the first segment. And provide a second resonant frequency to the resonator in the second section. .exist Figure 6 In the example, the frequency of the pattern was selected as =5GHz and =7GHz.

[0163] In step S730, the bandwidth of the first segment and the second segment is provided. .exist Figure 6 In the example, bandwidth Selected as approximately It has a very small bandwidth of 5%, which is 350MHz.

[0164] In step S740, impedance is provided for each resonator. arrive When shunt resonators 621, 622, 623, and 624 are constructed as LC resonators using lumped elements, the impedance is determined when selecting the inductance and capacitance values. arrive .

[0165] In fact, once the resonant frequencies of the j-th and j+1-th resonators of the parameter coupling are selected in step S720, the capacitance and inductance values ​​can be selected. This also determines the impedances of these two resonators in step S740. The resonant frequencies of the resonators in the first segment are determined to be the same as the resonant frequencies corresponding to those in step S720.

[0166] In step S750, normalized element values ​​are provided. to . This represents the normalized impedance at the input port. This represents the normalized impedance at the output port, and to This represents the normalized impedance of N resonators. In the case of N=4... Figure 6 In the example, for the Chebyshev response, the normalized filter coefficients found in the design table are: =1.0, =0.7128, =1.2003, =1.3212, =0.6476, and =1.1007.

[0167] In step S760, the admittance values ​​between the input port and the first segment, and between the second segment and the output port, are estimated using the following formulas. to and attenuation rate :

[0168] and , ,in .

[0169] For example, admittance inverters can be constructed accordingly by selecting inductance or capacitance values.

[0170] In step S770, the coupling coefficient is calculated. It represents the coupling degree between the j-th resonator included in the first segment and the (j+1)-th resonator included in the second segment:

[0171] .

[0172] In step S780, based on the coupling coefficient The AC flux applied to the Josephson junction coupling element is calculated using the following formula. :

[0173] ,

[0174] When the DC flux applied to the Josephson junction coupling element Depend on Give, for example to Figure 5 The Josephson junction coupling element 510 of the Josephson parameter coupler 500 described herein. L is the linear inductance of the Josephson junction coupling element, I... C It is the critical current of the Josephson junction. It is a magnetic flux quantum. It is the slope of the mutual inductance coupling between the j-th resonator and the (j+1)-th resonator relative to the flux bias applied to the Josephson junction coupling element, and and These are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively.

[0175] Figure 8 This is a schematic diagram illustrating an exemplary Josephson parametric coupler. Specifically, Figure 8 Showing according to Figure 7 The Josephson parametric coupler 800 is constructed using the process described above.

[0176] 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.

[0177] exist Figure 8 In the example, the Josephson parametric coupler 800 is implemented using lumped elements.

[0178] exist Figure 8 In the middle section, the first section 820, the Josephson junction coupling element 830, the pump source 835, and the second section 840 are demarcated by dashed lines.

[0179] Josephson junction coupling element 830 is inserted between and electrically connected to the first segment 820 and the second segment 840. Josephson junction coupling element 830 is... Figure 5 The Josephson junction coupling element 500 is described in the text.

[0180] The first segment 820 and the second segment 840 are parametrically coupled via a Josephson junction coupling element 830. The reactance of the Josephson junction coupling element 830 is modulated by a pump tone provided by a pump source 835.

[0181] As above Figure 6 and Figure 7 As explained in the document, each of the first segment 820 and the second segment 840 includes a shunt LC resonator, with an admittance inverter on each side of the shunt LC resonator.

[0182] Input port 310—the matching terminal—is connected to the shunt LC resonator via an admittance inverter formed by a combination of a capacitor network, such as a series capacitor labeled C5, and a pair of shunt capacitors. Since the shunt capacitor of the admittance inverter connecting input port 310 and the shunt LC resonator within the first section 320, and the inductor labeled L3, are connected in parallel with the capacitor of the shunt LC resonator, these capacitance values ​​can be added to determine the capacitance of the capacitor labeled C7.

[0183] Including, for example Figure 5 The Josephson junction coupling element 830 of the RF-SQUID, as explained above, is connected via another admittance inverter, including a series capacitor labeled C2, to the shunt LC resonator of the first segment 820 formed by a capacitor labeled C7 and an inductor labeled L3. As described above... Figure 6 and Figure 7 The discussion in the article is based on the The estimated admittance value of the admittance inverter and the configuration of the admittance inverter shown in section 630, i.e., C2 = To determine the capacitance value of the series capacitor labeled C2.

[0184] The shunt capacitor with value -C2 of the admittance inverter is not in Figure 8 As shown in the diagram. Since these shunt capacitors are connected in parallel to the capacitor labeled C7 of the LC shunt resonator and the capacitor labeled C1 of the Josephson junction coupling element 830, the capacitance value of the shunt capacitors of the admittance inverter—C2—can be added to these capacitors labeled C7 and C1. Similarly, the shunt capacitors forming part of the admittance inverter, which connects the input port 810 and the shunt LC resonator of the first segment 820, and the series capacitor labeled C5 can be incorporated by modifying the capacitance value of the capacitor labeled C7. Therefore, firstly, regarding the center frequency of the resonator... Determine the capacitance values ​​of capacitors labeled C1 and C7, and then modify them to incorporate the shunt capacitors of the admittance inverter on each side of the resonator.

[0185] 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 840 is arranged to have a second center frequency. The series capacitors labeled C3 and C6 can be identified in a similar manner to those labeled C2 and C5.

[0186] In this example, the Josephson parametric coupler 800 is designed to make =5GHz =7GHz =350MHz. The first segment 820 is designed with a passband of 5GHz center frequency, and the second segment 840 is designed with a center frequency of 7GHz. In this example, the values ​​of the components of the first segment 820 and the second segment 840 are selected such that the Josephson parametric coupler 800 has a total response of a 4-pole Chebyshev response with a bandwidth of 350MHz.

[0187] Josephson junction coupling element 830 is designed to provide appropriate pumping noise from pump source 835. And use appropriate When the RF-SQUID is biased, a 5 GHz signal is converted to a 7 GHz signal at the Josephson junction coupling element 830. Therefore, when a signal with a first frequency f1 = 5 GHz is input to the first port 810, the signal is converted to a signal with a second frequency f2 = 7 GHz and output at the second port 850. Within the bandwidth, the frequency of the input signal changes by f2 - f1 at the output. In this example, the DC flux... = 0.39 And AC flux = 0.05 .

[0188] Figure 9 References are shown Figure 8 exist Figure 8 Simulation results of the Josephson parametric coupler described in [the text].

[0189] Figure 9 Panel 930 is shown, which includes a device for use with... Figure 8 The simulation results were obtained by performing a simulation using the WRSpice program with the same specifications (such as operating frequency and transfer characteristics) for the circuit in question. The simulation was performed in transient mode, where the time-domain output was digitally demodulated to obtain the signal amplitude at port 850 of the device output. The pump amplitude in this simulation was... = 0.05 .

[0190] The x-axis 931 of panel 930 represents frequency detuning in GHz. The y-axis 932 of panel 400 represents relative amplitude in dB.

[0191] Curve 940 represents the relative magnitude of the power output at output port 850. For curve 940, the x-axis 931 is relative to... =7GHz.

[0192] The first curve 940 shows a flat response over a bandwidth of approximately 350 MHz, with a conversion gain of approximately 1.4 dB, consistent with the expected conversion gain from the Manley Rowe relation.

[0193] Therefore, simulation results show that, Figure 8 The Josephson parametric coupler 800 shown functions according to the design specifications.

[0194] Designs with more than one Josephson junction coupling element (130, 200, 330, 500, 830) in the circuit can exist to operate at more than two different frequencies. In this case, more than one pump tone is required.

[0195] The subjects and operations described in this specification 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 can include 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" can include, but are not limited to, quantum computers, quantum cryptography systems, topological quantum computers, or quantum simulators.

[0196] The terms quantum information and quantum data refer to information or data carried, held, or stored in quantum systems, where the smallest nontrivial system is a qubit, such as 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 two-level systems in the corresponding context. Such quantum systems can include multi-level systems, for example, systems with two or more levels. As examples, such systems can include atomic, electron, photon, ionic, or superconducting qubits. In some implementations, the ground state and first excited state are used to identify the fundamental computational state; however, it should be understood that other arrangements using higher-level excited states to identify computational states are feasible. It should be understood that a quantum memory is a device capable of storing quantum data for long periods with high fidelity and efficiency, such as a light-matter interface, where light is used for transmission and matter is used for storage and retention of quantum characteristics of the quantum data, such as superposition or quantum coherence.

[0197] 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 represent and manipulate information in more than one state 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).

[0198] 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 send 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 without bias resistors.

[0199] The fabrication of the quantum and classical circuit elements described herein requires the deposition of one or more materials, such as superconductors, dielectrics, and / or metals. Depending on the materials chosen, these materials can be deposited using deposition processes such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering), epitaxy, and other deposition processes. The processes used to fabricate the circuit elements described herein require the removal of one or more materials from the equipment during fabrication. Depending on the material to be removed, the removal process can include, for example, wet etching, dry etching, or stripping processes. The materials used to form the circuit elements described herein can be patterned using known photolithography techniques (e.g., photolithography or electron beam lithography).

[0200] During the 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 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 approximately 1.2 Kelvin), indium (superconducting critical temperature approximately 3.4 Kelvin), NbTi (superconducting critical temperature approximately 10 Kelvin), and niobium (superconducting critical temperature 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.

[0201] While this specification contains numerous details of specific implementations, these should not be construed as limiting the scope of the claims, but rather as descriptions of features specific to particular implementations. Some features described in this specification within the context of individual implementations can also be implemented in combination within a single implementation. Conversely, various features described in the context of a single implementation can also be implemented individually or in any suitable sub-combination in multiple implementations. Furthermore, although features may be described above as functioning in certain combinations and even initially claimed in this way, in some cases it is possible to remove one or more features from the claimed combination, and the claimed combination may be for sub-combinations or variations thereof.

[0202] Similarly, although the operations are depicted in a specific order in the accompanying drawings, this should not be construed as requiring that these operations be performed in the specific order shown or sequentially, or that all of the shown operations be performed to achieve the desired result. For example, the actions recounted in the claims can be performed in different orders and still achieve the desired result. In some cases, multitasking and parallel processing may be advantageous. Furthermore, the separation of the various components in the above implementations should not be construed as requiring such separation in all implementations.

[0203] Several embodiments of the invention 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 claims.

Claims

1. A Josephson parameter device, comprising: Input port; Output port; as well as The signal path between the input port and the output port, the signal path including: The first segment is coupled to the input port and has a first passband; The second section, coupled to the output port, has a second passband; and A Josephson junction coupling element is used for parametric coupling between a first segment and a second segment. The Josephson junction coupling element is coupled to the first segment and the second segment and is inserted between the first segment and the second segment. The Josephson junction coupling element is configured such that, in response to the input port receiving a first signal at a first frequency within a first passband and the Josephson junction coupling element receiving a pump tone, the Josephson junction coupling element converts the first signal into a second signal having a second frequency within a second passband. The Josephson junction coupling element includes: Josephson knot; A first resonator, having a first passband; and The second resonator has a second passband. The Josephson junction is inserted between the first resonator and the second resonator and connected to both resonators. The first segment includes at least one resonator with a first passband, arranged between the input port and the first resonator in the signal path. The second segment includes at least one resonator with a second passband, arranged between a second resonator in the signal path and the output port.

2. The Josephson parameter device as described in claim 1, in, The second frequency is the sum of the first frequency and the pump sound frequency.

3. The Josephson parameter device as described in claim 1, in, The frequency of the pump sound is the sum of the first frequency and the second frequency.

4. The Josephson parameter device as described in claim 1, in, 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. In this configuration, the first series inductor and the Josephson junction are connected in series with each other, and The second series inductor and the Josephson junction are connected in series with each other.

5. The Josephson parameter device as described in claim 1, in, The first and second resonators include transmission line stubs.

6. The Josephson parameter device as described in claim 1, in, The first and second resonators include transmission line-based resonators.

7. The Josephson parameter device as claimed in claim 1, wherein, At least one resonator having a first passband and at least one resonator having a second passband include shunt resonators.

8. The Josephson parameter device as described in claim 7, in, Each of the shunt resonators includes a shunt capacitor and a shunt inductor.

9. The Josephson parameter device as described in claim 7, in, Each of at least one resonator includes a resonator truncated section.

10. The Josephson parameter device as claimed in claim 7, in, Each of the shunt resonators includes a transmission line-based resonator.

11. The Josephson parameter device as claimed in claim 1, in, The Josephson junction coupling element is an RF SQUID.

12. The Josephson parameter device as claimed in claim 11, in, The RF SQUID is arranged such that, in response to a first external flux bias applied to the RF SQUID, the Josephson inductance value of the RF SQUID diverges, thereby reducing the passive inductive coupling between the first resonator and the second resonator.

13. A method for designing a Josephson parametric device, the Josephson parametric device comprising: Input port; Output port; as well as The signal path between the input port and the output port, the signal path including: The first segment is coupled to the input port and has a first passband; The second section, coupled to the output port, has a second passband; and The Josephson junction coupling element is inserted between the first and second segments. The method includes: A first number j resonators are provided in the first segment, and a second number Nj resonators are provided in the second segment; Provide the first resonant frequency to the resonator in the first section And provide a second resonant frequency to the resonator in the second section. And provides attenuation rate between the input port and the first section and between the second section and the output port. ; Provide bandwidth for the first and second segments. ; Provide impedance for each resonator arrive ; Provide normalized element values arrive , in, This represents the normalized impedance at the input port. This represents the normalized impedance at the output port, and arrive Let N represent the normalized impedances of the N resonators in the first and second segments, and Among them, the normalized element values ​​g0 to g N+1 Determined based on the tabulated values ​​of the response functions of the first and second segments; Calculate admittance value to Among them, the first admittance value This represents the admittance of the first circuit element to be placed between the input port and the resonator in the first segment adjacent to and coupled to the input port, the (N+1)th admittance value. Let represent the admittance of the (N+1)th circuit element to be arranged between the output port and the Nth resonator in the second segment adjacent to and connected to the output port, and let represent the admittance value of the i-th circuit element. This represents the admittance of the i-th circuit element to be placed between the (i-1)-th resonator and the i-th resonator. Among them, the first admittance value Depend on Give, Wherein, the i-th admittance value Depend on Give, and Among them, the N+1th admittance value Depend on Give, in, It is the impedance of the input port. It is the impedance of the output port, and It is the impedance of the i-th resonator. Let represent the resonant frequency of the i-th resonator, where i = 1, 2, …, N; Calculate the coupling coefficient Coupling coefficient This indicates the coupling degree between the j-th resonator included in the first segment and the (j+1)-th resonator included in the second segment. Where j is the first quantity and Nj is the second quantity. Wherein, coupling coefficient Depend on Give, Based on coupling coefficient Calculate the AC flux applied to the Josephson junction coupling element. .

14. The method as described in claim 13, in, Based on coupling coefficient Calculate the AC flux applied to the Josephson junction coupling element. based on , Among them, the DC flux applied to the Josephson junction coupling element Depend on Give, Where L is the linear inductance of the Josephson junction coupling element, and I... C It is the critical current of the Josephson junction. It is a magnetic flux quantum. It is the slope of the mutual inductance coupling between the j-th resonator and the (j+1)-th resonator relative to the flux bias applied to the Josephson junction coupling element, and and These are the inductance values ​​of the j-th resonator and the (j+1)-th resonator, respectively.

15. The method as described in claim 13, in, Josephson junction coupling elements include RF-SQUID.

16. The method of claim 13, in, The first quantity equals the second quantity, such that j = N / 2.

17. The method of claim 13, further comprising applying an AC flux to the Josephson junction coupling element. .

18. A method of using the Josephson parameter device as claimed in claim 1, the method comprising: Determine the first frequency of the first signal and the second frequency of the second signal; The frequency of the pump tone is determined such that when the pump tone is supplied to the Josephson junction coupling element, the first signal is converted into a second signal; The pump sound is supplied to the Josephson junction coupling element; and Provide the first signal of the first frequency to the input port.

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