Parametric device having josephson junction arrays

Abstract

Parametric devices for use in, for instance, quantum computing systems are provided. In one implementation, the parametric device includes a bridge circuit coupled between a first resonator and a second resonator. The bridge circuit includes a plurality of Josephson junction arrays. The parametric device includes a DC flux bias coupled to the bridge circuit through the first resonator. The parametric device includes an AC pump bias coupled to the bridge circuit through the second resonator. A first circuit can be coupled to the bridge circuit through the first resonator. The first circuit can be associated with a first frequency. A second circuit can be coupled to the bridge circuit through the second resonator. The second circuit can be associated with a second frequency. The second frequency can be different than the first frequency.

Description

PARAMETRIC DEVICE HAVING JOSEPHSON JUNCTION ARRAYSPRIORITY CLAIM

[0001] The present application is based on and claims priority to United States Provisional Application 63 / 353,095 having a fding date of June 17, 2022, which is incorporated by reference herein.FIELD

[0002] Aspects of the present disclosure are directed to parametric devices, such as parametric devices used in quantum computing systems, such as part of readout systems in quantum computing systems.BACKGROUND

[0003] A parametric device can provide for functionality based on application of an AC pump tone, which can allow for power to be transferred from the AC pump tone to a signal being processed by the parametric device. Parametric devices can be used as frequency converters, radio frequency amplifiers, radio frequency circulators, or other devices. Various parametric devices, from amplifiers to circulators, have been built with Josephson junctions. Parametric devices have been used in readout systems for quantum computing applications.

[0004] Quantum computing is a computing method that takes advantage of quantum effects, such as superposition of basis states and entanglement to perform certain computations more efficiently than a classical digital computer. In contrast to a digital computer, which stores and manipulates information in the form of bits, e.g., a “1” or “0.” quantum computing systems can manipulate information using quantum bits (‘“qubits”). A qubit can refer to a quantum device that enables the superposition of multiple states, e.g., data in both the “0” and “1” state, and / or to the superposition of data, itself, in the multiple states. In accordance with conventional terminology7, the superposition of a “0” and “1” state in a quantum system may be represented, e.g., as a |0) + b |1) The “0” and ‘“1” states of a digital computer are analogous to the |0) and |1) basis states, respectively of a qubit.SUMMARY

[0005] Aspects and advantages of embodiments of the present disclosure will be set forth in part in the following description, or can be learned from the description, or can be learned through practice of the embodiments.

[0006] One example aspect of the present disclosure is directed to a parametric device. The parametric device includes a bridge circuit coupled between a first resonator and a second resonator. The bridge circuit includes a plurality of Josephson junction arrays. The parametric device includes a DC flux bias coupled to the bridge circuit through the first resonator. The parametric device includes an AC pump bias coupled to the bridge circuit through the second resonator. A first circuit can be coupled to the bridge circuit through the first resonator. The first circuit can be associated with a first frequency. A second circuit can be coupled to the bridge circuit through the second resonator. The second circuit can be associated with a second frequency. The second frequency can be different than the first frequency.

[0007] Other aspects of the present disclosure are directed to various methods, systems, apparatuses, non-transitory computer-readable media, quantum devices, and electronic devices.

[0008] These and other features, aspects, and advantages of various embodiments of the present disclosure will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate example embodiments of the present disclosure and, together with the description, serve to explain the related principles.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Detailed discussion of embodiments directed to one of ordinary skill in the art is set forth in the specification, which refers to the appended figures, in which:

[0010] FIG. 1 depicts a schematic of a parametric device according to example embodiments of the present disclosure.

[0011] FIG. 2 depicts an example Josephson junction array according to example embodiments of the present disclosure.

[0012] FIG. 3 depicts an example circuit diagram of a parametric device according to example embodiment of the present disclosure.

[0013] FIG. 4 depicts example performance metrics associated with a parametric device according to example embodiments of the present disclosure.

[0014] FIG. 5 depicts a schematic of an example notch filter used in conjunction with a parametric device according to example embodiments of the present disclosure.

[0015] FIG. 6 depicts example performance metrics associated with a notch filter used in conjunction with a parametric device according to example embodiments of the present disclosure.

[0016] FIG. 7 depicts a circuit diagram of an example three-port parametric device according to example embodiments of the present disclosure.

[0017] FIG. 8 depicts an example quantum computing system according to example embodiments of the present disclosure.

[0018] FIG. 9 depicts an example readout system according to example embodiments of the present disclosure.DETAILED DESCRIPTION

[0019] Example aspects of the present disclosure are directed to parametric device(s). The parametric device(s) can be used, for instance, as a part of a readout system of a quantum computing system. A parametric device can provide for functionality based on application of an AC pump tone, which can allow for power to be transferred from the AC pump tone to a signal being processed by the parametric device. Parametric devices can be used as frequency converters, radio frequency amplifiers, radio frequency circulators, or other devices.

[0020] Parametric devices may include a coupler between an input circuit and an output circuit that is purely parametric or nearly purely parametric, meaning that any passive samefrequency coupling between circuits across the coupler can be zeroed out (or near zeroed out). Certain couplers have been designed to operate between input and output circuits which are at the same frequency. These couplers, however, are not parametric and can be optimized for achieving a particular static coupling strength (as opposed to parametric coupling that is dependent on, for instance, an AC pump tone).

[0021] Parametric couplers with passive coupling that is nulled have been achieved using Josephson couplers such as radio frequency superconducting quantum interference device(s) (RF SQUID(s)). These parametric couplers, however, can include a single Josephson junction or few Josephson junctions as active elements, which can limit the power handling of these devices to, for instance, about -95 dBm or less, output referred. High power couplers have been implemented using RF SQUID arrays. In addition, high power couplers have been implemented using superconducting nonlinear -asymmetric inductive elements (SNAILs) thatinclude superconducting loops of a plurality large Josephson junctions with a single smaller Josephson junction. Aspects of the present disclosure are directed to parametric devices that can include Josephson junction elements that are suitable for relatively high-power operation, such about -75 dBm or greater (output referred) while still exhibiting purely parametric or nearly purely parametric coupling between circuits of different frequencies.

[0022] In some embodiments, the parametric devices according to example embodiments of the present disclosure can include a coupler. The coupler can have an inductively-terminated balanced bridge containing an RF SQUID array or other Josephson junction array in each of four arms of the bridge circuit. The coupler can be disposed between an input circuit and an output circuit that operate at different frequencies from each other. The coupler can be inductively coupled to both the input circuit and the output circuit. A DC flux bias and an AC pump bias can be mutually coupled to the coupler. The DC flux bias can be configured to supply DC current, which can induce currents in the coupler to set an operating point. The AC pump bias can provide an AC parametric pump tone that induces currents that unbalance the bridge circuit. For half of the AC pump tone cycle the coupler can provide a positive coupling between the input circuit and the output circuit. In the second half of the AC pump tone cycle, the coupler can provide negative coupling. The passive coupling between the input circuit and the output circuit remains zero or near zero by symmetry.

[0023] According to example aspects of the present disclosure, a parametric device can include a bridge circuit coupled between a first resonator and a second resonator. The bridge circuit can include Josephson junction arrays, such as arrays of RF SQUIDs. An input circuit can be coupled to the parametric device through a first port. The first port can be associated with a first frequency (e.g., about 5 GHz). The first port can be coupled to the bridge circuit through a first match network. The first match network can be coupled to the bridge circuit (e.g., inductively coupled to the bridge circuit) through the first resonator. An output circuit can be coupled to the parametric device through a second port. The second port can be associated with a second frequency (e.g., about 7 GHz) that is different from the first frequency. The second port can be coupled to the bridge circuit through a second match network. The second match network can be coupled to the bridge circuit (e.g., inductively coupled to the bridge circuit) through the second resonator.

[0024] The parametric device can include a DC flux bias coupled (e.g., inductively coupled) to the bridge circuit via the first resonator. The parametric device can include an AC pump bias coupled (e.g.. inductively coupled) to the bridge circuit via the second resonator.According to some embodiments, the DC flux bias can be coupled to the bridge circuit via a first notch filter. The AC pump bias can be coupled to the bridge circuit via a second notch filter. The first notch filter and the second notch filter can be configured to filter or block signals at frequencies associated with the input circuit and the output circuit to reduce coupling between the input circuit and the output circuit to the DC or AC signal source termination.

[0025] The parametric device can be configured as a parametric amplifier or as a parametric frequency converter based on a frequency of the AC pump tone applied to the bridge circuit. For instance, in some embodiments, the AC pump tone can have a frequency that is based on a sum of the first frequency and the second frequency such that the parametric device operates as an amplifier. In some embodiment, the AC pump tone can have a frequency that is based on a difference between the first frequency and the second frequency such that the parametric device operates as a frequency converter.

[0026] In some embodiments, the first and second resonators can be constructed at least in part using the inductive terminations that are part of the bridge circuit. For instance, the first resonator can include a first capacitor configured to resonate with the badge circuit at the first frequency. The second resonator can include a second capacitor configured to resonate with the bridge circuit at the second frequency.

[0027] The bridge circuit can include a balanced bridge circuit having four Josephson junction arrays. In some embodiments, the Josephson junction arrays can be RF SQUID arrays. The use of RF SQUID arrays in the bridge circuit can allow the parametric device to handle relatively high signal power (e.g., -75 dBm or greater, output referred). This can be due to junctions in the RF SQUID arrays being significantly larger than ty pical junctions used in parametric couplers (e.g., Josephson junction having a critical current of about 16 uA relative to about 5 uA Josephson junctions). In some embodiments, the RF SQUID arrays can be arranged in a serpentine configuration. In the serpentine configuration, each RF SQUID array can have a plurality' of stages. Each stage can include at least one inductive path in parallel with a Josephson junction. The plurality of stages being arranged such that the RF SQUIDs are in an alternating pattern. In some embodiments, each RF SQUID array can include, for instance, about 20 to about 30 stages to accommodate increased power handling.

[0028] In some embodiments, because the bridge circuit is coupled to the DC flux bias and AC pump bias through resonators, notch filters can be used to make sure the additional connections do not load the bridge circuit. For instance, signals can couple from the bridgecircuit to the DC flux bias and the AC pump bias via the resonators and adversely affect losses in the bridge circuit. To mitigate this effect, a notch filter can be configured to filter or block frequencies of signals associated with frequencies of the input circuit and the output circuit. In some embodiments, the notch circuit(s) can include a double-stub filter circuit used to short out the load presented by the DC flux bias impedance and the AC pump bias impedance at both the first frequency (e.g., about 5 GHz) and the second frequency (e.g., about 7 GHz).

[0029] In some embodiments, the parametric device(s) according to example embodiments of the present disclosure can be configured as a parametric circulator. The parametric circulator can be a three-port device. For instance, the parametric circulator can have a first port and a third port that are coupled to circuits operating at the same frequency (e.g., about 5 GHz). The parametric circulator can include a second port that is operating at a different frequency (e.g., about 7 GHz) relative to the first port and the third port. The parametric circulator can include back-to-back bridge circuits coupling the first port to the third port. The second port can be coupled to the circulator at a node between the bridge circuits. Each of the ports can be coupled to the bridge circuit(s) via resonators. The resonators can be coupled to a transformer network, forming a two-pole configuration in each of the three branches of the circulator. The AC pump tone can have a frequency (e.g., about 2 GHz) based on a difference between the first frequency and the second frequency.

[0030] Aspects of the present disclosure can provide technical effects and benefits. For instance, the parametric device(s) according to example aspects of the present disclosure can provide for purely parametric or nearly purely parametric coupling between circuits of different frequencies while accommodating high power handling capabilities compared to state of the art Josephson parametric couplers. The parametric device(s) according to example aspects of the present disclosure can provide an improvement to quantum computing systems. For instance, example aspects of the present disclosure can provide for improved readout response in quantum computing applications, particularly by providing improved quantumnoise limited qubit readout performance with increased gain over a wide signal bandwidth. This is especially beneficial in real -world (e.g., noisy) quantum computing applications, which can present a need for rapid and accurate readout of reflection measurements on an increasing number of qubits.

[0031] Additional benefits and advantages of the disclosed technology can be achieved by reducing the size and number of hardware components that are required for implementationwithin the valuable real estate of a quantum computing system. For instance, parametric devices in accordance with the disclosed technology’ can be used to reduce or replace any larger conventional ferrite devices. In the context of qubit readout, these benefits reduce the requirements for readout hardware that is implemented in the cryogenic space of the quantum computer. This can be a substantial advantage in a scaled-up quantum computing system having hundreds of readout channels.

[0032] As used herein, the use of the term “about” in conjunction with a numerical value refers to within 15% of the stated numerical value. The use of the term near zero when referring to coupling between circuits refers to a value of coupling that does not induce any measurable detrimental effect between circuits. With reference now to the FIGS., example embodiments of the present disclosure will now be set forth.

[0033] FIG. 1 depicts a schematic of an example parametric device 100 according to example embodiments of the present disclosure. The parametric device 100 includes a parametric coupler 110 that can be coupled to a first circuit 120 (e.g., an input circuit) and to a second circuit 130 (e.g., output circuit). The first circuit 120 can communicate a signal having a first frequency (e.g., about 5 GHz). The second circuit can communicate a signal having a second frequency (e g., about 7 GHz).

[0034] In some embodiments, the first circuit 120 can include a signal source 122. The signal source 122 can communicate a signal at the first frequency to the parametric coupler 110 via a first match network 125. The first match network 125 can include one or more active or passive devices (e g., transmission lines, capacitors, inductors, etc.) operable to provide impedance matching with the parametric coupler 110. In some embodiments, the first match network 125 can include one or more resonators 124 configured to resonate at the first frequency.

[0035] The second circuit 130 can include a load 132. The second circuit 130 can communicate a signal at the second frequency from the parametric coupler 110 to the load 132 via a second match network 135. The second match network 135 can include one or more active or passive devices (e.g., transmission lines, capacitors, inductors, etc.) operable to provide impedance matching with the parametric coupler 110. In some embodiments, the second match network 135 can include one or more resonators 134 configured to resonate at the second frequency.

[0036] The parametric coupler 110 can include a bridge circuit 115 that is coupled between a first resonator 112 and a second resonator 114. The bridge circuit 115 can include aplurality of Josephson junction arrays, such as a balanced bridge of RF SQUID arrays. An example RF SQUID array will be discussed with reference to FIG. 2. Referring to FIG. 1, the bridge circuit 115 can be disposed between a first resonator 112 and a second resonator 114.

[0037] The first resonator 112 can be configured to resonate at the first frequency. The first resonator 112 can be inductively coupled to the first circuit 120. For instance, the first resonator 112 can be inductively coupled to the first match network 125 via a first mutual transformer 102 for the parametric coupler 110. In some embodiments, the first mutual transformer 102 can form a part of the first resonator 112.

[0038] The second resonator 114 can be configured to resonate at the second frequency. The second resonator 114 can be inductively coupled to the second circuit 130. For instance, the second resonator 114 can be inductively coupled to the second match network 135 via a second mutual transformer 104 for the parametric coupler 110. In some embodiments, the second mutual transformer 104 can form a part of the second resonator 114.

[0039] The parametric device 100 can include a DC flux bias 150 coupled to the parametric coupler 110 via the first resonator 112. The DC flux bias 150 can include a DC source 152 and a first notch filter 154. The DC flux bias 150 can be inductively coupled to first resonator 112 (e g., inductively coupled to the first mutual transformer 102). The first notch filter 154 can be configured to filter or block signals at the first frequency (e.g., about 5 GHz) and to filter or block signals at the second frequency (e.g., about 7 GHz).

[0040] The DC signal provided via the DC flux bias 150 can set an operating point of the parametric coupler 1 10. For instance, a DC current supplied by the DC flux bias 150 can induce currents in the parametric coupler 110 to set the operating point of the parametric coupler 110 but maintain its balance.

[0041] The parametric device 100 can include an AC pump bias 160 coupled to the parametric coupler 110 via the second resonator 114. The AC pump bias 160 can include an AC pump tone source 162 (e.g., a microwave generator) and a second notch filter 164. The AC pump bias 160 can be inductively coupled to the second resonator 114 (e.g., inductively coupled to the second mutual transformer 104). The second notch filter 164 can be configured to filter or block signals at the first frequency (e.g., about 5 GHz) and to filter or block signals at the second frequency (e.g., about 7 GHz).

[0042] The AC pump tone provided via the AC pump bias 160 can induce currents in the parametric coupler 110 to unbalance the parametric coupler 110. More specifically, the AC pump tone can induce currents that unbalance the parametric coupler 110 such that in half ofthe AC pump tone cycle, the parametric coupler 110 can provide positive coupling between the input circuit 120 and the output circuit 130. In the second half of the AC pump tone cycle, the parametric coupler 110 can provide negative coupling. The passive coupling between the input circuit 120 and the output circuit 130 can remain zero or near zero by symmetry.

[0043] FIG. 2 depicts an example Josephson junction array 200 that can be used in the bridge circuit 115 of the parametric coupler 110 according to example embodiments of the present disclosure. The Josephson junction array 200 can include active elements that are RF SQUID arrays. The Josephson junction array 200 can include N stages of RF SQUIDs, arranged in alternating fashion in a serpentine configuration.

[0044] More particularly, each of the RF SQUIDs in the array can include a pair of inductors and a Josephson junction. The first inductor can be associated with a label LI and the second inductor can be associated with a label L2. The Josephson junction can be associated with a label J. In FIG. 3, the LI inductors are labeled LX1 and the L2 inductors are labeled LX2, with X corresponding to the number or stage of RF SQUID along the array 200. The Josephson junction J is labeled JX, with X corresponding to the number or stage of the RF SQUID along the array 200. Each RF SQUID can include two inductors LX1 and LX2 in series. The two inductors LX1 and LX2 are arranged in parallel with the Josephson junction JX. In the serpentine configuration, the RF SQUIDs are arranged in an alternating pattern along the array such that a Josephson junction J(X+1) is coupled to a node between LX2 and L(X+1)1. Each Josephson junction JX can be associated with an inductance LJX(50).

[0045] The total inductance of an RF SQUID array containing N stages is given by:

[0046] 80 can be found by solving:(|)ext is the reduced flux associated with the DC signal provide by the DC flux bias 150.

[0047] In some embodiments, inductors LI and L2 in each RF SQUID array can be set such that 4L1 + L2 < Lj, where Lj is the zero-bias inductance of the Josephson junctions. The zero-bias inductance of the Josephson junctions is inversely proportional to the junction critical current. In this embodiment, the RF SQUID array can be uni-stable. In one specific example implementation, for a critical current Ic of about 16 uAa and Lj of about 20.6 pH, LI can be about 2.6 pH and L2 can be about 8 pH. An example RF SQUID array can have between about 20 stages to about 30 stages.

[0048] FIG. 3 depicts a circuit diagram of an example parametric device 100 according to example embodiments of the present disclosure. As show n, the bridge circuit 115 includes four arms of Josephson junction arrays 200 connected in a balanced bridge configuration. The first resonator 112 can include a first capacitor CgA and a first input inductor LgA. The second resonator 114 can include a second capacitor CgB and a second input inductor LgB. The first resonator 112 can be coupled to the first circuit 120 and DC flux bias 150 through the first mutual transformer 102 (MA). The second resonator 114 can be coupled to the second circuit 130 and AC pump bias 160 through the second mutual transformer 104 (MB).

[0049] The inductor LgA can form a part of the first mutual transformer 102 (MA). The inductor LgA is part of a loop containing the bridge circuit 115 and is resonated by capacitor CgA to form the first resonator 112. The inductor LgB can form a part of the second mutual transformer 104 (MB). The inductor LgB is part of the loop containing the bridge circuit 115 and is resonated by capacitor CgB to form the second resonator 114. The inductor LgA can be coupled to the inductor LA through the first mutual transformer 102 (MA). The inductor LgB can be coupled to the inductor LB through the second mutual transformer 104 (MB). LS in FIG. 3 is representative of the inductance of each of the Josephson junction arrays 200.

[0050] When the bridge circuit is balanced, inductors LgA and LgB are not coupled, so the second circuit 130 connected to LgB does not load the first circuit 120 connected to LgA. However, the bridge circuit will still appear as an inductance Ls in parallel with each of LgA and LgB. The inductance Lscan be set by the DC signal provided by the DC flux bias 150. The capacitor CgA can be configured to resonate with (e.g., have a capacitance selected to resonate with) a parallel combination of the inductance Ls of the bridge circuit and the inductance of the first input inductor LgA (along with any mutual inductance at the first input inductor LgA associated with the mutual transformer 102 and first circuit 120). The capacitor CgB can be configured to resonate with (e.g., have a capacitance selected to resonate with) the parallel combination of the inductance LS of the bridge circuit and the inductance of thesecond input inductor LgB associated with the mutual transformer 104 and second circuit 130).

[0051] In one example implementation, the first circuit 120 can operate at about 5 GHz and the second circuit 130 can operate at about 7 GHz. The bridge circuit can use the RF SQUID array shown in FIG. 2 with Josephson junctions having a critical current of about 16 uA. LI can be about 2.6 pH and L2 can be about 8.0 pH. Each Josephson junction array can have about 30 stages. The DC flux bias can be selected such that the Ls is about 318 pH. The inductances of LA, LgA, LB, and LgB can be about 400 pH. CgA can be determined to resonate with LgA and Ls and can be about 5.72 pF. CgB can be determined to resonate with LgB and Ls and can be about 2.92 pF. The above implementation is provided for example purposes only. Other suitable configurations can be implemented without deviating from the scope of the present disclosure.

[0052] FIG. 4 depicts example performance metrics associated with the Josephson parametric device 100 of FIG. 1 that includes a 4-pole configuration having a resonator 124 in the first match network 125 and a resonator 134 in the second matching network 135 and that is configured to operate as a frequency converter and driven with an AC pump tone at a difference frequency of about 2 GHz. FIG. 4 plots frequency (GHz) along the horizontal axis. FIG. 4 plots relative power (dB) along the vertical axis. Curve 302 depicts the S21 parameter for the parametric device 100. As shown, the S21 parameter is greater than 0. In other words, there is conversion gain that relates to the ratio of the second frequency and the first frequency. In addition, the power out of Port 2 is frequency shifted with respect to the input frequency (shown on the horizontal axis) by the pump frequency. In this regard, the S21 parameter refers to output at a frequency plus the pump frequency relative to the input at the frequency. Curve 304 depicts the SI 1 parameter for the parametric device. Port 1 can be the input to the parametric coupler 110 (coupled to the first circuit 120). Port 2 can be the output of the parametric coupler 110 (coupled to the second circuit 130).

[0053] As discussed with reference to FIG. 1, notch filter 154 can be part of the DC flux bias 150 and notch filter 164 can be part of the AC pump bias 160. Notch filter 154 can prevent the source impedance of the DC flux bias 150 from loading the coupler 110. Notch filter 164 can prevent the source impedance of the AC pump bias 160 from loading the coupler 110. Otherwise, signals can couple between the bridge circuit 115 and the AC pump bias 160 or DC flux bias 150, adversely affecting losses in the parametric device 100. Notch filter 154 and notch filter 164 can both be configured to filter or block signals at the firstfrequency of the parametric device 100 (e.g., the frequency of the first circuit 120) and the second frequency of the parametric device 100 (e.g., the frequency of the second circuit 130).

[0054] To reduce the effects of additional parasitic coupling between the DC flux bias 150 and the bridge circuit 115, and without introducing additional resonances in the circuit, the notch filter 154 can include a double-stub filter circuit having two open transmission line stubs) used to short out the load presented by the DC flux bias 150 impedance at both the first frequency and the second frequency.

[0055] FIG. 5 depicts a schematic of an example notch filter 154. Port 1 can be coupled to the DC source 152. Port 2 can be coupled to the mutual transformer 102 of FIG. 1 to couple the notch filter 154 to the parametric coupler 110. As shown in FIG. 5, the notch filter 154 can include two open stub transmission line elements 320 and 330. The transmission line elements 320 and 330 can each include an open stub transmission line (e.g., open stub microstrip). The transmission line elements 320 and 330 can be configured to short circuit the load presented by the DC flux bias 150 at the second frequency (e.g., about 7 GHz). The electrical length of the transmission lines 332 and 320 and the electrical length of the transmission line elements 332 and 330 notch out the first frequency (e.g., about 5 GHz). To reduce the effects of adding additional resonance to the parametric device 100, the transmission line element 320 can be placed about 45° aw ay (e.g., using transmission line element 322) from the mutual transformer 102 used to couple the notch filter 154 to the parametric coupler 110. In this way. when the transmission line elements 320 and 330 resonate, the transmission line elements 320 and 330 present a short circuit to the end of the 45° line, making the transmission line elements 320 and 330 look like a shorted inductive load from the reference plane of the mutual transformer 102.

[0056] The notch filter 164 can also have the configuration shown in FIG. 5. Port 1 can be coupled to the AC pump tone source 162. Port 2 can be coupled to the mutual transformer 104 of FIG. 1 to couple the notch filter 164 to the parametric coupler 110. As shown in FIG.5, the notch filter 164 can include tw o open stub transmission line elements 320 and 330. The transmission line elements 320 and 330 can each include an open stub transmission line (e.g., open stub microstrip). The transmission line elements 320 and 330 can be configured to short circuit the load presented by the AC pump bias 160 at the second frequency (e.g., about 7 GHz). The electrical length of the transmission lines 332 and 320 and the electrical length of the transmission line elements 332 and 330 notch out the first frequency (e.g., about 5 GHz). To reduce the effects of adding additional resonance to the parametric device 100, thetransmission line element 320 can be placed about 45° away (e.g., using transmission line element 322) from the mutual transformer 104 used to couple the notch filter 164 to the parametric coupler 110. In this way, when the transmission line elements 320 and 330 resonate, the transmission line elements 320 and 330 present a short circuit to the end of the 45° line, making the transmission line elements 320 and 330 look like a shorted inductive load from the reference plane of the mutual transformer 104.

[0057] FIG. 6 depicts example performance of the notch filters 154, 164 configured according to example embodiments of the present disclosure. FIG. 6 plots frequency (GHz) along the horizontal axis and signal strength (dB) along the vertical axis. Curve 352 depicts the SI 1 parameter of the notch filters 154, 164. Curve 354 depicts the S12 parameter of the notch filters 154. 164.

[0058] FIG. 7 depicts a parametric device 400 configured as a three-port device (e.g., circulator, directional amplifier, etc.) according to example embodiments of the present disclosure. The first port 420 (e.g., for coupling to a first circuit) and the second port (e.g., for coupling to a second circuit) can be operated at a different frequency. For instance, the first port 420 can be associated with a first frequency (e.g., about 5 GHz). The second port 430 can be associated with a second frequency (e.g., about 7 GHz).

[0059] A first bridge circuit 115 of Josephson junction arrays 200 can be coupled between resonators 112 and 114. The first port 420 can be coupled to the resonator 112 through mutual transformer 102. The second port 430 can be coupled to the resonator 114 through mutual transformer 104. AC pump bias line (not shown) can be coupled to the resonator 114 via a notch filter configured to filter out signals at the first frequency and the second frequency. DC flux bias line (not shown) can be coupled to the resonator 112 via a notch filter configured to filter out signals at the first frequency and the second frequency. The AC pump bias line can provide an AC pump tone (e.g., about 2 GHz) that is based on a difference between the first frequency and the second frequency to operate the device as a parametric circulator. The AC pump bias line can provide an AC pump tone that is based on a sum of the first frequency and the second frequency to operate the device as a directional amplifier. The first bridge circuit 115 can be configured and can operate similar to the bridge circuit discussed with reference to FIGS. 1-6.

[0060] The parametric device can include a third port 440 (e.g., for coupling to a third circuit). The third port 440 can be operated at the same frequency as the first port 420 (e.g., about 5 GHz). The parametric device 400 can include a second bridge circuit 415 ofJosephson junction arrays 200 coupled between the second resonator 114 and a third resonator 412. The third port 440 can be coupled to the third resonator 412 through mutual transformer 402. A DC flux bias line (not shown) can be coupled to the second resonator 114 via a notch filter to control an operating point of the two bridge circuits 115 and 415. Two AC pump bias lines (not shown) coupled to resonator 112 and 412 can provide AC pump tones for the first bridge circuit 115 and the second bridge circuit 415. The two AC pump tones can have the same frequency and can have a phase of 90 degrees relative to each other. The second bridge circuit 415 can be configured and can operate similar to the bridge circuit discussed with reference to FIGS. 1-6.

[0061] In this way, the parametric device 400 includes back-to-back bridge circuits with Josephson junction arrays configured between resonators according to example embodiments of the present disclosure. The resonators can be coupled to a transformer network (network of mutual transformers 102, 104, and 402). The parametric device 400 can further include capacitors 465 coupled to resonators 112 and 412.

[0062] FIG. 8 depicts an example quantum computing system 500. The system 500 is an example of a system of one or more classical computers and / or quantum computing devices in one or more locations, in which the systems, components, and techniques described below can be implemented. Those of ordinary skill in the art, using the disclosures provided herein, will understand that other quantum computing devices or systems can be used without deviating from the scope of the present disclosure.

[0063] The system 500 includes quantum hardware 502 in data communication with one or more classical processors 504. The classical processors 504 can be configured to execute computer-readable instructions stored in one or more memory devices to perform operations, such as any of the operations described herein. The quantum hardware 502 includes components for performing quantum computation. For example, the quantum hardware 502 includes a quantum system 510, control device(s) 512, and readout system(s) 514. The quantum system 510 can include one or more multi-level quantum subsystems, such as a register of qubits (e.g., qubits 520). In some implementations, the multi-level quantum subsystems can include superconducting qubits, such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc.

[0064] The t pe of multi-level quantum subsystems that the system 500 utilizes may vary. For example, in some cases it may be convenient to include one or more readout system(s) 514 attached to one or more superconducting qubits, e.g., transmon, flux, gmon, xmon, orother qubits. In other cases, ion traps, photonic devices or superconducting cavities (e.g., with which states may be prepared without requiring qubits) may be used. Further examples of realizations of multi-level quantum subsystems include fluxmon qubits, silicon quantum dots or phosphorus impurity qubits.

[0065] Quantum circuits may be constructed and applied to the register of qubits included in the quantum system 510 via multiple control lines that are coupled to one or more control devices 512. Example control devices 512 that operate on the register of qubits can be used to implement quantum gates or quantum circuits having a plurality of quantum gates G, e.g., Pauli gates, Hadamard gates, controlled-NOT (CNOT) gates, controlled-phase gates, T gates, multi-qubit quantum gates, coupler quantum gates, etc. The one or more control devices 512 may be configured to operate on the quantum system 510 through one or more respective control parameters (e.g., one or more physical control parameters). For example, in some implementations, the multi-level quantum subsystems may be superconducting qubits and the control devices 512 may be configured to provide control pulses to control lines to generate magnetic fields to adjust the frequency of the qubits.

[0066] The quantum hardware 502 may further include readout system(s) 514 (e.g., readout resonators). Measurement results 508 obtained via measurement devices may be provided to the classical processors 504 for processing and analyzing. In some implementations, the quantum hardware 502 may include a quantum circuit and the control device(s) 512 and readout system(s) 514 may implement one or more quantum logic gates that operate on the quantum system 502 through physical control parameters (e.g., microwave pulses) that are sent through wires included in the quantum hardware 502. Further examples of control devices include arbitrary waveform generators, wherein a DAC (digital to analog converter) creates the signal.

[0067] The readout system(s) 514 may be configured to perform quantum measurements on the quantum system 510 and send measurement results 508 to the classical processors 504. In addition, the quantum hardware 502 may be configured to receive data specifying physical control qubit parameter values 506 from the classical processors 504. As will be discussed with reference to FIG. 9, the parametric devices according to example embodiments of the present disclosure can be used in conjunction with the readout system(s) 514. The quantum hardware 502 may use the received physical control qubit parameter values 506 to update the action of the control device(s) 512 and readout system(s) 514 on the quantum system 510. For example, the quantum hardware 502 may receive data specifying new values representingvoltage strengths of one or more DACs included in the control devices 512 and may update the action of the DACs on the quantum system 510 accordingly. The classical processors 504 may be configured to initialize the quantum system 510 in an initial quantum state, e.g., by sending data to the quantum hardware 502 specifying an initial set of parameters 506.

[0068] In some implementations, the readout system(s) 514 can take advantage of a difference in the impedance for the |0) and 11) states of an element of the quantum system, such as a qubit, to measure the state of the element (e.g., the qubit). For example, the resonant frequency of a readout resonator can take on different values when a qubit is in the state |0) or the state 11), due to the nonlinearity of the qubit. Therefore, a microwave pulse reflected from the readout system(s) 514 carries an amplitude and phase shift that depend on the qubit state. In some implementations, a Purcell filter can be used in conjunction with the readout system(s) 514 to impede micro wave propagation at the qubit frequency.

[0069] In some embodiments, the quantum system 510 can include a plurality of qubits 520 arranged, for instance, in a two-dimensional grid 522. For clarity, the two-dimensional grid 522 depicted in FIG. 8 includes 4x4 qubits, however in some implementations the system 510 may include a smaller or a larger number of qubits. In some embodiments, the multiple qubits 520 can interact with each other through multiple qubit couplers, e.g., qubit coupler 524. The qubit couplers can define nearest neighbor interactions between the multiple qubits 520. In some implementations, the strengths of the multiple qubit couplers are tunable parameters. In some cases, the multiple qubit couplers included in the quantum computing system 500 may be couplers with a fixed coupling strength.

[0070] In some implementations, the multiple qubits 520 may include data qubits, such as qubit 526 and measurement qubits, such as qubit 528. A data qubit is a qubit that participates in a computation being performed by the system 500. A measurement qubit is a qubit that may be used to determine an outcome of a computation performed by the data qubit. That is, during a computation an unknown state of the data qubit is transferred to the measurement qubit using a suitable physical operation and measured via a suitable measurement operation performed on the measurement qubit.

[0071] In some implementations, each qubit in the multiple qubits 520 can be operated using respective operating frequencies, such as an idling frequency and / or an interaction frequency(s) and / or readout frequency and / or reset frequency. The operating frequencies can vary from qubit to qubit. For instance, each qubit may idle at a different operating frequency.The operating frequencies for the qubits 520 can be chosen before a computation is performed.

[0072] FIG. 8 depicts one example quantum computing system that can be used to implement the methods and operations according to example aspects of the present disclosure. Other quantum computing systems can be used without deviating from the scope of the present disclosure.

[0073] FIG. 9 depicts an example embodiment of a readout system 700 according to example aspects of the present disclosure. For example, FIG. 7 depicts a readout system 700 that can include a first readout device 710, a second readout device 720, and a third readout device 730. The first readout device 710 can include one or more of the devices / circuits disclosed in accordance with the subject technology, such as but not limited to parametric device 100 and / or parametric device 400. The first readout device 710 can include a plurality of readout resonators 740 and a control system 741 for coupling to a plurality of qubits 742, a filter 743, a readout signal source 744, a circulator / isolator 745, an amplifier 746, an AC pump tone source 747. an optional ferrite circulator 748, and phase shifters 749. The second readout device 720 can include a low-noise amplifier (LNA) 721, and third readout device 730 can include a receiver 731.

[0074] Referring more particularly to FIG. 9, the plurality of readout resonators 740 and control system 741 can be configured for coupling to a plurality of qubits 742. Qubits 742 can be formed in accordance with one or more of the same or different qubit technologies for quantum computing. For example, qubits 742 can be or can include superconducting qubits (e.g., transmon qubits), semiconductor quantum dots, defect-based qubits, topological nanowire qubits, or nuclear magnetic resonance qubits. Filter 743 (e.g., a Purcell filter or other bandpass filter) can be coupled to the plurality of readout resonators 740 and configured to produce a bandpass response for readout signals received by the plurality of readout resonators 740.

[0075] The readout system 700 of FIG. 9 can include at least a first Josephson parametric device configured to receive an output from the filter 743 as an input signal and to generate an output signal. As illustrated, first readout device 710 includes two Josephson parametric devices according to example aspects of the present disclosure, namely a first Josephson parametric device corresponding to circulator / isolator 745 (e.g., configured in accordance with parametric device 400) and a second Josephson parametric device corresponding to amplifier 746. The second parametric device can be an amplifier corresponding to parametricdevice 100 or a directional amplifier corresponding to parametric device 400. Additional circulator / isolator components may sometimes be included between circulator / isolator 745 and amplifier 746. When additional circulator / isolator components are included, such components can sometimes correspond to parametric circulator / isolators as described herein (e.g., parametric device 400) or can alternatively correspond to conventional Ferrite circulators (e.g., optional Ferrite circulator 748). In still further embodiments, a readout system 700 can include conventional Ferrite circulators coupled to a parametnc directional amplifier as described herein (e.g., parametric device 400).

[0076] Referring still to FIG. 9, circulator / isolator 745 can be implemented, for example, as parametric device 400. AC Pump tone signals for the first and second parametric couplings in circulator / isolator 745 can be provided from pump source 747, with one of phase shifters 749 implementing phase offset between the respective pump tone signals provided to the first and second parametric couplings.

[0077] Directional amplifier 746 forming a second Josephson parametric device can be configured to receive an output from circulator / isolator 745 forming a first Josephson parametric device as an input signal. Directional amplifier 746 can be further configured to generate an amplified output signal based on the readout from qubits 742. Amplifier 746 can be implemented, for example, as parametric device 100 or as a directional amplifier implemented, for example, as parametric device 400. AC Pump tone signals for the directional amplifier 746 can be provided from pump source 747.

[0078] Readout system 700 of FIG. 9 can also include additional readout devices provided in one or more temperature stages of the readout process. For example, Josephson parametric devices (e.g., circulator / isolator 745 implemented as a first Josephson parametric device and directional amplifier 746 implemented as a second Josephson parametric device) can be included in first readout device 710 provided for readout at lower temperature stages (e.g., mK stages). In some examples, a second readout device 720 can include a low-noise amplifier (LNA) 721 and / or other receiver components (e.g., receiver 731) and can be provided at one or more higher temperatures. For example, a readout system 700 can include a first readout device 710 including one or more Josephson parametric devices that are configured for operation in a first temperature range (e.g., a cryogenic temperature range inclusive of less than about 1 kelvin (K) or less than about 100 millikelvin (mK)). Readout system 700 can further include at least one second readout device 720 (e.g., LNA 721) that is coupled to and configured to receive an output from the first readout device 710, and that isconfigured for operation in a second temperature range. In some examples, the second temperature range can be higher than the first temperature range, for example but not limited to a range inclusive of about 4 K, or between about 1 K and about 10 K. Readout system 700 can further include at least one third readout device 730 (e.g., a receiver 731) that is coupled to and configured to receive an output from the second readout device 720, and that is configured for operation in a third temperature range. In some examples, the third temperature range can be higher than the second temperature range, for example but not limited to a range that is at or near room temperature (e.g., a range inclusive of about 300K, or between about 250 K and about 350 K).

[0079] Implementations of the digital, classical, and / or quantum subject matter and the digital functional operations and quantum operations described in this specification can be implemented in digital electronic circuitry, suitable quantum circuitry or, more generally, quantum computational systems, in tangibly -implemented digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. The term “quantum computing systems” may include, but is not limited to, quantum computers / computing systems, quantum information processing systems, quantum cry ptography systems, or quantum simulators.

[0080] Implementations of the digital and / or quantum subject matter described in this specification can be implemented as one or more digital and / or quantum computer programs (e.g., one or more modules of digital and / or quantum computer program instructions encoded on a tangible non-transitory storage medium for execution by, or to control the operation of, data processing apparatus). The digital and / or quantum computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory7device, one or more qubits / qubit structures, or a combination of one or more of them. Alternatively or in addition, the program instructions can be encoded on an artificially -generated propagated signal that is capable of encoding digital and / or quantum information (e.g., a machine-generated electrical, optical, or electromagnetic signal) that is generated to encode digital and / or quantum information for transmission to suitable receiver apparatus for execution by a data processing apparatus.

[0081] The terms quantum information and quantum data refer to information or data that is carried by, held, or stored in quantum systems, where the smallest non-trivial system is a qubit (i.e., a system that defines the unit of quantum information). It is understood that theterm “qubit” encompasses all quantum systems that may be suitably approximated as a two-level system in the corresponding context. Such quantum systems may include multi-level systems, e.g., with two or more levels. By way of example, such systems can include atoms, electrons, photons, ions, or superconducting qubits. In many implementations the computational basis states are identified with the ground and first excited states, however it is understood that other setups where the computational states are identified with higher level excited states (e.g., qudits) are possible.

[0082] The term “data processing apparatus” refers to digital and / or quantum data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing digital and / or quantum data, including by way of example a programmable digital processor, a programmable quantum processor, a digital computer, a quantum computer, or multiple digital and quantum processors or computers, and combinations thereof. The apparatus can also be, or further include, special purpose logic circuitry, e.g., an FPGA (field programmable gate array), or an ASIC (application-specific integrated circuit), or a quantum simulator, i.e., a quantum data processing apparatus that is designed to simulate or produce information about a specific quantum system. In particular, a quantum simulator is a special purpose quantum computer that does not have the capability to perform universal quantum computation. The apparatus can optionally include, in addition to hardware, code that creates an execution environment for digital and / or quantum computer programs, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0083] A digital or classical computer program, which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code, can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or can be written in a quantum programming language, e.g., QCL, Quipper, Cirq. etc..

[0084] A digital and / or quantum computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub-programs, or portions of code. A digital and / or quantum computer program can be deployed to be executed on one digital or one quantum computer or on multiple digital and / or quantum computers that are located at one site or distributed across multiple sites and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that may transmit quantum data using quantum systems, e.g. qubits. Generally, a digital data communication network cannot transmit quantum data, however a quantum data communication network may transmit both quantum data and digital data.

[0085] The processes and logic flows described in this specification can be performed by one or more programmable digital and / or quantum computers, operating with one or more digital and / or quantum processors, as appropriate, executing one or more digital and / or quantum computer programs to perform functions by operating on input digital and quantum data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry', e.g., an FPGA or an ASIC, or a quantum simulator, or by a combination of special purpose logic circuitry or quantum simulators and one or more programmed digital and / or quantum computers.

[0086] For a system of one or more digital and / or quantum computers or processors to be “configured to” or “operable to” perform particular operations or actions means that the system has installed on it software, firmware, hardware, or a combination of them that in operation cause the system to perform the operations or actions. For one or more digital and / or quantum computer programs to be configured to perform particular operations or actions means that the one or more programs include instructions that, when executed by digital and / or quantum data processing apparatus, cause the apparatus to perform the operations or actions. A quantum computer may receive instructions from a digital computer that, when executed by the quantum computing apparatus, cause the apparatus to perform the operations or actions.

[0087] Digital and / or quantum computers suitable for the execution of a digital and / or quantum computer program can be based on general or special purpose digital and / or quantum microprocessors or both, or any other kind of central digital and / or quantumprocessing unit. Generally, a central digital and / or quantum processing unit will receive instructions and digital and / or quantum data from a read-only memory, or a random access memory, or quantum systems suitable for transmitting quantum data, e.g. photons, or combinations thereof.

[0088] Some example elements of a digital and / or quantum computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and the memory can be supplemented by, or incorporated in, special purpose logic circuitry or quantum simulators. Generally, a digital and / or quantum computer will also include, or be operatively coupled to receive digital and / or quantum data from or transfer digital and / or quantum data to, or both, one or more mass storage devices for storing digital and / or quantum data, e.g., magnetic, magneto-optical disks, or optical disks, or quantum systems suitable for storing quantum information. However, a digital and / or quantum computer need not have such devices.

[0089] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memoiy . media and memory devices, including by way of example semiconductor memoiy devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks; and quantum systems, e.g.. trapped atoms or electrons. It is understood that quantum memories are devices that can store quantum data for a long time with high fidelity and efficiency, e.g., light-matter interfaces where light is used for transmission and matter for storing and preserving the quantum features of quantum data such as superposition or quantum coherence.

[0090] Control of the various systems described in this specification, or portions of them, can be implemented in a digital and / or quantum computer program product that includes instructions that are stored on one or more tangible, non-transitory machine-readable storage media, and that are executable on one or more digital and / or quantum processing devices. The systems described in this specification, or portions of them, can each be implemented as an apparatus, method, or electronic system that may7include one or more digital and / or quantum processing devices and memory7to store executable instructions to perform the operations described in this specification.

[0091] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but rather as descriptions of features that may be specific to particular implementations. Certain features that are described in this specification in the context of separate implementations can also be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation can also be implemented in multiple implementations separately or in any suitable sub combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

[0092] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the implementations described above should not be understood as requiring such separation in all implementations, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0093] While the present subject matter has been described in detail with respect to various specific example embodiments thereof, each example is provided by way of explanation, not limitation of the disclosure. Those skilled in the art, upon attaining an understanding of the foregoing, can readily produce alterations to, variations of, and / or equivalents to such embodiments. Accordingly, the subject disclosure does not preclude inclusion of such modifications, variations, and / or additions to the present subject matter as would be readily apparent to one of ordinary skill in the art. For instance, features illustrated and / or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present disclosure covers such alterations, variations, and / or equivalents.

Claims

WHAT IS CLAIMED IS:

1. A parametric device, comprising:a bridge circuit coupled between a first resonator and a second resonator, the bridge circuit comprising a plurality of Josephson junction arrays;a DC flux bias coupled to the bridge circuit through the first resonator; an AC pump bias coupled to the bridge circuit through the second resonator; wherein a first circuit is coupled to the bridge circuit through the first resonator, the first circuit associated with a first frequency;wherein a second circuit is coupled to the bridge circuit through the second resonator, the second circuit associated with a second frequency, the second frequency being different than the first frequency.

2. The parametric device of claim 1, wherein the first resonator comprises a first capacitor and a first input inductor, the first capacitor and the first input inductor configured to resonate with the bridge circuit at the first frequency, wherein the second resonator comprises a second capacitor and a second input inductor, the second capacitor and the second input inductor configured to resonate with the bridge circuit at the second frequency.

3. The parametric device of claim 1, wherein the bridge circuit comprises a balanced bridge of four Josephson junction arrays.

4. The parametric device of claim 1, where each Josephson junction array comprises a plurality of radio frequency superconducting quantum interference devices (RF SQUIDs) arranged in a serpentine configuration having a plurality of stages, each stage comprising at least one inductive path in parallel with a Josephson junction, the plurality of stages being arranged such that the plurality of RF SQUIDs are in an alternating pattern.

5. The parametric device of claim 4, wherein each Josephson junction array comprises about 20 or more stages.

6. The parametric device of claim 1, further comprising a first notch filter coupled to the DC flux bias and to the first resonator and a second notch filter coupled to the AC pump bias and to the second resonator.

7. The parametric device of claim 6, wherein at least one of the first notch filter and the second notch filter is configured to filter signals at the first frequency and to filter signals at the second frequency.

8. The parametric device of claim 6, wherein at least one of the first notch filter and the second notch filter comprises at least two open transmission line stubs.

9. The parametric device of claim 1 , wherein the AC pump bias is configured to provide an AC pump tone at a frequency determined based at least in part on a sum of the first frequency and the second frequency such that the parametric device operates as a parametric amplifier.

10. The parametric device of claim 1, wherein the AC pump bias is configured to provide an AC pump tone determined based at least in part on a difference of the first frequency and the second frequency such that the parametric device operates as a parametric frequency converter.

11. The parametric device of claim 1, wherein the parametric device is a three-port parametric device.

12. The parametric device of claim 11, wherein the three-port parametric device comprises a second bridge circuit coupled between a third resonator and the second resonator, the second bridge circuit comprising a plurality of Josephson junction arrays, wherein the third resonator is configured to resonate at the first frequency.

13. The parametric device of claim 12, wherein the first resonator is coupled to the first circuit via a first transformer, the second resonator is coupled to the second circuit via a second transformer, and the third resonator is coupled to a third transformer.

14. A readout system for a quantum computing system, the readout system comprising:a readout resonator;a filter configured to produce a bandpass response for a readout signal from the readout resonator;a parametric device coupled to the filter such that the parametric device receives the readout signal at a first port and generates an output signal at a second port, wherein the parametric device comprises:a bridge circuit coupled between a first resonator and a second resonator, the bridge circuit comprising a plurality of Josephson junction arrays, the first resonator associated with a first frequency, the second resonator associated with a second frequency that is different from the first frequency;a DC flux bias coupled to the bridge circuit through the first resonator; an AC pump bias coupled to the bridge circuit through the second resonator; a first notch filter coupled to the DC flux bias and to the first resonator; and a second notch filter coupled to the AC pump bias and the second resonator.

15. The readout system of claim 14, wherein the first port is coupled to the bridge circuit through a first match network, the first port associated with a first frequency, the first match network coupled to the first resonator, wherein the second port is coupled to the bridge circuit through a second match network, the second port associated with a second frequency, the second match network coupled to the second resonator, the second frequency being different from the first frequency.

16. The readout system of claim 14, wherein the first resonator comprises a first capacitor configured to resonate with the bridge circuit at the first frequency and the second resonator comprises a second capacitor configured to resonate with the bridge circuit at the second frequency.

17. The readout system of claim 14, wherein the first notch filter and the second notch filter are each configured to filter signals associated with the first frequency and the second frequency.

18. The readout system of claim 14, wherein the first notch filter and the second notch filter each comprise two open transmission line stubs.

19. A quantum computing system comprising:a plurality’ of qubits;a readout system configured to perform readout of the plurality of qubits, the readout system comprising at least one parametric device, the parametric device comprising;a bridge circuit coupled between a first resonator and a second resonator, the bridge circuit comprising a plurality of Josephson junction arrays, the first resonator comprising a first capacitor configured to resonate with the bridge circuit, the second resonator comprising a second capacitor configured to resonate with the bridge circuit;a DC flux bias coupled to the bridge circuit through the first resonator; an AC pump bias coupled to the bridge circuit through the second resonator;a first circuit coupled to the bridge circuit, the first circuit associated with a first frequency;a second circuit coupled to the bridge circuit, the second circuit associated with a second frequency, the second frequency being different from the first frequency.

20. The quantum computing system of claim 19. wherein a first notch filter is coupled to the DC flux bias and to the first resonator; and a second notch filter is coupled to the AC pump bias and the second resonator, wherein the first notch filter and the second notch filter are each configured to filter the first frequency and the second frequency.

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