Patent Publication Number: US-2022231435-A1

Title: Methods and Devices for Impedance Multiplication

Description:
PRIORITY AND RELATED APPLICATIONS 
     This application is a continuation of U.S. application Ser. No. 16/664,716, filed Oct. 25, 2019, which is a continuation of U.S. application Ser. No. 16/136,124, filed Sep. 19, 2018, now U.S. Pat. No. 10,461,445, which claims priority to U.S. Provisional Application No. 62/632,323, filed Feb. 19, 2018, entitled “Superconducting Logic Components,” U.S. Provisional Application No. 62/630,657, filed Feb. 14, 2018, entitled “Superconducting Logic Gate,” and U.S. Provisional Application No. 62/585,436, filed Nov. 13, 2017, entitled “Methods and Devices for Impedance Multiplication,” each of which is hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This relates generally to superconducting devices, including but not limited to, superconductor-based impedance multiplication devices. 
     BACKGROUND 
     Impedance is a measure of the opposition to current flow in an electrical circuit. Impedance multiplication allows a small current to produce a high impedance. A high impedance can be useful in many applications, such as in voltage dividers and reducing load on input signals. 
     Superconductors are materials capable of operating in a superconducting state with zero electrical resistance under particular conditions. Additionally, in some circumstances, superconductors have high electrical resistance while in a non-superconducting state. Moreover, the superconductors generate heat when operating in a non-superconducting state, and when transitioning from a superconducting state to a non-superconducting state in some circumstances. 
     SUMMARY 
     There is a need for systems and/or devices with more efficient and effective methods for generating high impedance values. Such systems, devices, and methods optionally complement or replace conventional systems, devices, and methods for generating high impedance values. 
     In one aspect, some embodiments include an electric circuit having: (1) a first superconducting component having a first terminal, a second terminal, and a constriction region between the first terminal and the second terminal; (2) a second superconducting component having a third terminal and a fourth terminal; and (3) a first electrically-insulating component that thermally couples the first superconducting component and the second superconducting component such that heat produced at the constriction region is transferred through the first component to the second superconducting component. 
     In another aspect, some embodiments include a method of cascaded impedance multiplication. The method includes: (1) supplying a first current to a first superconducting component such that the first superconducting component is in a superconducting state; (2) supplying a second current to a second superconducting component having a constriction region; (3) in response to supplying the second current, transitioning the constriction region from a superconducting state to a non-superconducting state; (4) transferring resistive heat generated at the constriction region while in the non-superconducting state to the first superconducting component; and (5) in response to transferring the resistive heat, transitioning the first superconducting component to the non-superconducting state. 
     In another aspect, some embodiments include an electric circuit having a first superconducting component including: (a) a first terminal; (b) a second terminal; (c) a first portion between the first terminal and the second terminal, the first portion having a first superconducting current threshold; and (d) a second portion between the first terminal and the second terminal, the second portion having a second superconducting current threshold, less than the first superconducting current threshold; where the first portion is positioned in proximity to the second portion such that resistive heat from the second portion is transferred to the first portion. 
     In yet another aspect, some embodiments include a method of fabricating a superconducting device including: (1) providing a thin film of superconducting material; (2) patterning the thin film to produce a first superconducting component and a second superconducting component; and (3) providing an electrically-insulating component thermally coupling the first superconducting component and the second superconducting component, where the second superconducting component includes a constriction region adjacent to the electrically-insulating component. 
     In yet another aspect, some embodiments include a superconductor circuit configured to perform any of the methods described herein. 
     Thus, devices and circuits are provided with methods for fabricating and operating superconductor components, thereby increasing the effectiveness, efficiency, and user satisfaction with such circuits and devices. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the various described embodiments, reference should be made to the Detailed Description below, in conjunction with the following drawings in which like reference numerals refer to corresponding parts throughout the figures. 
         FIGS. 1A-1C  are block diagrams illustrating representative circuits in accordance with some embodiments. 
         FIG. 1D  is a prophetic graph of current and voltage for a representative superconducting component in accordance with some embodiments. 
         FIGS. 2A-2E  illustrate a prophetic example of a representative operating sequence of the circuit of  FIG. 1A  in accordance with some embodiments. 
         FIG. 3  is a block diagram illustrating another representative circuit in accordance with some embodiments. 
         FIGS. 4A-4H  illustrate a prophetic example of a representative operating sequence of the circuit of  FIG. 3  in accordance with some embodiments. 
         FIG. 5  is a block diagram illustrating another representative circuit in accordance with some embodiments. 
         FIGS. 6A-6D  illustrate a prophetic example of a representative operating sequence of the circuit of  FIG. 5  in accordance with some embodiments. 
         FIG. 7  is a block diagram illustrating another representative circuit in accordance with some embodiments. 
         FIGS. 8A-8D  illustrate a prophetic example of a representative operating sequence of the circuit of  FIG. 7  in accordance with some embodiments. 
         FIGS. 9A-9B  are block diagrams illustrating representative circuits in accordance with some embodiments. 
         FIGS. 10A-10D  illustrate a prophetic example of a representative operating sequence of the circuit of  FIG. 9B  in accordance with some embodiments. 
         FIG. 11  is a block diagram illustrating another representative circuit in accordance with some embodiments. 
         FIG. 12  is a block diagram illustrating a detection circuit including the circuit of  FIG. 1B  in accordance with some embodiments. 
         FIGS. 13A-13C  illustrate components of a representative circuit in accordance with some embodiments. 
         FIG. 14  is a flow diagram illustrating a representative method of operating an impedance multiplication circuit in accordance with some embodiments. 
         FIG. 15  is a flow diagram illustrating a representative method of fabricating an impedance multiplication circuit in accordance with some embodiments. 
         FIGS. 16A-16C  illustrate components of a representative circuit in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the various described embodiments. However, it will be apparent to one of ordinary skill in the art that the various described embodiments may be practiced without these specific details. In other instances, well-known methods, procedures, components, circuits, and networks have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
     Many modifications and variations of this disclosure can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. The specific embodiments described herein are offered by way of example only, and the disclosure is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled. 
     The present disclosure includes descriptions of circuits and devices for impedance amplification. In accordance with some embodiments, impedance amplification is achieved by positioning two superconductors in proximity to one another such that there is no, or negligible, electrical (and quantum) coupling between the two superconductors, but there is thermal coupling between the two superconductors. In accordance with some embodiments, impedance amplification is achieved by positioning a normal conductor (e.g. made from a metal or any other resistive material) non-superconductor in proximity to a superconductor such that there is no, or negligible, electrical (and quantum) coupling between the normal conductor and the superconductor, but there is thermal coupling between the two. Moreover, for embodiments having two superconductors, one of the superconductors is configured so that a small input current will cause a portion of the superconductor to transition to a non-superconducting state. The transition to the non-superconducting state is accompanied by heat generation due to the resistance of the superconductor increasing when it is in the non-superconducting state. In this example, the generated heat is transferred to the second superconductor and, together with an input current applied to the second superconductor, causes the second superconductor to transition to the non-superconducting state. Moreover, in this example, the second superconductor is configured such that the non-superconducting region of the second superconductor spreads and becomes significantly larger in size than the non-superconducting portion of the first superconductor. In this way, the impedance in the second superconductor is triggered by the small input current on the first superconductor yet is significantly larger than the impedance of the first superconductor. In other examples, the transition to the non-superconducting state of the second superconductor can be driven by heat generation that can result from a current flowing through a first non-superconducting material (e.g., a normal metal or any other resistive material). 
     In some embodiments, the small input current is provided by a photodetector component (e.g., as illustrated in  FIG. 12 ) or a qubit component. In some embodiments, the qubit component includes a transmon qubit device, an Xmon qubit device, and/or a Josephson junction device. In some embodiments, the qubit component is coupled to the first superconductor component via a coupling circuit (e.g., resonator circuit). 
       FIGS. 1A-1B  are block diagrams illustrating representative circuits in accordance with some embodiments.  FIG. 1A  shows circuit  100  having superconducting component  102  and superconducting component  112 .  FIG. 1A  further shows terminals  106  and  108  connected to superconducting component  102  and terminals  114  and  116  connected to superconducting component  112 . Superconducting component  102  includes constriction region  104  adjacent to coupling component  110 , which thermally-couples superconducting components  102  and  112 . In some embodiments, the superconducting component  102  is replaced with a non-superconducting component, e.g., a resistive component formed from a metal material, a semiconducting material or any other resistive material. In some embodiments, the coupling component  110  is composed of a thermally-conductive, electrically-insulating material. In some embodiments, the coupling component  110  is composed of a same material as the superconducting components  102  and  112 , but is sized such that it operates in an insulating state rather than a superconducting state. In some embodiments in which the coupling component  110  is composed of a potentially-superconducting material, the coupling component  100  has a width, denoted W 1 , in the range of 5 nanometers (nm) to 20 nm. In some embodiments, the coupling component  110  is on a distinct plane from the superconducting components  102  and  112  (e.g., as illustrated in  FIG. 13B ). In some embodiments, the coupling component  110  is composed of a dielectric material. In some embodiments in which the coupling component  110  is composed of a non-superconducting material, the coupling component  100  has a width, denoted W 1 , in the range of 5 nm to 100 nm. In some embodiments, the coupling component  100  has a length, denoted L 1 , long enough so as to inhibit tunneling effects between the components  102  and  112  and short enough so as to be less than a photon&#39;s mean free path (e.g., in the range of 5 nm to 1 micron). 
       FIG. 1B  shows circuit  120  having superconducting component  122  and superconducting component  112 .  FIG. 1B  further shows terminals  106  and  108  connected to superconducting component  122  and terminals  114  and  116  connected to superconducting component  112 . Superconducting component  122  includes constriction region  124  adjacent to coupling component  126 , which thermally-couples superconducting components  122  and  112 . Circuit  120  is similar to circuit  100  in  FIG. 1A , except that the shapes of the respective constriction regions and coupling components differ. In some embodiments, the constriction regions  124  and  104  have a width, denoted W 2 , large enough to be able to operate in the superconducting state (e.g., greater than 10 nm) and minimized to reduce power consumption of the circuit (e.g., a width in the range of 10 nm to 200 nm). In some embodiments, the constriction regions  124  and  104  have a length, denoted L 2 , large enough to be able to operate in the superconducting state (e.g., greater than 10 nm) and minimized to reduce power consumption of the circuit (e.g., a length in the range of 10 nm to 200 nm). In some embodiments, the adjacent portions of the superconducting components  102  and  122  are sized to facilitate heat dissipation from the constriction region (e.g., 5, 10, or 20 times as large as the constriction region). In some embodiments, the superconducting component  112  has a length, denoted L 3 , in the range of 10 nm to 200 nm. 
     The shapes of the superconducting components, constriction regions, and coupling components shown in  FIGS. 1A-1B  are intended as non-limiting examples. As one skilled in the art would recognize after reading the instant application, other geometric and irregular shapes could be used. 
       FIG. 1C  shows circuit  150  having superconducting components  102  and  112  (as illustrated in  FIG. 1A ) with components  152  and  156  coupled to terminals  114  and  116  respectively, and with components  163  and  166  coupled to terminals  106  and  108  respectively. In this example, terminals  106  and  108  can be understood to be respective gate terminals and terminals  114  and  116  can be understood to be drain and source terminals. In some embodiments, various components can be coupled to terminals  106 ,  108 ,  114 , and  116  in many different configurations: components can be coupled to terminals  106  and/or  108  in addition to, or instead of, being coupled to terminals  114  and  116 ; the circuit can also be configured with a resistive component, e.g., a resistor on terminals  106  and/or  108 ; the circuit can be configured with a resistive component, on terminals  106  and/or  108 , and with an inductor on terminal  114 ; the circuit can be configured with a resistive component, on terminals  106  and/or  108  and with an inductor on terminal  116 ; the circuit can be configured with at least one inductor on terminal  114  or terminal  116 ; and the circuit can be configured with any combination of resistors and inductors on terminals  106  and/or  108  in combination with either an inductor on terminal  114  or terminal  116 . One of ordinary skill in the art having the benefit of this disclosure will appreciated that many other configurations of components on the terminal  106 ,  108 ,  114 , and  116  are possible without departing from the scope of the present disclosure. 
       FIG. 1C  further shows current  162  (e.g., a drain-source current) supplied to superconducting component  112  and current  160  (e.g., a gate current) supplied to superconducting component  102 . Table 1 below illustrates examples of components  152  and  156  in accordance with some embodiments. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Example Components and Relative Currents 
               
            
           
           
               
               
               
               
            
               
                 Component 152 
                 Component 156 
                 Current 160 
                 Current 162 
               
               
                   
               
               
                 None 
                 None 
                 Higher 
                 Lower 
               
               
                 Resistor 
                 Inductor 
                 Lower 
                 Low-to-High 
               
               
                 Inductor 
                 Inductor 
                 Lower 
                 Lower 
               
               
                 Resistor 
                 None 
                 Higher 
                 Lower 
               
               
                 None 
                 Inductor 
                 Lower 
                 Low-to-High 
               
               
                   
               
            
           
         
       
     
     In accordance with some embodiments, the components  152  and  156  in Table 1 are interchangeable based on the circuitry coupled via terminal  154  and  158 . Adding a resistor to the circuit  150  (e.g., as component  163 ) allows for control of current flow in some embodiments. For example, if a current source is coupled such that the resistor and a superconductor are in parallel with one another (e.g., resistor  1204  and photodetector  1212  in  FIG. 12 ), the current from the current source will flow through the superconductor while it is in the superconducting state and will be redirected (or, at least a large portion of the current will be redirected) through the resistor (and, optionally, from the resistor to a superconducting component in circuit  120 ) while the superconductor is in the non-superconducting state. In some embodiments, adding an inductor to the circuit  150  (e.g., as component  152  and/or component  156 ) prevents latch-up of the component  112  and allows for more current  162  to be supplied to the superconducting component  112  and less current  160  to be supplied to the superconducting component  102 , relative to a case where an inductor is not present. 
     Table 2, below, shows advantages and disadvantages of relative currents of Table 1 in accordance with some embodiments. As shown in Table 2, reducing the current  160  supplied to the superconductor  102  increases sensitivity (e.g., the superconductor  102  operates closer to a superconducting current threshold while in the non-superconducting state) and lowers power consumption in accordance with some embodiments. As also shown in Table 2, reducing the current  162  supplied to the superconductor  112  increases switching speed, but also reduces a signal-to-noise ratio in accordance with some embodiments. As one of skill in the art would recognize after reading the present disclosure, in some applications it would be more beneficial to have a high current  162 , while in other applications it would be more beneficial to have a lower current  162 . 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Advantages and Disadvantages of Relative Amounts of Current 
               
            
           
           
               
               
               
            
               
                   
                 Current 162 
                 Current 160 
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                   
                 Lower 
                 Higher speed 
                 Higher Sensitivity 
               
               
                   
                   
                 Lower Signal-to-Noise 
                 Lower Power Consumption 
               
               
                   
                   
                 Ratio 
               
               
                   
                 Higher 
                 Higher Signal-to-Noise 
                 Higher Speed 
               
               
                   
                   
                 Ratio 
                 Higher Power Consumption 
               
               
                   
                   
                 Lower Speed 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 1D  shows a prophetic graph of current and voltage of the superconducting component  112  in accordance with some embodiments. As shown in  FIG. 1D , while the current supplied to the superconductor  112  (e.g., current  162 ) is between I retrap−  and I retrap+  the superconductor  112  operates in the superconducting state with no voltage drop. While current supplied to the superconductor  112  is above I sw+ , or below the superconductor  112  operates in the non-superconducting (conducting) state. While a current supplied to the superconductor  112  is between the switching current and the corresponding retrapping current, e.g., between I sw+  and I retrap+  or between I sw−  and I retrap− , the superconductor  112  maintains its prior state. For example, if the superconductor  112  was in the superconducting state, it will stay in the superconducting state. Likewise, if the superconductor  112  was in the non-superconducting state, it will stay in the non-superconducting state (e.g., due to insufficient self-cooling of the superconductor  112 ). 
     Supplying a current  162  in excess of the switching current (e.g., above I sw+ ) causes the superconductor  112  to latch in the non-superconducting state (stay in the non-superconducting state until the current  162  is removed or reduced) in accordance with some embodiments. Adding an inductor (e.g., as component  152  and/or component  156 ) prevents the latching effect (e.g., allows the superconductor  112  to transition back to the superconducting state) in accordance with some embodiments. A transition time of the superconductor  112  is based on the inductance of the inductor (e.g., the time constant T is equal to the ratio of inductance to resistance) in accordance with some embodiments. For example, the transition time is optionally in the range of 50 picoseconds (ps) to 200 ps. 
       FIGS. 2A-2E  illustrate a prophetic example of a representative operating sequence of circuit  100  of  FIG. 1A  in accordance with some embodiments.  FIG. 2A  shows circuit  100  at a first time. At the first time, current  202  is applied to superconducting component  102  (via terminal  106 ) and current  204  is applied to superconducting component  112  (via terminal  114 ). In  FIG. 2A  both superconducting components  102 ,  112  are in a superconducting state (e.g., a zero electrical resistance state). 
       FIG. 2B  shows circuit  100  at a second time subsequent to the first time. At the second time, a portion of the constriction region  104 , denoted as region  206 , has transitioned to a non-superconducting state (e.g., a non-zero electrical resistance state). In some embodiments, current  202  exceeds a superconducting current threshold and thus triggers the transition of the constriction region  104  to the non-superconducting state. 
       FIG. 2C  shows circuit  100  at a third time subsequent to the second time. At the third time, non-superconducting region  206  has expanded and a portion of superconducting component  112 , denoted as region  208 , has transitioned to the non-superconducting state. In some embodiments, heat generated by region  206  transfers through coupling component  110  to superconducting component  112 . The transferred heat lowers a superconducting current threshold for superconducting component  112  and current  204  exceeds the lowered threshold, thus transitioning region  208  to the non-superconducting state. 
       FIG. 2D  shows circuit  100  at a fourth time subsequent to the third time. At the fourth time, non-superconducting region  206  has shrunk and region  208  has expanded. In some embodiments, the width of superconducting component  102  is sufficient to dissipate heat from region  206  and thus prevent further expansion of region  206 . In some embodiments, the width of superconducting component  112  is insufficient to prevent further expansion of region  208 . 
       FIG. 2E  shows circuit  100  at a fifth time subsequent to the fourth time. At the fifth time, superconducting component  102  has transitioned back to the superconducting state, and region  208  has further expanded. In some embodiments, superconducting component  102  does not transition back to the superconducting state at the fifth time. In some embodiments, at least a portion of superconducting component  102  maintains the non-superconducting state due to heat transfer from superconducting component  112  via coupling component  110 . In some embodiments, the portion of the superconducting component is maintained in the non-superconducting state until the current  204  is removed. In some embodiments, the portion of the superconducting component is maintained in the non-superconducting state for a preset amount of time that is based on an inductance coupled to the superconducting component  102 . 
     Thus,  FIGS. 2A-2E  illustrate a process of generating an expanded non-superconducting region (e.g., region  208  in  FIG. 2E ) in superconducting component  112  from an input current (e.g., input current  202  in  FIG. 2A ) applied to superconducting component  102 . In this way, in some embodiments, a small input current may be used to generate a high impedance in superconducting component  112  (e.g., 1 mega Ohm). 
       FIG. 3  is a block diagram illustrating circuit  300  in accordance with some embodiments.  FIG. 3  shows circuit  300  having superconducting component  102  and superconducting component  302 .  FIG. 3  further shows terminals  106  and  108  connected to superconducting component  102  and terminals  114  and  116  connected to superconducting component  302 . Superconducting component  102  includes constriction region  104  adjacent to coupling component  110 , which thermally-couples superconducting components  102  and  302 .  FIG. 3  also shows coupling components  304  (e.g., components  304 - 1  through  304 - 6 ) thermally coupling portions of superconducting component  302  to one another. Although  FIG. 3  shows the component  302  increasing in size from the terminal  114  to the terminal  116 , in some embodiments, the component  302  does not increase in size. The shapes of the superconducting components, constriction regions, and coupling components shown in  FIG. 3  are intended as non-limiting examples. As one skilled in the art would recognize after reading the instant application, other geometric and irregular shapes could be used. 
       FIGS. 4A-4H  illustrate a prophetic example of a representative operating sequence of circuit  300  of  FIG. 3  in accordance with some embodiments.  FIG. 4A  shows circuit  300  at a first time. At the first time, current  402  is applied to superconducting component  102  (via terminal  106 ) and current  404  is applied to superconducting component  302  (via terminal  114 ). In  FIG. 4A  both superconducting components  102 ,  302  are in a superconducting state (e.g., a zero electrical resistance state). 
       FIG. 4B  shows circuit  300  at a second time subsequent to the first time. At the second time, a portion of constriction region  104 , denoted as region  406 , has transition to a non-superconducting state (e.g., a non-zero electrical resistance state). In some embodiments, current  402  exceeds a superconducting current threshold and thus triggers the transition of the constriction region  104  to the non-superconducting state. 
       FIG. 4C  shows circuit  300  at a third time subsequent to the second time. At the third time, a portion of superconducting component  302 , denoted as region  408 , has transitioned to the non-superconducting state. In some embodiments, heat generated by non-superconducting region  406  transfers through coupling component  110  to superconducting component  302 . The transferred heat lowers a superconducting current threshold for superconducting component  302  and current  404  exceeds the lowered threshold, thus transitioning region  408  to the non-superconducting state. 
       FIG. 4D  shows circuit  300  at a fourth time subsequent to the third time. At the fourth time, non-superconducting regions  406  and  408  have expanded.  FIG. 4E  shows circuit  300  at a fifth time subsequent to the fourth time. At the fifth time, non-superconducting region  406  has shrunk and superconducting region  408  has expanded. In some embodiments, the width of superconducting component  102  is sufficient to dissipate heat from region  406  and thus prevent further expansion of region  406 . In some embodiments, the width of superconducting component  302  is insufficient to prevent further expansion of region  408 . Additionally, at the fifth time, portions of superconducting component  302 , denoted as regions  410  and  412 , have transitioned to the non-superconducting state. In some embodiments, heat generated by region  408  transfers through coupling components  304 - 1  and  304 - 2  to regions  410  and  412  of superconducting component  302 . The transferred heat transitions regions  410  and  412  to the non-superconducting state. 
       FIG. 4F  shows circuit  300  at a sixth time subsequent to the fifth time. At the sixth time, superconducting component  102  has transitioned back to the superconducting state, and regions  410  and  412  have expanded.  FIG. 4G  shows circuit  300  at a seventh time subsequent to the sixth time. At the seventh time, regions  410  and  412  have expanded into region  414  and portions of superconducting component  302 , denoted as regions  416 ,  418 ,  420 , and  422 , have transitioned to the non-superconducting state. In some embodiments, heat generated by region  414  transfers through coupling components  304 - 3 - 304 - 6  to regions  416 ,  418 ,  420 , and  422  of superconducting component  302 . The transferred heat transitions regions  416 ,  418 ,  420 , and  422  to the non-superconducting state. 
       FIG. 4H  shows circuit  300  at an eighth time subsequent to the seventh time. At the eighth time, non-superconducting regions  416 ,  418 ,  420 , and  422  have expanded into region  424 . In some embodiments, the portion of the superconducting component  302  is maintained in the non-superconducting state until the current  404  is removed. In some embodiments, the portion of the superconducting component  302  is maintained in the non-superconducting state for a preset amount of time that is based on an inductance coupled to the superconducting component  302 . 
     Thus,  FIGS. 4A-4H  illustrate a process of generating expanded non-superconducting regions (e.g., regions  408 ,  414 , and  424  in  FIG. 4H ) in superconducting component  302  from an input current (e.g., input current  402  in  FIG. 4A ) applied to superconducting component  102 . In this way, in some embodiments, a small input current may be used to generate a high impedance in superconducting component  302  (e.g., 10 mega Ohm). 
       FIG. 5  is a block diagram illustrating circuit  500  in accordance with some embodiments.  FIG. 5  shows circuit  500  having superconducting component  102  and a component  502 . Similar to component  708  in  FIG. 7 , described below, in some embodiments, component  502  is a superconductor, while in some other embodiments, component  502  is a non-superconducting component, e.g., a resistive component formed from a metal material, a semiconducting material or any other resistive material. In some embodiments, component  502  comprises a metal and/or doped semiconductor. In embodiments in which component  502  comprises a metal or doped semiconductor, some heat is generated through region  504  of component  502  as current flows between terminals  114  and  116 . 
       FIG. 5  further shows terminals  106  and  108  connected to the superconducting component  102  and terminals  114  and  116  connected to the component  502 . Superconducting component  102  includes constriction region  501  adjacent to region  504  of component  502 , which thermally-couples components  102  and  502 . Although not shown in  FIG. 5 , in some embodiments, the components  102  and  502  are thermally coupled by a coupling component, such as the coupling component  110  shown in  FIG. 1B . 
     The circuit  500  in  FIG. 5  is similar to the circuit  100  in  FIG. 1A , except that only a portion of the component  502 , region  504 , is in close proximity to the superconducting component  102 . In some circumstances, having only a portion of the component  502  in proximity to the superconducting component  102  allows for more control over the heat transfer between the components  102  and  502  and reduces heat dissipation effects of the component  502  by isolating the region  504 . 
     In the embodiments shown in  FIGS. 5 through 10D , the superconducting components or regions that are positioned adjacent to each other so as to allow the transfer of heat from one to the other are, at the same time, positioned so as to inhibit (e.g., prevent) cooper pair and/or electron tunneling between those superconducting components or regions (e.g., 10 nm, 100 nm, or more apart). 
       FIGS. 6A-6D  illustrate a prophetic example of a representative operating sequence of circuit  500  of  FIG. 5  in accordance with some embodiments.  FIG. 6A  shows circuit  500  at a first time. At the first time, current  602  is applied to superconducting component  102  (via terminal  106 ) and current  604  is applied to component  502  (via terminal  114 ). In  FIG. 6A  both components  102  and  502  are in a superconducting state (e.g., a zero electrical resistance state). 
       FIG. 6B  shows circuit  500  at a second time subsequent to the first time. At the second time, a portion of constriction region  501 , denoted as region  606 , has transition to a non-superconducting state (e.g., a non-zero electrical resistance state). In some embodiments, current  602  exceeds a superconducting current threshold and thus triggers the transition of constriction region  104  to the non-superconducting state. 
       FIG. 6C  shows circuit  500  at a third time subsequent to the second time. At the third time, non-superconducting region  606  has expanded and a portion of component  502  (which is a superconducting component in this example), denoted as region  608 , has transitioned to the non-superconducting state. In some embodiments, heat generated by region  606  transfers to region  608  of superconducting component  502 , as denoted by arrows  607 . The transferred heat lowers a superconducting current threshold for superconducting component  502  and current  604  exceeds the lowered threshold, thus transitioning region  608  to the non-superconducting state. 
       FIG. 6D  shows circuit  500  at a fourth time subsequent to the third time. At the fourth time, non-superconducting region  606  has shrunk and non-superconducting region  608  has expanded. In some embodiments, the width of superconducting component  102  is sufficient to dissipate heat from region  606  and thus prevent further expansion of region  606 . In some embodiments, the width of superconducting component  502  is insufficient to prevent further expansion of region  608 . In some embodiments, the region  608  is maintained in the non-superconducting state until the current  604  is removed. In some embodiments, the region  608  is maintained in the non-superconducting state for a preset amount of time that is based on an inductance coupled to the superconducting component  502 . 
       FIG. 7  is a block diagram illustrating circuit  700  in accordance with some embodiments.  FIG. 7  shows circuit  700  having superconducting component  702  and component  708 .  FIG. 7  further shows terminals  704  and  706  connected to the component  702  and terminals  710  and  712  connected to the component  708 . Superconducting component  702  includes a narrow region  703  adjacent to region  709  of component  708 , which thermally-couples superconducting components  702  and  708 . 
     In some embodiments, component  708  is a superconductor. In some embodiments, component  708  is a non-superconducting component, e.g., a resistive component formed from a metal material, a semiconducting material or any other resistive material. In some embodiments, component  708  comprises a metal and/or doped semiconductor. In embodiments in which component  708  comprises a metal or doped semiconductor, some heat is generated through region  709  of component  708  as current flows between terminals  710  and  712 . In some embodiments, component  708  comprises a metal and/or doped semiconductor and is configured such that exceeding a threshold current generates sufficient heat to transition component  702  from the superconducting state to the non-superconducting state. In some embodiments, the threshold current corresponds to a thermal coupling strength between region  709  of component  708  and region  703  of superconducting component  702 . 
     Similar to that described above in reference to  FIG. 1C , circuit  700  optionally has one or more components, e.g., resistive and/or inductive components, like components  152 ,  156 ,  163 , and  166  described above, coupled to various combinations of terminals  710  and  712 , which can be understood to be respective gate terminals in this example, and also various combinations of terminals  704  and  706 , which can be understood to be respective drain and source terminals in this example. In some embodiments, component configurations can include: a resistive component, e.g., a resistor, on terminals  710  and/or  712 ; the circuit can be configured with a resistive component, on terminals  710  and/or  712  and with an inductor on terminal  704 ; the circuit can be configured with a resistive component, on terminals  710  and/or  713  and with an inductor on terminal  706  and; the circuit can be configured with at least one inductor on terminal  704  or terminal  706 ; and the circuit can be configured with any combination of resistors and inductors on terminals  710  and/or  712  in combination with either an inductor on terminal  704  or terminal  706 . One of ordinary skill in the art having the benefit of this disclosure will appreciated that many other configurations of components on the terminal  106 ,  108 ,  114 , and  116  are possible without departing from the scope of the present disclosure. 
       FIGS. 8A-8D  illustrate a prophetic example of a representative operating sequence of circuit  700  of  FIG. 7  in accordance with some embodiments.  FIG. 8A  shows circuit  700  at a first time. At the first time, current  802  is applied to superconducting component  702  (via terminal  704 ) and current  804  is applied to superconducting component  708  (via terminal  710 ). In  FIG. 8A  both superconducting components  702  and  708  are in a superconducting state (e.g., a zero electrical resistance state). 
       FIG. 8B  shows circuit  700  at a second time subsequent to the first time. At the second time, a portion of superconducting component  708 , denoted as region  806 , has transition to a non-superconducting state (e.g., a non-zero electrical resistance state). In some embodiments, current  804  exceeds a superconducting current threshold and thus triggers the transition of region  806  to the non-superconducting state. 
       FIG. 8C  shows circuit  700  at a third time subsequent to the second time. At the third time, non-superconducting region  806  has expanded and a portion of superconducting component  702 , denoted as region  808 , has transitioned to the non-superconducting state. In some embodiments, heat generated by region  806  transfers to region  808  of superconducting component  702 . In some embodiments, the transferred heat lowers a superconducting current threshold for superconducting component  702  and current  802  exceeds the lowered threshold, thus transitioning region  808  to the non-superconducting state. In some embodiments, the transferred heat causes a temperature of the superconducting component  702  to exceed a superconducting threshold temperature, thereby transitioning region  808  to the non-superconducting state.  FIG. 8D  shows circuit  700  at a fourth time subsequent to the third time. At the fourth time, non-superconducting region  808  has expanded. 
       FIGS. 9A-9B  are block diagrams illustrating representative circuits in accordance with some embodiments.  FIG. 9A  shows circuit  900  having superconducting component  904  and terminals  902  and  906  connected to superconducting component  904 . Superconducting component  904  includes a constriction region  905  adjacent to region  907 , which thermally couples regions  905  and  907 . In some embodiments, regions  905  and  907  and thermally coupled by an electrically-insulating, thermally-conductive substrate on which superconducting component  904  is mounted or positioned, as discussed below with reference to  FIGS. 13A-13C .  FIG. 9B  shows circuit  909  having superconducting component  910  and terminals  912  and  914  connected to superconducting component  910 . Superconducting component  910  includes narrow region  916  adjacent to region  918 , which thermally couples regions  916  and  918 . In some embodiments, regions  916  and  918  and thermally coupled by an electrically-insulating, thermally-conductive substrate on which superconducting component  910  is mounted or positioned, as discussed below with reference to  FIGS. 13A-13C . 
       FIGS. 10A-10D  illustrate a prophetic example of a representative operating sequence of circuit  909  of  FIG. 9B  in accordance with some embodiments.  FIG. 10A  shows circuit  909  at a first time. At the first time, current  1002  is applied (e.g., by a current source  920 , or by the output of another circuit, not shown) to superconducting component  910  (via terminal  912 ). In  FIG. 10A  superconducting component  910  is in a superconducting state (e.g., a zero electrical resistance state). 
       FIG. 10B  shows circuit  909  at a second time subsequent to the first time. At the second time, a portion of superconducting component  910 , denoted as region  1004 , has transition to a non-superconducting state (e.g., a non-zero electrical resistance state). In some embodiments, current  1002  exceeds a superconducting current threshold and thus triggers the transition of region  1004  to the non-superconducting state. 
       FIG. 10C  shows circuit  909  at a third time subsequent to the second time. At the third time, a portion of superconducting component  910 , denoted as region  1006 , has transitioned to the non-superconducting state. In some embodiments, heat generated by region  1004  transfers to region  1006  of superconducting component  910 . The transferred heat transitions region  1006  to the non-superconducting state.  FIG. 10D  shows circuit  909  at a fourth time subsequent to the third time. At the fourth time, non-superconducting regions  1004  and  1006  have expanded. 
       FIG. 11  is a block diagram illustrating circuit  1100  in accordance with some embodiments.  FIG. 11  shows circuit  1100  having superconducting component  1102  and terminals  1104  and  1106  connected to superconducting component  1102 . Superconducting component  1102  includes narrow region  1108  adjacent to region  1110 , which thermally-couples regions  1108  and  1110 . Superconducting component  1102  also includes regions  1112  and  1114  near regions  1116  and  1118 , which thermally-couples region  1112  to region  1116  and region  1114  to region  1118 . The functionality of thermally-coupled regions is described above, e.g., with respect to  FIGS. 4A-4H and 10A-10D . 
       FIG. 12  is a block diagram illustrating a detection circuit  1200  including the circuit  120  of  FIG. 1B  in accordance with some embodiments. The circuit  1200  also includes a photodetector  1212  (e.g., a photodiode that includes silicon, germanium, indium gallium arsenide, lead sulfide, and/or mercury cadmium telluride). In some embodiments, the photodetector  1212  is voltage-biased (e.g., using an optional voltage source). The photodetector  1212  is optionally any type of photodetector including, e.g., a superconducting nanowire single photon detector (SNSPD), a photodiode, and the like. In  FIG. 12 , the photodetector  1212  is electrically coupled to the circuit  120  via one or more resistors  1204  and/or one or more other electrical components (e.g., wires, inductors, etc.). 
       FIG. 12  also illustrates that the circuit  1200  optionally includes a readout circuit  1216 , sources  1210  and  1218  (e.g., current and/or voltage sources), and/or additional electrical components, such as a capacitor  1214 . In some embodiments, the readout circuit  1216  includes one or more superconductor and/or semiconductor components. In some embodiments, the readout circuit  1216  is configured to transition to a state that indicates whether a resistance of the circuit  120  is a logical 0 (e.g., resistance is greater than a predefined resistance threshold) or a logical 1 (e.g., resistance is less than the predefined resistance threshold), and thereby facilitates providing the logical state of the photodetector to other circuits or system components. In some embodiments, the readout circuit  1216  is configured to measure a current flowing through the circuit  120  or a voltage drop over the circuit  120 . For example, in some embodiments, the readout circuit  1216  is a voltage readout circuit. In some embodiments, the readout circuit  1216  includes a resistor (e.g., 50 ohms) and the readout circuit is configured to measure a voltage drop over the resistor. In some embodiments, the readout circuit  1216  includes a voltage source or a current source. 
     In some embodiments, the source  1210  provides an electrical signal (e.g., an electrical current) that is used to bias the photodetector  1212  and/or the circuit  120 . In some embodiments, the source  1218  provides an electrical signal (e.g., an electrical current) that is used to bias the readout circuit  1216  and/or the circuit  120 . 
     An example operating sequence of the circuit  1200  is as follows. First, one or more photons are received by the photodetector  1212 . The one or more photons cause the photodetector  1212  to have increased resistance (e.g., due to a transition of a superconducting component to a non-superconducting state). The increased resistance redirects current from the source  1210  to the circuit  120 , e.g., via the optional resistor(s)  1204 . The redirected current causes the circuit  120  to transition to a non-superconducting state (e.g., as shown in  FIGS. 2A-2E ). Once the circuit  120  has transitioned to the non-superconducting state additional voltage from the source  1218  drops across the circuit  120 . Finally, the readout circuit  1216  detects the additional voltage drop and determines that the one or more photons were received. 
       FIGS. 13A-13C  illustrate components of a representative circuit in accordance with some embodiments.  FIG. 13A  shows superconducting components  1302  and  1304  on a substrate  1300  (e.g., a silicon substrate).  FIG. 13A  also shows a coupling component  1308  (e.g., an electrically-insulating, thermally-conductive component) between the superconducting component  1302  and the superconducting component  1304 .  FIG. 13B  shows the superconducting components  1302  and  1304  on the substrate  1310  (e.g., a substrate composed of an electrically-insulating, thermally-conductive material).  FIG. 13C  shows the superconducting components  1302  and  1304  on the substrate  1300 .  FIG. 13C  further shows a layer  1312  (e.g., a layer composed of an electrically-insulating, thermally-conductive material) over the substrate  1300  and the superconducting components  1302  and  1304 . 
       FIG. 14  is a flow diagram illustrating a method  1400  of operating an impedance multiplication circuit in accordance with some embodiments. In some embodiments, the method  1400  is performed by a superconducting circuit, such as circuit including one or more of the circuits  100 ,  120 ,  300 ,  500 ,  700 ,  900 ,  909 , and  1100 . 
     The circuit receives ( 1402 ) a first current at a first superconducting component such that the first superconducting component is in a superconducting state. The circuit receives ( 1404 ) a second current at a second superconducting component having a constriction region. For example,  FIGS. 6A-6D  illustrate receiving the currents  602  and  604  at superconducting components  102  and  502 . 
     In response to receiving the second current, the constriction region transitions ( 1406 ) from the superconducting state to a non-superconducting state. Resistive heat generated at the constriction region is transferred ( 1408 ) to the first superconducting component. In some embodiments, the resistive heat is generated while the constriction region is in the non-superconducting state. In response to transferring the resistive heat, the first superconducting component transitions ( 1410 ) to the non-superconducting state. The circuit produces ( 1412 ) an output indicative of the first superconducting component being in the non-superconducting state. For example, an impedance of the circuit and/or a voltage drop across the circuit corresponds to the first superconducting component being in the non-superconducting state.  FIGS. 6A-6D  illustrate transitioning constriction region  104  of superconducting component  102  to a non-superconducting state and transferring heat generated at the constriction region  104  to superconducting component  502 , thereby transitioning portion  608  of superconducting component  502  to the non-superconducting state. 
     In some embodiments, the second current is less than the first current. For example, in accordance with some embodiments, the current  602  is less than the current  604  in  FIG. 6A . 
     In some embodiments, the resistive heat is transferred via an electrically-insulating, thermally-conductive component positioned between the first superconducting component and the second superconducting component. For example, the heat is transferred via layer  1312  shown in  FIG. 13C . 
     In some embodiments, while in non-superconducting states, the first superconducting component has a first impedance and the second superconducting component has a second impedance that is less than the first impedance. 
       FIG. 15  is a flow diagram illustrating a method  1500  of fabricating an impedance multiplication circuit in accordance with some embodiments. In accordance with some embodiments, a method of fabricating a superconducting device includes: (1) providing ( 1502 ) a layer (e.g., a thin film) of superconducting material; (2) patterning ( 1504 ) the layer to produce a first superconducting component (e.g., superconducting component  1302 ,  FIG. 13A ) and a second superconducting component (e.g., superconducting component  1304 ); and (3) providing ( 1506 ) an electrically-insulating component (e.g., coupling component  1308 ) thermally coupling the first superconducting component and the second superconducting component. In some embodiments, producing the second superconducting component includes producing a constriction region adjacent to the electrically-insulating component. In some embodiments, the constriction region is produced after producing the second superconducting component (e.g., by etching the second superconducting component). 
     In some embodiments, providing the electrically-insulating component includes patterning the layer to include the electrically-insulating component and oxidizing the electrically-insulating component to decrease electric conductivity of the electrically-insulating component. 
     In some embodiments, providing the electrically-insulating component includes: (1) providing a second layer of thermally-conductive material; and (2) oxidizing the second layer to decrease electric conductivity of the electrically-insulating component. In some embodiments, providing the electrically-insulating component includes providing a thermally-conductive, electrically-insulating material (e.g., layer  1312 ,  FIG. 13C ) coupling the first superconducting component and the second superconducting component. For example, providing the electrically-insulating component includes depositing a thermally-conductive layer of aluminum nitride (AlN) or diamond between the thin film and the substrate and/or on the thin film. As another example, providing the electrically-insulating component includes depositing the thin film on an electrically-insulating, thermally-conductive substrate (e.g., substrate  1310 ,  FIG. 13B ). 
       FIGS. 16A-16C  illustrate components of a representative circuit in accordance with some embodiments.  FIG. 16A  shows circuit  1600  (e.g., functionally similar to circuit  150  in  FIG. 1C ) including component layers  1602  and  1604  and coupling layer  1606 . Component layer  1602  includes one or more superconducting, conducting, and/or semiconducting components. In some embodiments, component layer  1602  includes a component that generates heat as current is passed through it (e.g., a resistor). In accordance with some embodiments, component layer  1602  (e.g., an uppermost layer) includes superconducting component  102  and terminals  106  and  108  (see  FIG. 1A , not shown in  FIG. 16A , but coupled to pads  1608  and  1610  respectively). Component layer  1604  includes one or more superconducting, conducting, and/or semiconducting components. In accordance with some embodiments, component layer  1604  (e.g., a lower layer than component layer  1602 ) includes superconducting component  112  and terminals  114  and  116  (see  FIG. 1A , not shown in  FIG. 16A , but coupled to pads  1612  and  1614  respectively). Coupling layer  1606  is positioned between, and thermally couples, component layers  1602  and  1604 . In various embodiments, coupling layer  1606  is thermally conductive, electrically insulating, and/or comprises a passivity layer adapted to inhibit oxidation of component layer  1604 . In accordance with some embodiments, coupling layer  1606  includes coupling component  110  (see  FIG. 1A ). In some embodiments, the coupling layer  1606  is composed of silicon dioxide. In some embodiments, the coupling layer  1606  has a thickness between 30 nm and 100 nm. 
       FIG. 16A  also shows inductor  1607  and thermal buffer  1609  on component layer  1604 . In accordance with some embodiments, thermal buffer  1609  is positioned and sized so as to provide passive cooling to inductor  1607 , by preventing heat from the overlap region between points B and B′ from spreading to inductor  1607 . In some embodiments, thermal buffer  1609  is a wider superconducting section connected at the end of a narrower superconducting section. In some embodiments, the width of thermal buffer  1609  is at least five times the width of the narrower superconducting section to limit and/or stop the growth of a hotspot. For example, thermal buffer  1609  is sized and positioned to limit growth of a hotspot that forms between points B and B′, and to prevent it from spreading into inductor  1607 . 
     In accordance with some embodiments, inductor  1607  is positioned and sized to prevent latch-up of other superconducting components on component layer  1604 . For example, inductor  1607  is coupled to component  112  (see  FIG. 1C ) and operates as described above with respect to component  156  and  FIG. 1C . In some embodiments, inductor  1607  is adapted to have an inductance value of at least 50 nanoHenry (nH). In some embodiments, inductor  1607  is adapted to (e.g., sized to) prevent latching of a superconductor component between points B and B′, and allow for a self-reset behavior of the superconductor component when the superconductor component current-biased close to its threshold superconducting current. 
     In some embodiments, component layer  1604  includes a superconducting wire between points B and B′ (e.g., component  112 ,  FIG. 1C ). In some embodiments, the superconducting wire is composed of niobium nitride (NbN). In some embodiments, the superconducting wire has a width of at least 150 nanometers (nm) to prevent the wire from being photosensitive while current-biased. In some embodiments, the superconducting wire has a width of at most 1000 nm to keep switching power dissipation below 1 microWatt (μW). In some embodiments, the superconducting wire has a width between 150 nm and 1000 nm. 
     In some embodiments, component layer  1602  includes a superconducting wire between points B and B′ (e.g., component  102 ,  FIG. 1C ). In some embodiments, the superconducting wire on component layer  1602  is 2 to 10 times wider than the superconducting wire on component layer  1604  (e.g., to promote heat transfer from the component layer  1602  to the component layer  1604 ). In some embodiments, the width of the superconducting wire on component layer  1602  is between 300 nm and 10 micron (μm). 
     In some embodiments, component layers  1602  and  1604  each optionally include a plurality of sub-layers. In some embodiments, the sub-layers include one or more of: a seed sub-layer (e.g., aluminum nitride (AlN)), a superconducting sub-layer (e.g., NbN), a cap sub-layer (e.g., amorphous silicon), and/or a protective sub-layer (e.g., amorphous silicon). In some embodiments, the seed sub-layer has a thickness between 1 nm and 10 nm. In some embodiments, the superconducting sub-layer has a thickness between 3 nm and 20 nm. In some embodiments, the cap sub-layer has a thickness between 1 nm and 5 nm and is deposited in-situ. In some embodiments, the protective sub-layer has a thickness between 3 nm and 20 nm. In some embodiments, during manufacture, the superconducting sub-layer is etched leaving side-wall portions of the superconducting sub-layer exposed, and the protective sub-layer is then added (e.g., deposited) to protect the side-walls of the superconducting sub-layer from oxidation and/or processing damage from subsequent manufacturing steps. In some embodiments, coupling layer  1606  is deposited over the protective sub-layer. 
     In some embodiments, component layer  1602  is composed of a material that operates in a non-superconducting state at the desired operating temperature of the circuit  1600 . For example, component layer  1602  includes a conducting sub-layer (e.g., composed of titanium (Ti) and/or tungsten (W)). In some embodiments, the conducting sub-layer has a thickness between 10 nm and 100 nm. 
       FIG. 16A  shows overlap of components on component layers  1602  and  1604  only between points B and B′. Minimizing or preventing overlap of components on component layers  1602  and  1604 , as shown in  FIG. 16A , allows for directed heat transfer between the layers and reduces unwanted heat transfer between the component layers.  FIG. 16A  also shows widening of components on component layers  1602  and  1604  beyond points B and B′ (e.g., thermal buffer  1609 ). The widening of components allows for more passive cooling and reduces the impact of heat transfer at locations outside of B and B′. In some embodiments (not shown), the components of component layers  1602  and  1604  taper from the pads to reduce current crowding effects. 
       FIG. 16B  shows a cross-sectional view of circuit  1600  along the A-A′ axis shown in  FIG. 16A . As shown in  FIG. 16B , in some embodiments, component layer  1604  is adjacent to substrate  1620  (e.g., component layer  1604  is deposited on substrate  1620 ). In some embodiments, one or more additional layers are positioned between substrate  1620  and component layer  1604 . Coupling layer  1606  is between component layer  1604  and component layer  1602  (e.g., coupling layer  1606  is deposited on component layer  1604 ). In some embodiments, coupling layer  1606  comprises one or more sub-layers having different compositions. In some embodiments, component layer  1602  is adjacent to coupling layer  1606  (e.g., component layer  1602  is deposited on coupling layer  1606 ). 
     In some embodiments, as shown in  FIG. 16C , coupling layer  1606  encompasses more than one side of component layers  1602  and  1604 . In some embodiments, coupling layer  1606  is deposited over component layer  1604  (e.g., so as to operate as a protective layer for components on component layer  1604 ). In some embodiments, a portion of coupling layer  1606  is removed (e.g., is etched away) and component layer  1602  is positioned in place of the removed portion (e.g., component layer  1602  is deposited within the removed portion). 
     In light of these principles and embodiments, we now turn to certain additional embodiments. 
     In accordance with some embodiments, an electric circuit includes: (1) a first superconducting component having a first terminal, a second terminal, and a constriction region between the first terminal and the second terminal; (2) a second superconducting component having a third terminal and a fourth terminal; and (3) a first electrically-insulating component that thermally couples the first superconducting component and the second superconducting component such that heat produced at the constriction region is transferred through the first component to the second superconducting component. For example,  FIG. 1A  shows superconducting component  102  with terminals  106  and  108  and superconducting component  112  with terminals  114  and  116 .  FIG. 1A  further shows coupling component  110  thermally coupling superconducting components  102  and  112 . 
     In some embodiments, the first electrically-insulating component is an electrically-insulating, thermally-conductive connector (e.g., coupling component  1308 ,  FIG. 13A ) positioned between the first superconducting component and the second superconducting component (e.g., as shown in  FIG. 1A ). 
     In some embodiments: (1) the second superconducting component includes a plurality of regions between the third terminal and the fourth terminal; and (2) the circuit includes a plurality of electrically-insulating components (e.g., components  304 ,  FIG. 3 ) positioned so as to thermally couple the plurality of regions and facilitate transition of the plurality of regions to the non-superconducting state via heat transfer (e.g., resistive or phononic) through the plurality of regions. 
     In some embodiments, heat transferred by the plurality of electrically-insulating components increase an impedance of the second superconducting device while the second superconducting device is in the non-superconducting state. 
     In some embodiments, the first electrically-insulating component is an electrically-insulating, thermally-conductive substrate (e.g., substrate  1310 ,  FIG. 13B ) on which the first superconducting component and the second superconducting component are positioned. 
     In some embodiments: (1) the second superconducting component has a first portion (e.g., portion  504 ,  FIG. 5 ) between the third terminal and the fourth terminal; and (2) the second superconducting component is positioned so that the first portion of the second superconducting component is in proximity with the first superconducting component such that heat produced at the first superconducting component transfers to the first portion. For example,  FIGS. 6A-6D  illustrate such a heat transfer. 
     In some embodiments, the first portion is in closer proximity to the first superconducting component than any other portion of the second superconducting component (e.g., in close proximity to the constriction region). For example,  FIG. 5  shows portion  504  in closer proximate to superconducting component  102  than any other portion of superconducting component  502 . 
     In some embodiments, the second superconducting component includes, between the third terminal and the fourth terminal, a second portion and a third portion each positioned in proximity to the first portion such that heat produced at the first portion transfers to the second portion and the third portion. 
     In some embodiments, the circuit further includes: (1) a first current source (e.g., current source  1210 ,  FIG. 12 ) coupled to the first terminal of the first superconducting component (e.g., superconducting component  102 ), the first current source configured to supply a first current (e.g., current  202 ,  FIG. 2A ) that exceeds a threshold current for the first superconducting component, where: (a) the first current causes the constriction region (e.g., constriction region  104 ,  FIG. 1A ) to transition from a superconducting state to a non-superconducting state, and (b), in the non-superconducting state, the constriction region generates heat that is transferred to the second superconducting component via the first electrically-insulating component (e.g., as illustrated in  FIGS. 2B-2D ); and (2) a second current source (e.g., current source  1218 ,  FIG. 12 ) coupled to the third terminal of the second superconducting component, the second current source configured to supply a second current (e.g., current  204 ,  FIG. 2A ), where a combination of the second current and the heat transferred from the constriction region causes the second superconducting component to transition from the superconducting state to the non-superconducting state. 
     In some embodiments, while in the non-superconducting state, the first superconducting component has a first impedance and the second superconducting component has a second impedance that is greater than the first impedance. 
     In some embodiments, first superconducting component and the second superconducting component are positioned so as to inhibit (e.g., prevent) cooper pair and/or electron tunneling between the first and second superconducting components (e.g., are 10 nm, 1000 nm, or more apart). 
     In some embodiments, the circuit further includes: (1) a photon detection component (e.g., photodetector  1212 ,  FIG. 12 ) coupled, via one or more resistors (e.g., resistor(s)  1204 ), to the first terminal of the first superconducting component, the photon detector component configured to output a first current to the first superconducting component upon detection of a threshold number of photons; and (2) an output component (e.g., readout circuit  1216 ) coupled to the fourth terminal of the second superconducting component, the output component configured to be responsive to a voltage drop across the second superconducting component; where the first current exceeds a current threshold of the first superconducting component, thereby transitioning the constriction region to a non-superconducting state; and where the voltage drop is responsive to the second superconducting component transitioning to the non-superconducting state. 
     In accordance with some embodiments, an electric circuit includes a first superconducting component (e.g., component  910 ,  FIG. 9B ) comprising: (1) a first terminal (e.g., terminal  912 ); (2) a second terminal (e.g., terminal  914 ); (3) a first portion between the first terminal and the second terminal (e.g., region  916 ), the first portion having a first superconducting current threshold; and (4) a second portion between the first terminal and the second terminal (e.g., region  918 ), the second portion having a second superconducting current threshold, less than the first superconducting current threshold; where the first portion is positioned in proximity to the second portion such that resistive heat from the second portion is transferred to the first portion (e.g., as illustrated in  FIGS. 10A-10D ). 
     In some embodiments: (1) the circuit further includes a current source (e.g., current source  920 ,  FIGS. 9A and 10A ) coupled to the first terminal of the first superconducting device, the current source configured to supply a first current (e.g., current  1002 ,  FIG. 10A ) that is less than the first superconducting current threshold and greater than the second superconducting current threshold; (2), responsive to the first current, the second portion is configured to transition from a superconducting state to a non-superconducting state; and (3), responsive to a combination of the first current and the resistive heat from the second portion, the first portion is configured to transition from the superconducting state to the non-superconducting state. 
     It will also be understood that, although the terms first, second, etc. are, in some instances, used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first current could be termed a second current, and, similarly, a second current could be termed a first current, without departing from the scope of the various described embodiments. The first current and the second current are both currents, but they are not the same condition unless explicitly stated as such. 
     The terminology used in the description of the various described embodiments herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used in the description of the various described embodiments and the appended claims, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises,” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     As used herein, the term “if” is, optionally, construed to mean “when” or “upon” or “in response to determining” or “in response to detecting” or “in accordance with a determination that,” depending on the context. Similarly, the phrase “if it is determined” or “if [a stated condition or event] is detected” is, optionally, construed to mean “upon determining” or “in response to determining” or “upon detecting [the stated condition or event]” or “in response to detecting [the stated condition or event]” or “in accordance with a determination that [a stated condition or event] is detected,” depending on the context. 
     As used herein, a “superconducting circuit” or “superconductor circuit” is a circuit having one or more superconducting materials. For example, a superconductor switch circuit is a switch circuit that includes one or more superconducting materials. As used herein, a “superconducting” material is a material that is capable of operating in a superconducting state (under particular conditions). For example, a superconducting material is a material that operates as a superconductor (e.g., operates with zero electrical resistance) when cooled below a particular temperature (e.g., a threshold temperature) and having less than a threshold current flowing through it. A superconducting material is also sometimes called herein a superconduction-capable material. In some embodiments, the superconducting materials operate in an “off” state where little or no current is present. In some embodiments, the superconducting materials can operate in a non-superconducting state during which the materials have a non-zero electrical resistance (e.g., a resistance in the range of one thousand to ten thousand ohms). For example, a superconducting material supplied with a current greater than a threshold superconducting current for the superconducting material transitions from a superconducting state having zero electrical resistance to a non-superconducting state having non-zero electrical resistance. As an example, superconducting layer  118  is a layer that is capable of operating in a superconducting state (e.g., under particular operating conditions). 
     As used herein, a “wire” is a section of material configured for transferring electrical current. In some embodiments, a wire includes a section of material conditionally capable of transferring electrical current. For example, a wire made of a superconducting material that is capable of transferring electrical current while the wire is maintained at a temperature below a threshold temperature. As another example, a wire made of semiconducting material is capable of transferring electrical current while the wire is maintained at a temperature above a freeze-out temperature. A cross-section of a wire (e.g., a cross-section that is perpendicular to a length of the wire) optionally has a regular (e.g., flat or round) shape or an irregular shape. While some of the figures show wires having rectangular shapes, any shape could be used. In some embodiments, a length of a wire is greater than a width or a thickness of the wire (e.g., the length of a wire is at least 5, 6, 7, 8, 9, or 10 times greater than the width and the thickness of the wire). In some cases, a wire is a section of a superconducting layer. 
     The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the scope of the claims to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen in order to best explain the principles underlying the claims and their practical applications, to thereby enable others skilled in the art to best use the embodiments with various modifications as are suited to the particular uses contemplated.