Josephson parametric device having the same frequency ports

Abstract

A Josephson parametric device (e.g., a circulator / isolator or directional amplifier) ​​can include multiple resonant modes, multiple couplings, an input port, and an output port. The multiple resonant modes include a first, a second, and a third resonant mode, the first and third resonant modes both configured to operate at a first resonant frequency, and the second resonant mode configured to operate at a second resonant frequency different from the first resonant frequency. The multiple couplings include a passive coupling between the first resonant mode and the third resonant mode, a first parametric coupling between the first resonant mode and the second resonant mode, and a second parametric coupling between the second resonant mode and the third resonant mode. The input port is coupled to the first resonant mode of the device, and the output port is coupled to the third resonant mode of the device.

Description

Technical Field

[0001] Claims of Priority This application claims the benefit of priority of U.S. Provisional Patent Application No. 63 / 177,174, filed on April 20, 2021, which is hereby incorporated by reference in its entirety for all purposes.

[0002] The present disclosure generally relates to systems, devices, and computer-implemented methods that include Josephson parametric devices having the same frequency ports.

Background Art

[0003] Various parametric devices, from amplifiers to circulators, have been constructed using Josephson junctions. Parametric amplifiers have come to be used in the first gain stage of qubit readout for quantum computing applications. Quantum computing is a computing method that utilizes quantum effects such as superposition and entanglement of the ground state to execute specific calculations more efficiently than classical digital computers. For example, in contrast to digital computers that store and manipulate information in the form of bits of "1" or "0", quantum computing systems can manipulate information using qubits ( "qubits"). Qubits may refer to quantum devices that enable superposition of data in multiple states, such as both the states of "1" and "0", and / or the superposition of data itself in multiple states. According to conventional terminology, the superposition of the "1" and "0" states in a quantum system can be represented as, for example, a|0> + b|1>. The "1" and "0" states of a digital computer are respectively similar to the |0> and |1> ground states of a qubit.

Summary of the Invention

Means for Solving the Problems

[0004] Aspects and advantages of embodiments of the present disclosure are described in part in the following description, or may be learned from the description, or may be learned through practice of the embodiments.

[0005] One exemplary aspect of the present disclosure is directed to a parametric device. The parametric device can include a plurality of resonant modes (e.g., a first resonant mode, a second resonant mode, and a third resonant mode), a passive coupling, an input port, and an output port. The first resonant mode and the third resonant mode are both configured to operate at a first resonant frequency, and the second resonant mode is configured to operate at a second resonant frequency different from the first resonant frequency. The passive coupling is disposed between the first resonant mode and the third resonant mode. The input port is coupled to the first resonant mode of the parametric device, and the output port is coupled to the third resonant mode of the parametric device.

[0006] These and other features, aspects, and advantages of the various embodiments of the present disclosure will become better understood with reference to the following description and the appended claims. The accompanying drawings, which are incorporated herein and constitute a part of this specification, illustrate exemplary embodiments of the present disclosure and, together with the description, explain the related principles.

[0007] A detailed discussion of embodiments directed to those of ordinary skill in the art is described in the specification with reference to the accompanying figures.

Brief Description of the Drawings

[0008]

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DETAILED DESCRIPTION OF THE INVENTION

[0009] Exemplary aspects of the present disclosure are directed to systems, devices, and computer-implemented methods for implementing Josephson parametric devices having the same frequency ports. Josephson parametric devices can include, but are not limited to, circulators, isolators, and / or directional amplifiers. Such devices can be configured to operate in multiple different resonance modes while substantially configuring the resonance mode associated with the device input port to be the same as another resonance mode associated with the device output port. In the context of qubit readout, a circuit including one or more Josephson parametric devices can provide an improved readout response and a beneficial reduction in the cryogenic space required for readout system hardware for a quantum computer.

[0010] More specifically, exemplary aspects of the disclosed technology are directed to improved Josephson parametric devices. In some exemplary embodiments, the parametric device can include at least one Josephson junction device configured to function as a modulation reactance. In some examples, the Josephson junction device is configured to operate as a superconducting quantum interference device (SQUID). The Josephson junction device can provide parametric coupling between selected resonance modes of the parametric device, such as between first, second, and third resonance modes. The various resonance modes can be embodied by resonator structures (e.g., first, second, and third resonator structures) such as, but not limited to, lumped element LC resonators, transmission line resonators, or any other resonance circuit (e.g., electrical, optomechanical, etc.).

[0011] According to another exemplary aspect of the present disclosure, a Josephson parametric device including first, second, and third resonance modes can be configured to have the same frequency ports. This can be achieved at least in part by configuring two of the three resonance modes to operate at the same first frequency. These same frequency modes and corresponding ports can form the input and output modes / ports for the parametric device. For example, the first and third resonance modes of the parametric device can both be configured to operate at a first resonance frequency, and the second resonance mode can be configured to operate at a second resonance frequency different from the first resonance frequency. The input port can be coupled to the first resonance mode of the device, and the output port can be coupled to the third resonance mode of the device. In some exemplary embodiments, the second resonance mode is also configured to function as an external port, in which case the parametric device can be configured to operate as a circulator. In other exemplary embodiments, the second resonance mode is terminated internally (e.g., by being coupled to an impedance that provides an internal termination for the second resonance mode), in which case the parametric device can be configured to operate as an isolator. In further exemplary embodiments, the parametric device can be configured to operate as a directional amplifier.

[0012] In some exemplary embodiments, a combination of passive coupling and parametric coupling is included to couple various resonance modes to each other in a parametric device. For example, the coupling between an input port and an output port corresponding to the coupling between a first resonance mode and a third resonance mode can be a passive coupling. In some embodiments, the passive coupling between the first resonance mode and the third resonance mode can be a capacitive coupling. In some embodiments, the passive coupling between the first resonance mode and the third resonance mode can be an inductive coupling. Circuit simplification and size reduction can be advantageously achieved by providing a device configuration that accommodates at least one passive coupling that replaces what would otherwise be a parametric coupling. In addition, the output signal provided at the output port remains coherent with the input signal provided at the input port without requiring the coherence of the pump and signal generators used in the parametric coupling.

[0013] Furthermore, the parametric device can include a first parametric coupling between a first resonance mode and a second resonance mode and a second parametric coupling between the second resonance mode and a third resonance mode. In some embodiments, the first and second parametric couplings each include a respective Josephson junction device (e.g., a SQUID coupler) that is parametrically pumped at a respective parametric pump frequency. When the parametric device is configured to operate as a circulator / isolator, the first parametric coupling and the second parametric coupling are configured to receive a pump tone signal characterized by a pump frequency defined as the difference between a first resonance frequency and a second resonance frequency. When the parametric device is configured to operate as a directional amplifier, the first parametric coupling and the second parametric coupling are configured to receive a pump tone signal characterized by a pump frequency defined as the sum of a first resonance frequency and a second resonance frequency. In both the isolator / circulator configuration and the directional amplifier configuration, the phase of the pump tone signal provided to the first parametric coupling can be shifted (e.g., shifted by a phase offset of about 90 degrees) relative to the phase of the pump tone signal provided to the second parametric coupling.

[0014] According to another exemplary aspect of the present disclosure, a reduction in the number of pump tone sources and corresponding signal generators can be achieved by the nature of the parametric device design having the same frequency ports. For example, the parametric device can include a signal generator configured to function as a single source for generating pump tone signals provided to both a first parametric coupling and a second parametric coupling within the parametric device. Since the two pump tones (e.g., a first pump tone signal provided to the first parametric coupling and a second pump tone signal provided to the second parametric coupling) are at the same frequency, it is possible to implement a single signal generator.

[0015] According to another exemplary aspect of the present disclosure, additional resonant modes and matching circuits can be incorporated within the parametric device in order to obtain better broadband response in both the transmission and isolation of device signals. More specifically, in some examples, the matching circuit can include one or more additional first resonant modes coupled between the first resonant mode and the input port, one or more additional second resonant modes coupled to the second resonant mode, and one or more additional third resonant modes coupled between the third resonant mode and the output port. More specifically, in some embodiments, the parametric device can include three first resonant modes, three second resonant modes, and three third resonant modes, and each iteration within a given resonant mode is configured to operate at substantially the same resonant frequency.

[0016] Furthermore, the matching circuit can provide impedance matching to various device ports over a specified frequency band. In some exemplary embodiments, the matching circuit can also include additional passive couplings between the first resonant mode and one or more additional first resonant modes, between one or more additional first resonant modes and the input port, between the second resonant mode and one or more additional second resonant modes, between one or more additional second resonant modes and the internal termination or the second port, between the third resonant mode and one or more additional third resonant modes, and between one or more additional third resonant modes and the output port. Such additional passive couplings can include capacitive couplings and / or inductive couplings without requiring additional parametric couplings.

[0017] In some specific implementations, bandpass network synthesis techniques can be used to specifically design the device bandwidth in a way that is advantageously useful for the overall device performance. For example, in quantum computing readout applications, the matching circuit is designed to achieve a parametric device bandwidth exceeding about 10 MHz. In some examples, the matching circuit is designed to achieve a parametric device bandwidth exceeding about 20 MHz. In some examples, the matching circuit is designed to achieve a parametric device bandwidth of up to about 500 MHz (1 / 2 GHz). In some examples, the matching circuit is designed to achieve a parametric device bandwidth within the range between about 20 MHz and about 500 MHz. This achieves significant benefits compared to known parametric device configurations that provide circuit gain and isolation in a relatively narrow band of about 10 MHz or less.

[0018] According to another exemplary aspect of the present disclosure, one or more of the disclosed parametric devices can be incorporated into a readout system for a quantum computing device. For example, the readout system can include a plurality of resonators, a filter, and at least a first Josephson parametric device. The plurality of resonators can be configured to couple to a plurality of qubits. The qubits can be formed according to one or more of the same or different qubit technologies for quantum computing. For example, the qubits can be superconducting qubits (e.g., transmon qubits), semiconductor quantum dots, trapped ion qubits, photonic qubits, defect-based qubits, topological nanowire qubits, or nuclear magnetic resonance qubits, or can include them. The filter (e.g., a Purcell filter or other bandpass filter) can be coupled to the plurality of resonators and configured to generate a bandpass response for the readout signals received by the plurality of resonators.

[0019] When a readout system according to the disclosed technology includes a first Josephson parametric device, such a device can be configured to receive the output from the filter as an input signal and generate a first output signal. The first Josephson parametric device can more specifically also include first, second, and third resonance modes, where the first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. The Josephson parametric device can include a plurality of couplings including a passive coupling between the first resonance mode and the third resonance mode, a first parametric coupling between the first resonance mode and the second resonance mode, and a second parametric coupling between the second resonance mode and the third resonance mode.

[0020] In some exemplary embodiments of the disclosed technology, the readout system can additionally or alternatively include a second Josephson parametric device. More specifically, the second Josephson parametric device can be configured to receive the first output signal from the first Josephson parametric device as an input signal and generate a second output signal. The second Josephson parametric device can include fourth, fifth, and sixth resonance modes, where the fourth resonance mode and the sixth resonance mode are both configured to operate at a third resonance frequency, and the fifth resonance mode is configured to operate at a fourth resonance frequency different from the third resonance frequency. The second Josephson parametric device can also include a plurality of couplings including a passive coupling between the fourth resonance mode and the sixth resonance mode, a first parametric coupling between the fourth resonance mode and the fifth resonance mode, and a second parametric coupling between the fifth resonance mode and the sixth resonance mode.

[0021] When multiple Josephson parametric devices are incorporated into a readout system or other quantum computing applications, one or more of the devices can be configured to operate as a circulator or isolator, and one or more of the other devices can be configured to operate as a directional amplifier. For example, in one particular embodiment, a first Josephson parametric device can be configured to operate as a circulator, and a second Josephson parametric device can be configured to operate as a directional amplifier. In such an example, a first parametric coupling between a first resonance mode and a second resonance mode, and a second parametric coupling between the second resonance mode and a third resonance mode can be configured to receive a pump tone signal characterized by a pump frequency defined as the difference between a first resonance frequency and a second resonance frequency. A first parametric coupling between a fourth resonance mode and a fifth resonance mode, and a second parametric coupling between the fifth resonance mode and a sixth resonance mode can be configured to receive a pump tone signal characterized by a pump frequency defined as the sum of a third resonance frequency and a fourth resonance frequency. Since the first Josephson parametric device is configured to operate as a circulator / isola tor, the received input signal of the first Josephson parametric device is transmitted forward as a first output signal, and reverse transmission is prevented. Since the second Josephson parametric device is configured to operate as an amplifier, an amplified version of the first output signal is generated by the second Josephson parametric device and provided as a second output signal.

[0022] A readout system incorporating one or more of the disclosed parametric devices can also include additional readout devices provided at one or more temperature stages of the readout process. For example, a Josephson parametric device can be provided for readout at a lower temperature stage, and an additional readout device can be provided for readout at a higher temperature stage or subsequent signal processing. In some examples, a low noise amplifier (LNA) and / or receiver components can be provided at one or more higher temperatures. For example, the readout system can include one or more Josephson parametric devices configured to operate in a first temperature range (e.g., a cryogenic temperature range including less than about 1 Kelvin (K) or less than about 100 millikelvin (mK)). The readout system can further include one or more readout devices (e.g., LNA devices) coupled to and configured to receive an output from the one or more Josephson parametric devices and configured to operate in a second temperature stage. In some examples, the second temperature range can be higher than the first temperature range and can be, for example, but not limited to, a range including about 4K, or a range between about 1K and about 10K. The readout system can further include one or more readout devices (e.g., a receiver) coupled to the LNA device and configured to receive the output from the LNA device and configured to operate in a third temperature range. In some examples, the third temperature range can be higher than the second temperature range and can be, for example, but not limited to, room temperature or near room temperature (e.g., a range including about 300K, or a range between about 250K and about 350K).

[0023] Yet another exemplary aspect of the disclosed technology generally relates to quantum computing systems and related apparatus that incorporate one or more of the disclosed Josephson parametric devices. For example, a quantum computing system can include quantum hardware and a readout system. The quantum hardware can include a plurality of qubits. The readout system can be coupled to the plurality of qubits to receive readout responses of the plurality of qubits. The readout system can include one or more Josephson parametric devices. Each Josephson parametric device can include at least first, second, and third resonance modes, where the first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. Each Josephson parametric device can also include a plurality of couplings including a passive coupling between the first resonance mode and the third resonance mode, a first parametric coupling between the first resonance mode and the second resonance mode, and a second parametric coupling between the second resonance mode and the third resonance mode. In some examples, the one or more Josephson parametric devices include a first Josephson parametric device configured to operate as a circulator or isolator and a second Josephson parametric device configured to operate as a directional amplifier.

[0024] Systems and methods according to exemplary aspects of the present disclosure can provide several technical effects and benefits, including, but not limited to, improvements to computing technology (e.g., quantum computing technology). For example, exemplary aspects of the present disclosure can provide improved readout response in quantum computing applications by providing improved quantum noise-limited qubit readout performance with increased gain over a wide signal bandwidth. This is particularly beneficial in real-world (e.g., noisy) quantum computing applications that demonstrate the need for rapid and accurate readout of reflectometry measurements for an increasing number of qubits.

[0025] Additional benefits and advantages of the disclosed technology can be achieved by reducing the size and number of hardware components required for implementation within the valuable real estate of a quantum computing system. Many Josephson parametric amplifiers operate in reflection mode, so several circulators may be required to separate the input and amplified signals. The parametric circulator according to the disclosed technology can be used to reduce or replace any larger conventional ferrite circulator. In addition, parametric devices designed using the same frequency ports reduce the number of different phase coherent pump tones required for effective device operation. In the context of qubit readout, these benefits reduce the requirements for readout hardware implemented within the cryogenic space of a quantum computer. This can be a substantial advantage in a scaled-up quantum computing system with hundreds of readout channels.

[0026] Since the input port and the output port have the same frequency and are coherent with each other regardless of the phase of the entire pump, the additional benefits and advantages of the disclosed technology can be achieved in the context of qubit readout applications. Thus, in the context of qubit readout, the readout receiver can be configured to be phase-locked to the readout transmitter without requiring a precise phase relationship between the pump generator and the readout transmitter.

[0027] One exemplary aspect of the present disclosure is directed to a parametric device. The parametric device can include a first resonance mode, a second resonance mode, a third resonance mode, a passive coupling, an input port, and an output port. The first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. The passive coupling is disposed between the first resonance mode and the third resonance mode. The input port is coupled to the first resonance mode of the parametric device, and the output port is coupled to the third resonance mode of the parametric device.

[0028] In some implementations, the parametric device can be configured to operate as a circulator or an isolator. In such implementations, a first parametric coupling can be provided between the first resonance mode and the second resonance mode, and a second parametric coupling can be provided between the second resonance mode and the third resonance mode. The first parametric coupling and the second parametric coupling are configured to receive a pump tone signal characterized by a pump frequency defined as the difference between the first resonance frequency and the second resonance frequency. The phase of the pump tone signal provided to the first parametric coupling is shifted with respect to the phase of the pump tone signal provided to the second parametric coupling.

[0029] In some implementations, the parametric device can be configured to operate as a directional amplifier. In such an implementation, a first parametric coupling can be provided between a first resonance mode and a second resonance mode, and a second parametric coupling can be provided between the second resonance mode and a third resonance mode. The first parametric coupling and the second parametric coupling are configured to receive a pump tone signal characterized by a pump tone frequency defined as the sum of a first resonance frequency and a second resonance frequency. The phase of the pump tone signal provided to the first parametric coupling is shifted relative to the phase of the pump tone signal provided to the second parametric coupling.

[0030] Another exemplary aspect of the present disclosure is directed to a readout system for a quantum computing device. The readout system can include a plurality of resonators, a filter, and a first Josephson parametric device. The plurality of resonators are configured to couple to respective ones of a plurality of qubits. The filter is coupled to the plurality of resonators and is configured to generate a bandpass response to readout signals received by the plurality of resonators. The first Josephson parametric device is configured to receive an output from the filter as an input signal and generate a first output signal. The first Josephson parametric device includes a first, a second, and a third resonance mode and a plurality of couplings. The first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. The plurality of couplings include a passive coupling between the first resonance mode and the third resonance mode, a first parametric coupling between the first resonance mode and the second resonance mode, and a second parametric coupling between the second resonance mode and the third resonance mode.

[0031] Another exemplary aspect of the present disclosure is directed to a quantum computing system. The quantum computing system can include quantum hardware and a readout system. The quantum hardware includes a plurality of qubits. The readout system is coupled to the plurality of qubits to receive readout responses of the plurality of qubits. The readout system includes one or more Josephson parametric devices. Each Josephson parametric device includes first, second, and third resonance modes and a plurality of couplings. The first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency. The second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. The plurality of couplings includes a passive coupling between the first resonance mode and the third resonance mode, a first parametric coupling between the first resonance mode and the second resonance mode, and a second parametric coupling between the second resonance mode and the third resonance mode.

[0032] Reference is now made to the figures, and exemplary embodiments of the present disclosure are discussed in further detail.

[0033] FIG. 1 shows an exemplary block diagram of a first exemplary parametric device according to an exemplary aspect of the present disclosure. More specifically, parametric device 100 corresponds to a Josephson parametric circulator having co-frequency ports. Parametric device 100 can include a plurality of resonance modes, such as a first (A) resonance mode 110, a second (B) resonance mode 120, and a third (C) resonance mode 130. The various resonance modes 110, 120, and 130 can be embodied by resonator structures (e.g., first, second, and third resonator structures) such as, but not limited to, lumped element LC resonators, transmission line resonators, or any other resonance circuits (e.g., electrical, optomechanical, etc.).

[0034] Each resonance mode of the parametric device 100 is coupled to a corresponding port. More specifically, the first resonance mode 110 is coupled to the first (A) port 111, the second resonance mode 120 is coupled to the second (B) port 121, and the third resonance mode 130 is coupled to the third (C) port 131. The first port 111 is configured to function as an input port for the parametric device 100, and the third port 131 is configured to function as an output port for the parametric device 100. In some implementations, the second port 121 provides an additional external port such that the parametric device 100 is configured to operate as a circulator. In other implementations, the parametric device 100 includes an impedance coupled to the second resonance mode 120 and providing an internal termination (e.g., 50 ohm termination) for the second resonance mode 120 such that the parametric device 100 is configured to operate as an isolator.

[0035] Still referring to FIG. 1, the parametric device 100 can be configured to have co-frequency ports. This can be achieved, at least in part, by configuring two of the three resonance modes 110, 120, and 130 to operate at the same first frequency. These co-frequency modes and corresponding ports can form input and output modes / ports for the parametric device 100. For example, the first resonance mode 110 and the third resonance mode 130 of the parametric device 100 can both be configured to operate at a first resonance frequency, and the second resonance mode 120 can be configured to operate at a second resonance frequency different from the first resonance frequency.

[0036] In some exemplary embodiments, the parametric device 100 includes a combination of passive coupling and parametric coupling provided to couple various resonance modes 110, 120, and 130 to each other. For example, the coupling between the first port 111 (e.g., input port) and the third port 131 (e.g., output port) corresponds to the coupling between the first resonance mode 110 and the third resonance mode 130, such as a passive coupling 140. In some embodiments, the passive coupling 140 between the first resonance mode 110 and the third resonance mode 130 can be a capacitive coupling. In some embodiments, the passive coupling 140 between the first resonance mode 110 and the third resonance mode 130 can be an inductive coupling. Circuit simplification and size reduction can be advantageously achieved by providing a device configuration that accommodates at least one passive coupling that replaces what would otherwise be a parametric coupling. In addition, the output signal provided at the third port 131 remains coherent with the input signal provided at the first port 111 without requiring the coherence of the pump and signal generators used in the parametric coupling within the device.

[0037] Furthermore, the parametric device 100 can include a first parametric coupling 150 between a first resonance mode 110 and a second resonance mode 120, and a second parametric coupling 160 between the second resonance mode 120 and a third resonance mode 130. In some embodiments, the first parametric coupling 150 and the second parametric coupling 160 each include a respective Josephson junction device (e.g., a SQUID coupler) that is parametrically pumped at a respective parametric pump frequency. When the parametric device 100 is configured to operate as a circulator / isolator, the first parametric coupling 150 and the second parametric coupling 160 are each configured to receive a first pump tone signal 155 characterized by a first pump frequency and a second pump tone signal 165 characterized by a second pump frequency. The first pump frequency of the first pump tone signal 155 and the second pump frequency of the second pump tone signal 165 can be the same frequency. Thus, in some implementations, a single signal generator can be used as a source to provide both the first pump tone signal 155 and the second pump tone signal 165.

[0038] The same frequency of the first pump tone signal 155 and the second pump tone signal 165 can be defined as the difference between a first resonance frequency (e.g., the frequencies of the first resonance mode 110 and the third resonance mode 130) and a second resonance frequency (e.g., the frequency of the second resonance mode 120). For example, if the first resonance mode 110 and the third resonance mode 130 are each configured to operate at a first resonance frequency of about 4.0 GHz, and the second resonance mode 120 is configured to operate at a second resonance frequency of about 6.17 GHz, the first pump frequency of the first pump tone signal 155 provided to the first parametric coupling 150 and the second pump frequency of the second pump tone signal 165 provided to the second parametric coupling 160 can be the difference between 6.17 GHz and 4.0 GHz, i.e., about 2.17 GHz. The phase of the first pump tone signal 155 provided to the first parametric coupling 150 can be shifted (e.g., shifted by a phase offset of about ±π / 2 or ±90 degrees) relative to the phase of the second pump tone signal 165 provided to the second parametric coupling 160.

[0039] Referring now to FIG. 2, a second exemplary parametric device (e.g., parametric device 200) according to an exemplary aspect of the present disclosure is similar to the parametric device 100 of FIG. 1, and additional resonance modes and matching circuits are incorporated to obtain a better broadband response in both the transmission and separation of device signals. Accordingly, the parametric device 200 is shown to include similar reference numerals for the first resonance mode 110, the first port 111, the second resonance mode 120, the second port 121, the third resonance mode 130, the third port 131, the passive coupling 140, the first parametric coupling 150, the first pump tone signal 155, the second parametric coupling 160, and the second pump tone signal 165. The description of FIG. 1 applied to such elements applies to the embodiments shown in and described with reference to FIG. 2.

[0040] The parametric device 200 of FIG. 2 includes a plurality of additional resonance modes, for example, one or more additional first resonance modes 110', 110" coupled between the first resonance mode 110 and the first port 111, one or more additional second resonance modes 120', 120" coupled to the second resonance mode 120, and one or more additional third resonance modes 130', 130" coupled between the third resonance mode 130 and the third port 131. More specifically, in some embodiments, the parametric device 200 can include three first resonance modes 110, 110', and 110", three second resonance modes 120, 120', and 120", and three third resonance modes 130, 130', and 130", and each iteration within a given resonance mode is configured to operate at substantially the same resonance frequency. In some embodiments, each of the first resonance modes 110, 110', and 110", and each of the third resonance modes 130, 130', and 130" can be configured to operate at a first resonance frequency (e.g., 4.0 GHz), and each of the second resonance modes 120, 120', and 120" can be configured to operate at a second resonance frequency different from the first resonance frequency (e.g., 6.17 GHz). The first resonance mode 110, the second resonance mode 120, and the third resonance mode 130 are configured to function as a core circulator device as shown in FIG. 1. The additional resonance modes 110', 110", 120', 120", 130', and 130" are designed to provide impedance matching to the respective 50 ohm ports corresponding to the first port 111, the second port 121, and the third port 131 over a specified frequency band (e.g., Δω).

[0041] Furthermore, the matching circuit of the parametric device 200 can provide impedance matching to the first port 111 and the third port 131 over a specified frequency band. In some exemplary embodiments, the matching circuit can also include additional passive couplings. More specifically, the parametric device 200 can include additional passive couplings 112, 112', and 112" between the first resonance mode 110 and one or more additional first resonance modes 110', 110", and between the additional first resonance mode 110" and the first port 111. The parametric device 200 can also include additional passive couplings 122, 122', and 122" between the second resonance mode 120 and one or more second resonance modes 120', 120", and between one or more additional second resonance modes 120" and the second port 121. Furthermore, the parametric device 200 can include additional passive couplings 132, 132', and 132" between the third resonance mode 130 and one or more additional third resonance modes 130', 130", and between the additional third resonance mode 130" and the third port 131. Such additional passive couplings can include capacitive couplings and / or inductive couplings without requiring additional parametric couplings.

[0042] FIG. 3 shows an exemplary circuit diagram for implementing the parametric device 200 of FIG. 2 according to an exemplary aspect of the present disclosure. The resonance modes (e.g., resonance modes 110, 110', 110", 120, 120', 120", 130, 130', and 130" of FIG. 2) are implemented as parallel LC circuits in the figure of FIG. 3, and the passive couplings (e.g., couplings 112, 112', 112", 122, 122', 122", 132, 132', 132", and 140) are implemented as capacitors. The first (A) port 111 of FIG. 2 is labeled Term1 in FIG. 3, and the third (C) port 131 is labeled Term3. The second (B) port 121 of FIG. 2 is labeled Term2 in FIG. 3 and is assumed to be terminated with a 50 ohm load. Since the second (B) port (Term2) 121 is terminated, the parametric device 200 is a two-port isolator.

[0043] Still referring to FIG. 3, the matching networks for the first, second, and third resonance modes (e.g., the first resonance modes 110, 110', 110", the second resonance modes 120, 120', 120", and the third resonance modes 130, 130', 130") are for the matching circuits at each of the three ports (e.g., the first port 111, the second port 121, and the third port 131), with coefficients g 0 = 1.0, g 1 = 0.6291, g 2 = 0.9702, g 3 = 0.6291, g 4 = 1.0 are used and implemented based on a three-pole Chebyshev prototype. Here, the coefficient g 0 represents the circulator core, and g 4 represents the port.

[0044] The first parametric coupling 150 and the second parametric coupling 160 in FIG. 2 are represented as circuit components X1 and X2, respectively, in the diagram of FIG. 3. The first parametric coupling element labeled X1 in FIG. 3 is modeled as an rf-SQUID that provides a pump-modulated mutual coupling between a resonator (first resonance mode 110) composed of C1 and L1 and a resonator (second resonance mode 120) composed of C2 and L2. The second parametric coupling element labeled X2 in FIG. 3 similarly provides a pump-modulated mutual coupling between a resonator (third resonance mode 130) composed of C3 and L3 and a resonator (resonance mode 120) composed of C2 and L2. The capacitor C13 in FIG. 3 provides a passive equal-frequency coupling between the first resonance mode 110 and the third resonance mode 130 in FIG. 2, corresponding to the passive coupling 140 in FIG. 2. The value of the capacitor C13 can be determined via

[0045] [Number]

[0046] and can be determined via, where g 0 , g 1 are the 0th and 1st coefficients of a bandpass prototype used to synthesize an impedance matching network, Z A1 and Z C1 are the impedances of the first resonance mode 110 and the third resonance mode 130, and w is the ratio bandwidth of the network. C AC is the capacitance of the capacitor C13, ω A is the resonance frequency of the first resonance mode, and J AC is the value of the corresponding admittance inverter realized by the capacitor C13.

[0047] Table 1 below shows component values (referring to the elements labeled in FIG. 2) for an exemplary implementation of a parametric device 200 configured to be used as a circulator / isolator circuit of the disclosed technology. FIG. 4 shows a harmonic balance simulation in ADS of the figure shown in FIG. 3 using the component values shown in Table 1. The first and second parametric couplings 150, 160 are configured to have zero passive mutual coupling and a modulated coupling amplitude of 17ph. This can be achieved using rf-SQUID coupling elements as shown in FIGS. 10-11. Both couplers providing the first pump tone signal 155 and the second pump tone signal 165 are modulated at an intermediate frequency of 2.17 GHz, and there is a 90-degree phase shift between the first pump tone signal 155 provided to X1 (i.e., the first parametric coupling 150) and the second pump tone signal 165 provided to X2 (i.e., the second parametric coupling 160).

[0048]

Table 1

[0049] In some specific implementations, it is possible to use band - pass network synthesis techniques to specifically design the device bandwidth of the components in FIG. 2 or FIG. 3 in a way that is beneficial to the overall device performance. For example, in quantum computing read - out applications, the matching circuit is designed to achieve a bandwidth of parametric device 200 exceeding about 10 MHz. In some examples, the matching circuit is designed to achieve a bandwidth of parametric device 200 exceeding about 20 MHz. In some examples, the matching circuit is designed to achieve a bandwidth of parametric device 200 up to about 500 MHz (1 / 2 GHz). In some examples, the matching circuit is designed to achieve a bandwidth of parametric device 200 within the range between about 20 MHz and about 500 MHz. This achieves significant benefits compared to known parametric device configurations that provide circuit gain and isolation in a relatively narrow band of about 10 MHz or less.

[0050] FIG. 4 shows an exemplary graph of harmonic - balance simulation results related to the exemplary circuit diagram of FIG. 3 according to an exemplary aspect of the present disclosure. The red trace labeled dBm_s11 in FIG. 4 corresponds to the reflection (S11) of the input signal in dB from the first (A) port 111. Over the bandwidth of the circuit (designed with 100 MHz centered at 4 GHz), the first (A) port 111 exhibits a return loss better than 20 dB. The pink trace labeled dBm_3 corresponds to the forward transmission from the first (A) port 111 to the third (C) port 131. A single transmission over the pass - band of the circuit can be observed in FIG. 4. The blue curve labeled dBm_2 corresponds to the "reverse transmission" or isolation from the first (A) port 111 to the second (B) port 121. The parametric device 200 provides isolation exceeding 20 dB in this direction within the bandwidth of the circuit. The signal at the second (B) port 121 is converted to the 6.17 GHz band, but the corresponding s - parameter is plotted in FIG. 4 (blue trace) with respect to the frequency of the input signal.

[0051] FIG. 5 shows an exemplary block diagram of a third exemplary parametric device according to an exemplary aspect of the present disclosure. More specifically, parametric device 300 corresponds to a Josephson parametric amplifier having the same frequency ports. Parametric device 300 can include a Josephson junction device configured to function as a modulation reactance. Parametric device 300 can include a plurality of resonance modes, for example, a first (A) resonance mode 310, a second (B) resonance mode 320, and a third (C) resonance mode 330. The various resonance modes 310, 320, and 330 can be embodied by resonator structures (e.g., first, second, and third resonator structures) such as, but not limited to, lumped element LC resonators, transmission line resonators, or any other resonance circuit (e.g., electrical, optomechanical, etc.).

[0052] Each resonance mode of parametric device 300 is coupled to a corresponding port. More specifically, the first resonance mode 310 is coupled to the first (A) port 311, the second resonance mode 320 is coupled to the second (B) port 321, and the third resonance mode 330 is coupled to the third (C) port 331. The first port 311 is configured to function as an input port for parametric device 300, and the third port 331 is configured to function as an output port for parametric device 300. In some implementations, the second port 321 provides an additional external port.

[0053] Still referring to FIG. 5, the parametric device 300 can be configured to have the same frequency ports. This can be achieved, at least in part, by configuring two of the three resonance modes 310, 320, and 330 to operate at the same first frequency. These same frequency modes and corresponding ports can form the input and output modes / ports for the parametric device 300. For example, the first resonance mode 310 and the third resonance mode 330 of the parametric device 300 can both be configured to operate at the first resonance frequency, and the second resonance mode 320 can be configured to operate at a second resonance frequency different from the first resonance frequency.

[0054] In some exemplary embodiments, the parametric device 300 includes a combination of passive coupling and parametric coupling provided to couple the various resonance modes 310, 320, and 330 to each other. For example, the coupling between the first port 311 functioning as an input port and the third port 331 functioning as an output port corresponds to the coupling between the first resonance mode 310 and the third resonance mode 330 and can be a passive coupling 340. In some embodiments, the passive coupling 340 between the first resonance mode 310 and the third resonance mode 330 can be a capacitive coupling. In some embodiments, the passive coupling 340 between the first resonance mode 310 and the third resonance mode 330 can be an inductive coupling. Circuit simplification and size reduction can be advantageously achieved by providing a device configuration that accommodates at least one passive coupling that replaces what would otherwise be a parametric coupling. In addition, the output signal provided at the third port 331 remains coherent with the input signal provided at the first port 311 without requiring the coherence of the pump and signal generators used in the parametric coupling within the device.

[0055] Furthermore, the parametric device 300 can include a first parametric coupling 350 between a first resonance mode 310 and a second resonance mode 320, and a second parametric coupling 360 between the second resonance mode 320 and a third resonance mode 330. In some embodiments, the first parametric coupling 350 and the second parametric coupling 360 each include respective SQUID couplers that are parametrically pumped at respective parametric pump frequencies. The parametric device 300 can be configured to operate as a directional amplifier such that the first parametric coupling 350 and the second parametric coupling 360 each receive a first pump tone signal 355 characterized by a first pump frequency and a second pump tone signal 365 characterized by a second pump frequency. The first pump frequency of the first pump tone signal 355 and the second pump frequency of the second pump tone signal 365 can be the same frequency. Thus, in some implementations, a single signal generator can be used as a source to provide both the first pump tone signal 355 and the second pump tone signal 365.

[0056] The same frequency of the first pump tone signal 355 and the second pump tone signal 365 can be defined as the sum of a first resonance frequency (e.g., the frequencies of the first resonance mode 310 and the third resonance mode 330) and a second resonance frequency (e.g., the frequency of the second resonance mode 320). For example, if the first resonance mode 310 and the third resonance mode 330 are each configured to operate at a first resonance frequency of about 4.0 GHz, and the second resonance mode 320 is configured to operate at a second resonance frequency of about 8.17 GHz, the first pump frequency of the first pump tone signal 355 provided to the first parametric coupling 350 and the second pump frequency of the second pump tone signal 365 provided to the second parametric coupling 360 can be the sum of 8.17 GHz and 4.0 GHz, i.e., about 12.17 GHz. The phase of the first pump tone signal 355 provided to the first parametric coupling 350 can be shifted (e.g., shifted by a phase offset of about ±π / 2 or ±90 degrees) relative to the phase of the second pump tone signal 365 provided to the second parametric coupling 360.

[0057] Referring now to FIG. 6, a fourth exemplary parametric device (e.g., parametric device 400) according to an exemplary aspect of the present disclosure is similar to the parametric device 300 of FIG. 5, and additional resonance modes and matching circuits are incorporated to obtain a better broadband response in both the transmission and separation of device signals. Accordingly, the parametric device 400 is shown to include similar reference numerals for the first resonance mode 310, the first port 311, the second resonance mode 320, the second port 321, the third resonance mode 330, the third port 331, the passive coupling 340, the first parametric coupling 350, the first pump tone signal 355, the second parametric coupling 360, and the second pump tone signal 365. The description of FIG. 6 applied to such elements applies to the embodiments shown in and described with reference to FIG. 5.

[0058] The parametric device 400 of FIG. 6 includes a plurality of additional resonance modes, such as one or more additional first resonance modes 310', 310" coupled between the first resonance mode 310 and the first port 311, one or more additional second resonance modes 320', 320" coupled to the second resonance mode 320, and one or more additional third resonance modes 330', 330" coupled between the third resonance mode 330 and the third port 331. More specifically, in some embodiments, the parametric device 400 can include three first resonance modes 310, 310', and 310", three second resonance modes 320, 320', and 320", and three third resonance modes 330, 330', and 330", and each iteration within a given resonance mode is configured to operate at substantially the same resonance frequency. In some embodiments, each of the first resonance modes 310, 310', and 310", and each of the third resonance modes 330, 330', and 330" can be configured to operate at a first resonance frequency (e.g., 4.0 GHz), and each of the second resonance modes 320, 320', and 320" can be configured to operate at a second resonance frequency (e.g., 8.17 GHz) different from the first resonance frequency. The resonance modes 310, 320, and 330 are configured to function as a core-directed amplifier device as shown in FIG. 5. The additional resonance modes 310', 310", 320', 320", 330', and 330" are designed to provide impedance matching to the respective 50 ohm ports corresponding to the first port 311, the second port 321, and the third port 331 over a specified frequency band (e.g., Δω).

[0059] Furthermore, the matching circuit of the parametric device 400 can provide impedance matching to the first port 311 and the third port 331 over a specified frequency band. In some exemplary embodiments, the matching circuit can also include additional passive coupling. More specifically, the parametric device 400 can include additional passive couplings 312, 312', and 312" between the first resonance mode 310 and one or more additional first resonance modes 310', 310", and between the additional first resonance mode 310" and the first port 311. The parametric device 400 can also include additional passive couplings 322, 322', and 322" between the second resonance mode 320 and one or more additional second resonance modes 320', 320", and between one or more additional second resonance modes 320" and the second port 321. Furthermore, the parametric device 400 can include additional passive couplings 332, 332', and 332" between the third resonance mode 330 and one or more additional third resonance modes 330', 330", and between the additional third resonance mode 330" and the third port 331. Such additional passive couplings can include capacitive coupling and / or inductive coupling without requiring additional parametric coupling.

[0060] Still referring to FIG. 6, the circuit topology of the parametric device 400 configured to operate as a directional amplifier is similar in many respects to the circuit topology of the parametric device 200 of FIG. 2. However, the first parametric coupling 350 connecting the first resonance mode 310 to the second resonance mode 320 and the second parametric coupling 360 connecting the second resonance mode 320 to the third resonance mode 330 are driven by a sum-frequency pump, causing a parametric amplification process. The second (B) port 321 is internally terminated (e.g., terminated with a 50-ohm port). Since the second (B) port 321 is active in the sense of being related to the reflection gain, its matching circuit is described by different coefficients that are passive (e.g., having no reflection gain). The coefficients used for the matching circuits of the first (A) port 311 and the third (C) port 331 are the same as those of the parametric device 200 in FIGS. 2 - 3 configured to operate as a circulator, g 0 = 1.0, g 1 = 0.6291, g 2 = 0.9702, g 3 = 0.6291, g 4 = 1.0. However, the matching circuit at the second (B) port 321 is g 0 = 1.0, g 1 = 0.6068, g 2 = 0.6742, g 3 = 0.3836, g 4 = 0.8992. Similar to the previous example, the coefficient g 0 corresponds to the amplifier core, and g 4 corresponds to the port.

[0061] FIG. 7 shows the calculation of the S-parameters of an exemplary circuit based on FIG. 6. The orange curve labeled S_(C0,A0) is the forward gain from the first (A) port 311 to the third (C) port 331, showing a gain of 20 dB over the 100 MHz design bandwidth. The green curve labeled S_(A0,C0) represents the reverse gain from the third (C) port 331 to the first (A) port 311, which is unity (0 dB). Thus, the amplifier has gain in one direction but not in the reverse direction. The blue curve labeled S_(A0,A0) is the reflection from the first (A) port 311 (partially overlapping the maroon curve), indicating that the input of the amplifier is matched with a return loss better than 5 dB. The maroon curve labeled S_(A0,B0) represents the transmission of any signal (or actually noise) entering the amplifier from the second (B) port 321 towards the first (A) port 311, showing an isolation better than 5 dB between these ports. In the context of qubit readout, this last characteristic of the amplifier is important since it is crucial that the amplified noise from the amplifier does not affect the readout resonator and the qubit.

[0062] FIG. 8 shows an exemplary circuit diagram for implementing the parametric device 400 of FIG. 6 according to an exemplary aspect of the present disclosure. The circuit diagram of FIG. 8 is used for simulation in ADS. The circuit topology shown in FIG. 8 is similar to the circuit topology shown in FIG. 3, but due to different frequencies and different prototypes used for the second resonance mode in this example, the component values are different. Various resonance modes (e.g., resonance modes 310, 310', 310", 320, 320', 320", 330, 330', 330") are implemented as parallel LC circuits in the diagram of FIG. 7, and the passive couplings (e.g., couplings 312, 312', 312", 322, 322', 322", 332, 332', 332", and 340) are implemented as capacitors. The first (A) port 311 of FIG. 6 is labeled Term1 in FIG. 7, and the third (C) port 331 is labeled Term3. The second (B) port 321 of FIG. 6 is labeled Term2 in FIG. 7 and is assumed to be terminated with a 50-ohm load. The second (B) port (Term2) 321 is internally terminated (e.g., terminated with a 50-ohm load). The first and third resonance modes (e.g., resonance modes 310, 310', 310", 330, 330', and 330") are configured to operate at a first resonance frequency of 4.0 GHz, and the second resonance mode (e.g., resonance modes 320, 320', 320") is configured to operate at a second resonance frequency of 8.17 GHz.

[0063] The first parametric coupling 350 and the second parametric coupling 360 of FIG. 6 are represented as circuit components X1 and X2, respectively, in the figure of FIG. 8. Since the parametric device 400 shown in FIG. 8 is configured to operate as a directional amplifier, the parametric couplings 350 and 360 are driven by a sum-frequency pump, causing a parametric amplification process. More specifically, X1 and X2 are configured to receive a pump frequency corresponding to the sum of the first and second resonant frequencies, i.e., 12.17 GHz. The first parametric coupling element labeled X1 in FIG. 8 is modeled as an rf-SQUID that provides a pump-modulated mutual coupling between a resonator (first resonant mode 310) composed of C1 and L1 and a resonator (second resonant mode 320) composed of C2 and L2. The second parametric coupling element labeled X2 in FIG. 8 similarly provides a pump-modulated mutual coupling between a resonator (third resonant mode 330) composed of C3 and L3 and a resonator (second resonant mode 320) composed of C2 and L2. The amplitude of the pump tone signal provided at X1 corresponds to the modulation of the mutual coupling between the corresponding modes by 23 pH, and X2 is similarly driven at 12.17 GHz to modulate the corresponding mutual coupling by 22 pH and has an 83-degree phase shift with respect to the X1 drive. The first resonant mode 310 and the third resonant mode 330 each have an additional 0.15 nH from the coupler, and the second resonant mode 320 has an additional inductance of 0.075 nH.

[0064] Table 2 below shows component values (referring to the elements labeled in FIG. 6) for an exemplary implementation of a parametric device 400 configured to be used as a directional amplifier circuit of the disclosed technique.

[0065] [Table 2]

[0066] FIG. 9 shows the results of harmonic balance simulation in the ADC of the figure in FIG. 8 using the component values in Table 2. The various curves shown indicate the transmission in dB from input port A to termination port B (red) and output port C (blue), and the reflection at port A (pink). A gain of approximately 17 dB is achieved in the forward direction (blue curve labeled dBm_3), and the return loss at the input port is better than 10 dB (pink curve labeled dBm_s11). As predicted from theory, there is also a gain from the input port to the termination port (red curve labeled dBm_2). The higher gain seen here is consistent with the Manley - Rowe gain 10log 10 (8.17 GHz / 4 GHz)~3 dB]. The simulated response in FIG. 9 is reasonably consistent with the theoretically calculated response in FIG. 7. An important advantage of the device described here is that the input and output ports have the same frequency and are coherent with each other regardless of the phase of the overall pump. Thus, in the context of qubit readout, the readout receiver can be configured to phase - lock to the readout transmitter, and there is no need to require a precise phase relationship between the pump generator and the readout transmitter.

[0067] FIGS. 10A and 10B show the simulation parameters for the input signal at 4.0 GHz as a function of the signal phase with respect to the pump phase in terms of phase (degrees) and magnitude (dB), respectively. More specifically, FIG. 10A demonstrates in simulation that the amplified output of the directional amplifier follows the phase of the input signal (with a certain offset). FIG. 10B shows that the magnitude of the s - parameter does not depend on the signal phase with respect to the pump.

[0068] FIG. 11 shows a block diagram of a first exemplary coupling circuit for a parametric device according to an aspect of the present disclosure. More specifically, a coupling circuit 500 as shown in FIG. 11 can be used to implement one or more of the parametric devices 100, 200, 300, or 400 shown in the present disclosure. The coupling circuit 500 can include a first resonance mode 510, a first matching network 515, a second resonance mode 520, a second matching network 525, a third resonance mode 530, a third matching network 535, a passive coupling 540, a DC source 542, a first magnetic flux portion 544, a second magnetic flux portion 546, a first parametric coupling 550, a first Josephson junction 551, a first pump tone source 552, a third magnetic flux portion 554, a second parametric coupling 560, a second Josephson junction 561, a second pump tone source 562, and a fourth magnetic flux portion 564. The first pump tone source 552 and the second pump tone source 562 can be obtained from a single signal generator (not shown).

[0069] Still referring to FIG. 11, the various components of the coupling circuit 500 can correspond to the components shown in FIGS. 1-2 and described with reference to FIGS. 1-2 when the coupling circuit 500 is used to implement a circulator / isolator. Similarly, the various components of the coupling circuit 500 can correspond to the components shown in FIGS. 5-6 and described with reference to FIGS. 5-6 when the coupling circuit 500 is used to implement a directional amplifier. The descriptions of the corresponding components from FIGS. 1-2, FIGS. 5-6, and other related figures and descriptions are considered to be applicable to the corresponding components shown in FIG. 11 when appropriate.

[0070] For example, the first resonance mode 510 of FIG. 11 can correspond to, for example, the first resonance mode 110 of FIGS. 1 to 2, or the first resonance mode 310 of FIGS. 5 to 6. As shown in the figure, the first resonance mode 510 of FIG. 11 can be an LC resonator including a first capacitor 511 and a first inductor 512. The first matching network 515 of FIG. 11 can correspond to the additional first resonance modes 110', 110" and passive couplings 112, 112', 112" of FIG. 2, or the additional first resonance modes 310', 310" and passive couplings 312, 312', 312" of FIG. 6. The second resonance mode 520 of FIG. 11 can correspond to, for example, the second resonance mode 120 of FIGS. 1 to 2, or the second resonance mode 320 of FIGS. 5 to 6. As shown in the figure, the second resonance mode 520 of FIG. 11 can be an LC resonator including a second capacitor 521 and a second inductor 522. The second matching network 525 of FIG. 11 can correspond to the additional second resonance modes 120', 120" and passive couplings 122, 122', 122" of FIG. 2, or the additional second resonance modes 320', 320" and passive couplings 322, 322', 322" of FIG. 6. The third resonance mode 530 of FIG. 11 can correspond to, for example, the third resonance mode 130 of FIGS. 1 to 2, or the third resonance mode 330 of FIGS. 5 to 6. As shown in the figure, the third resonance mode 530 of FIG. 11 can be an LC resonator including a third capacitor 531 and a third inductor 532. The third matching network 535 of FIG. 11 can correspond to the additional third resonance modes 130', 130" and passive couplings 132, 132', 132" of FIG. 2, or the additional third resonance modes 330', 330" and passive couplings 332, 332', 332" of FIG. 6. The first resonance mode 510 and the third resonance mode 530 are both configured to operate at a first resonance frequency, and the second resonance mode 520 is configured to operate at a second resonance frequency different from the first resonance frequency.

[0071] Still referring to FIG. 11, the coupling circuit 500 includes a passive coupling 540 coupled between a first resonance mode 510 and a third resonance mode 530, which particularly corresponds to capacitive coupling. The first parametric coupling couples the first resonance mode 510 to the second resonance mode 520, and the second parametric coupling couples the second resonance mode 520 to the third resonance mode 530. The first parametric coupling 550 and the second parametric coupling 560 can each include respective Josephson junctions 551, 561, which are depicted as X-shaped circuit elements in the coupling circuit 500. More specifically, the first parametric coupling 550 located between the first resonance mode 510 and the second resonance mode 520 can correspond to an rf-SQUID composed of a first Josephson junction 551, an inductor 512, and an inductor 522. The second parametric coupling 560 located between the second resonance mode 520 and the third resonance mode 530 can correspond to an rf-SQUID composed of a second Josephson junction 561, an inductor 522, and an inductor 532.

[0072] The first parametric coupler 550 is pumped by a first pump tone source 552, and the second parametric coupler 560 is pumped by a second pump tone source 562. The first pump tone source 552 and the second pump tone source 562 are configured to be at the same frequency, but the phase of the first pump tone source 552 provided to the first parametric coupler 550 is shifted relative to the phase of the second pump tone source 562 provided to the second parametric coupler 560. In some exemplary embodiments, both the first pump tone source 552 and the second pump tone source 562 are provided by the same signal generator, thus minimizing the hardware space compared to implementations that do not have the same frequency ports that require pump sources at different frequencies. When the coupling circuit 500 is used to implement a circulator / isolator, the first pump tone source 552 and the second pump tone source 562 are generated at the same frequency defined as the difference between the first resonance frequency of the first resonance mode 510 and the third resonance mode 530 and the second resonance frequency of the second resonance mode 520. When the coupling circuit 500 is used to implement a directional amplifier, the first pump tone source 552 and the second pump tone source 562 are generated at the same frequency defined as the sum of the first resonance frequency of the first resonance mode 510 and the third resonance mode 530 and the second resonance frequency of the second resonance mode 520.

[0073] The configuration of circuit components in the coupling circuit 500, as well as the provision of the DC source 542, the first pump tone source 552, and the second pump tone source 562, induces current and corresponding magnetic flux within the coupling circuit 500. For example, the DC source 542 can be coupled to an inductor 543 that pairs with the second inductor 522 to form a bias transformer that induces a current resulting in a first magnetic flux portion 544 and a second magnetic flux portion 546. The first magnetic flux portion 544 can help ensure substantially zero passive coupling through an rf-SQUID including a first Josephson junction 551 such that only parametric coupling is provided between the first resonance mode 510 and the second resonance mode 520. The second magnetic flux portion 546 can help ensure substantially zero passive coupling through an rf-SQUID including a second Josephson junction 561 such that only parametric coupling is provided between the second resonance mode 520 and the third resonance mode 530. The first pump tone source 552 can be coupled to a first pump inductor 553 that pairs with the first inductor 512 to form a first pump transformer that induces a current resulting in a third magnetic flux portion 554. The second pump tone source 562 can be coupled to a second pump inductor 563 that pairs with the third inductor 532 to form a second pump transformer that induces a current resulting in a fourth magnetic flux portion 564. The first magnetic flux portion 544 and the third magnetic flux portion 554 are applied to the Josephson junction device 551 within the first parametric coupling 550. The second magnetic flux portion 546 and the fourth magnetic flux portion 564 are applied to the Josephson junction device 561 within the second parametric coupling 560.

[0074] FIG. 12 shows a block diagram of a second exemplary coupling circuit for a parametric device according to an aspect of the present disclosure. More specifically, a coupling circuit 600 as shown in FIG. 12 can be used to implement one or more of the parametric devices 100, 200, 300, or 400 shown in the present disclosure. The coupling circuit 600 includes a first resonance mode 610, a first matching network 615, a second resonance mode 620, a second matching network 625, a third resonance mode 630, a third matching network 635, a first parametric coupling 650 including a Josephson junction (JJ) array corresponding to a first plurality of JJ devices 651, 652, 653, 654, and a second parametric coupling 660 including a Josephson junction (JJ) array corresponding to a second plurality of JJ devices 661, 662, 663, 664.

[0075] Still referring to FIG. 12, the various components of the coupling circuit 600 can correspond to the components shown in FIGS. 1-2 and described with reference to FIGS. 1-2 when the coupling circuit 600 is used to implement a circulator / isolator. Similarly, the various components of the coupling circuit 600 can correspond to the components shown in FIGS. 5-6 and described with reference to FIGS. 5-6 when the coupling circuit 600 is used to implement a directional amplifier. The description of the corresponding components from FIGS. 1-2, FIGS. 5-6, and other related figures and descriptions is considered to apply to the corresponding components shown in FIG. 12 where appropriate.

[0076] For example, the first resonance mode 610 in FIG. 12 can correspond to, for example, the first resonance mode 110 in FIGS. 1 - 2 or the first resonance mode 310 in FIGS. 5 - 6. As shown, the first resonance mode 610 in FIG. 12 can be an LC resonator including a first capacitor 611 and a first inductor 612. The first matching network 615 in FIG. 12 can correspond to the additional first resonance modes 110', 110" and passive couplings 112, 112', 112" in FIG. 2, or the additional first resonance modes 310', 310" and passive couplings 312, 312', 312" in FIG. 6. The second resonance mode 620 in FIG. 12 can correspond to, for example, the second resonance mode 120 in FIGS. 1 - 2 or the second resonance mode 320 in FIGS. 5 - 6. As shown, the second resonance mode 620 in FIG. 12 can be an LC resonator including a second capacitor 621 and a second inductor 622. The second matching network 625 in FIG. 12 can correspond to the additional second resonance modes 120', 120" and passive couplings 122, 122', 122" in FIG. 2, or the additional second resonance modes 320', 320" and passive couplings 322, 322', 322" in FIG. 6. The third resonance mode 630 in FIG. 12 can correspond to, for example, the third resonance mode 130 in FIGS. 1 - 2 or the third resonance mode 330 in FIGS. 5 - 6. As shown, the third resonance mode 630 in FIG. 12 can be an LC resonator including a third capacitor 631 and a third inductor 632. The third matching network 635 in FIG. 12 can correspond to the additional third resonance modes 130', 130" and passive couplings 132, 132', 132" in FIG. 2, or the additional third resonance modes 330', 330" and passive couplings 332, 332', 332" in FIG. 6. The first resonance mode 610 and the third resonance mode 630 are both configured to operate at a first resonance frequency, and the second resonance mode 620 is configured to operate at a second resonance frequency different from the first resonance frequency.

[0077] Still referring to FIG. 12, the coupling circuit 600 includes a balanced JJ coupler that uses a first Josephson junction (JJ) array (e.g., a first plurality of JJ devices 651-654) as part of a first parametric coupling 650 between a first resonance mode 610 and a second resonance mode 620, and a second Josephson junction (JJ) array (e.g., a second plurality of JJ devices 661-664) as part of a second parametric coupling 660 between the second resonance mode 620 and a third resonance mode 630. The first plurality of JJ devices 651-654 forming the first JJ array and the second plurality of JJ devices 661-664 forming the second JJ array are depicted as X-shaped circuit elements in the coupling circuit 600 and can correspond to any Josephson junction device such as, for example, an rf-SQUID device or other suitable device. By including JJ arrays 650, 660 instead of a single JJ device as in the coupling circuit 500 of FIG. 11, a higher saturation power within the coupling circuit 600 can be achieved. Although not shown in FIG. 12, the coupling circuit 600 can also include additional circuit components such as, but not limited to, passive coupling (e.g., capacitive coupling) between the first resonance mode 610 and the third resonance mode 630, a pump transformer, and a bias transformer (such as those implemented by the DC source 542, the first pump tone source 552, the second pump tone source 562, and corresponding inductors and associated circuit components in FIG. 11).

[0078] FIG. 13 shows an exemplary embodiment of a readout device according to an exemplary aspect of the present disclosure. For example, FIG. 13 shows 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 according to the technology of the subject matter, such as, but not limited to, parametric devices 100, 200, 300, 400, or coupling circuits 500, 600. 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 signal source 744, a circulator / isolator 745, a directional amplifier 746, a pump source 747, an optional ferrite circulator 748, and a phase shifter 749. The second readout device 720 can include a low noise amplifier (LNA) 721, and the third readout device 730 can include a receiver 731.

[0079] More specifically, referring to FIG. 13, the plurality of readout resonators 740 and the control system 741 can be configured to couple to the plurality of qubits 742. The qubits 742 can be formed according to one or more of the same or different qubit technologies for quantum computing. For example, the qubits 742 can be or include superconducting qubits (e.g., transmon qubits), semiconductor quantum dots, trapped ion qubits, photonic qubits, defect-based qubits, topological nanowire qubits, or nuclear magnetic resonance qubits. The filter 743 (e.g., a Purcell filter or other bandpass filter) is coupled to the plurality of readout resonators 740 and can be configured to generate a bandpass response to the readout signals received by the plurality of readout resonators 740.

[0080] The readout system 700 of FIG. 13 can include at least a first Josephson parametric device configured to receive the output from the filter 743 as an input signal and generate an output signal. As shown, the first readout device 710 includes two Josephson parametric devices, namely, a first Josephson parametric device corresponding to the circulator / isolator 745 and a second Josephson parametric device corresponding to the directional amplifier 746. Additional circulator / isolator components can sometimes be included between the circulator / isolator 745 and the directional amplifier 746. When additional circulator / isolator components are included, such components can sometimes correspond to parametric circulators / isolators (e.g., parametric devices 100, 200 shown in FIGS. 1 - 3) as described herein, or alternatively, can correspond to conventional ferrite circulators (e.g., optional ferrite circulator 748). In a further embodiment, the readout system 700 can include a conventional ferrite circulator coupled to a parametric directional amplifier (e.g., parametric devices 300, 400 shown in FIGS. 5 - 6 and FIG. 8) as described herein.

[0081] Still referring to FIG. 13, the circulator / isolator 745 can be implemented, for example, as the parametric device 100 or 200 shown in FIGS. 1-3. Thus, the circulator / isolator 745 can include first, second, and third resonance modes, where the first and third resonance modes are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. The circulator / isolator 745 can also include a plurality of couplings including a passive coupling between the first and third resonance modes, a first parametric coupling between the first and second resonance modes, and a second parametric coupling between the second and third resonance modes. The first parametric coupling between the first and second resonance modes and the second parametric coupling between the second and third resonance modes in the circulator / isolator 745 can be configured to receive a pump tone signal characterized by a pump frequency defined as the difference between the first resonance frequency and the second resonance frequency. The pump tone signals for the first and second parametric couplings in the circulator / isolator 745 can be provided from a pump source 747, and one of the phase shifters 749 implements a phase offset between the respective pump tone signals provided to the first and second parametric couplings.

[0082] The directional amplifier 746 that forms the second Josephson parametric device can be configured to receive the output from the circulator / isolator 745 that forms the first Josephson parametric device as an input signal. The directional amplifier 746 can further be configured to generate an amplified output signal based on the readout from the qubit 742. The directional amplifier 746 can be implemented, for example, as the parametric device 300 or 400 shown in FIGS. 5-6 and FIG. 8. Thus, the directional amplifier 746 can include fourth, fifth, and sixth resonance modes, where the fourth and sixth resonance modes are both configured to operate at a third resonance frequency, and the fifth resonance mode is configured to operate at a fourth resonance frequency different from the third resonance frequency. The directional amplifier 746 can also include a plurality of couplings including a passive coupling between the fourth and sixth resonance modes, a first parametric coupling between the fourth and fifth resonance modes, and a second parametric coupling between the fifth and sixth resonance modes. The first parametric coupling between the fourth and fifth resonance modes and the second parametric coupling between the fifth and sixth resonance modes in the directional amplifier 746 can be configured to receive a pump tone signal characterized by a pump frequency defined as the sum of the third resonance frequency and the fourth resonance frequency. The pump tone signals for the first and second parametric couplings in the directional amplifier 746 can be provided from a pump source 747, and one of the phase shifters 749 implements a phase offset between the respective pump tone signals provided to the first and second parametric couplings.

[0083] The readout system 700 of FIG. 13 can also include additional readout devices provided at one or more temperature stages of the readout process. For example, Josephson parametric devices (e.g., a circulator / isolator 745 implemented as a first Josephson parametric device and a directional amplifier 746 implemented as a second Josephson parametric device) can be included within a first readout device 710 provided for readout at a lower temperature stage, and additional readout devices (e.g., a second readout device 720 and a third readout device 730) can be provided for readout at a higher temperature stage or subsequent signal processing. In some examples, the second readout device 720 can include a low-noise amplifier (LNA) 721 and / or other receiver components (e.g., a receiver 731) and can be provided at one or more higher temperatures. For example, the readout system 700 can include a first readout device 710 that includes one or more Josephson parametric devices (e.g., a circulator / isolator 745 implemented as a first Josephson parametric device and a directional amplifier 746 implemented as a second Josephson parametric device) configured to operate in a first temperature range (e.g., a cryogenic temperature range including less than about 1 kelvin (K) or less than about 100 millikelvin (mK)). The readout system 700 can further include at least one second readout device 720 (e.g., an LNA 721) coupled to and configured to receive an output from the first readout device 710 and configured to operate in a second temperature stage. In some examples, the second temperature range can be higher than the first temperature range and can be, for example, but not limited to, a range including about 4K or a range between about 1K and about 10K.The readout system 700 can be coupled to a second readout device 720, receive the output from the second readout device 720, and further include at least one third readout device 730 (e.g., a receiver 731) configured to operate in a third temperature range. In some examples, the third temperature range can be higher than the second temperature range and can be, for example, but not limited to, room temperature or a range near room temperature (e.g., a range including about 300K, or a range between about 250K and about 350K).

[0084] FIG. 14 shows an exemplary quantum computing system 800. The quantum computing system 800 is an example of a system on one or more classical computers or quantum computing devices at one or more locations where the systems, components, and techniques described below can be implemented. Those skilled in the art will understand that other quantum computing architectures or systems can be used without departing from the scope of the present disclosure using the disclosure provided herein.

[0085] The quantum computing system 800 can include quantum hardware 802 that communicates with one or more classical processors 804. One or more parameters 806 can be communicated from the one or more classical processors 804 to the quantum hardware 802, and one or more measurement results 808 can be communicated from the quantum hardware 802 to the one or more classical processors 804. The quantum hardware 802 can include components for performing quantum computing. For example, the quantum hardware 802 can include a quantum system 810, a control system 812, and a readout system 814. In some implementations, the control system 812 of FIG. 14 can correspond to the control system 741 of FIG. 13. In some implementations, the readout system 814 of FIG. 14 can correspond to or include aspects of the readout system 700 of FIG. 13.

[0086] Referring more specifically to FIG. 14, the quantum system 810 can include one or more multi-level quantum subsystems, such as a register of qubits. In some implementations, the multi-level quantum subsystem can include superconducting qubits such as flux qubits, charge qubits, transmon qubits, gmon qubits, etc. The type of multi-level quantum subsystem utilized by the quantum computing system 800 can vary. For example, in some cases, it may be convenient to include one or more readout devices within a readout system 814 attached to one or more superconducting qubits, such as transmon qubits, flux qubits, gmon qubits, xmon qubits, or other qubits. In other cases, ion traps, photonic devices, or superconducting cavities can be used. Further examples of the realization of the multi-level quantum subsystem include fluxmon qubits, silicon quantum dots, or phosphorus impurity qubits.

[0087] The quantum circuit can be constructed and applied within a register of qubits included in the quantum system 810 via a plurality of control lines coupled to the control system 812. The control system 812 can include control devices operating on the register of qubits and can be used to implement quantum gates, or quantum circuits having a plurality of quantum gates, such as Pauli gates, Hadamard gates, controlled NOT (CNOT) gates, controlled phase gates, T gates, multi-qubit quantum gates, coupler quantum gates, etc. The control system 812 can be configured to operate on the quantum system 810 via one or more respective control parameters (e.g., one or more physical control parameters). For example, in some implementations, the multi-level quantum subsystem can be a superconducting qubit, and the control devices within the control system 812 can be configured to provide control pulses to the control lines to generate a magnetic field for adjusting the frequency of the qubit.

[0088] The quantum hardware 802 of FIG. 14 may further include a readout system 814, such as one including one or more readout devices. For example, in some implementations, the readout system 814 can include a first readout device 710, a second readout device 720, and a third readout device 730 as shown in the readout system 700 of FIG. 13. Thus, the readout system 814 can include one or more Josephson parametric devices. Each Josephson parametric device within the readout system 814 can include at least first, second, and third resonance modes, where the first resonance mode and the third resonance mode are both configured to operate at a first resonance frequency, and the second resonance mode is configured to operate at a second resonance frequency different from the first resonance frequency. Each Josephson parametric device within the readout system 814 can also include a plurality of couplings including a passive coupling between the first resonance mode and the third resonance mode, a first parametric coupling between the first resonance mode and the second resonance mode, and a second parametric coupling between the second resonance mode and the third resonance mode. In some examples, one or more Josephson parametric devices within the readout system 814 include a first Josephson parametric device (e.g., the circulator / isolator 745 of FIG. 13) configured to operate as a circulator or isolator, and a second Josephson parametric device (e.g., the directional amplifier 746 of FIG. 13) configured to operate as a directional amplifier.

[0089] Still referring to FIG. 14, measurement results 808 obtained via a measurement device within quantum hardware 802 can be provided to classical processor 804 for processing and analysis. In some implementations, quantum hardware 802 can include a quantum circuit and a control system 812, and readout system 814 can implement one or more quantum logic gates operating on quantum system 810 via physical control parameters (e.g., microwave pulses) transmitted via wires included within quantum hardware 802. Further examples of control devices include any waveform generator where a DAC (digital-to-analog converter) creates a signal.

[0090] Readout system 814 can be configured to perform quantum measurements on quantum system 810 and transmit measurement results 808 to classical processor 804. In addition, quantum hardware 802 can be configured to receive data specifying physical control qubit parameter values (e.g., parameter 806) from classical processor 804. Quantum hardware 802 can use the received physical control qubit parameter values (e.g., parameter 806) to update the operation of control system 812 and readout system 814 on quantum system 810. For example, quantum hardware 802 can receive data specifying new values representing the voltage strength of one or more DACs included within control system 812, and accordingly update the operation of the DACs on quantum system 810. Classical processor 804 can be configured to initialize quantum system 810 to an initial quantum state, for example, by transmitting data specifying an initial set of parameters 806 to quantum hardware 802.

[0091] The readout system 814 can utilize the impedance difference between the |0> state and the |1> state of elements (such as qubits) of a quantum system like qubits to measure the state of the elements. For example, the resonance frequency of the readout resonator within the readout system 814 can take different values when the qubit is in the state |0> or the state |1> due to the non-linearity of the qubit. Thus, the microwave pulse reflected from the readout device within the readout system 814 carries an amplitude and / or phase shift that depends on the qubit state. In some implementations, a parcel filter (such as filter 743 in FIG. 13) can be used in combination with the readout device within the readout system 814 to impede microwave propagation at the qubit frequency.

[0092] The digital, classical, and / or quantum subjects described herein, as well as the implementations of digital functional operations and quantum operations, can be implemented tangibly in digital electronic circuits, in suitable quantum circuits, or more generally, in digital and / or quantum computer hardware, in digital and / or quantum computer software or firmware that includes the structures disclosed herein and their structural equivalents, or in one or more combinations thereof. The term "quantum computing system" can include, without limitation, a quantum computer / computing system, a quantum information processing system, a quantum cryptographic system, or a quantum simulator.

[0093] The implementations of the digital and / or quantum subject matter described herein 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, a data processing apparatus). The digital and / or quantum computer storage medium can be a machine-readable storage medium, a machine-readable storage substrate, a random or serial access memory device, one or more qubit / 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 propagation signal (e.g., a machine-generated electrical, optical, or electromagnetic signal) generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by a data processing apparatus and capable of encoding digital and / or quantum information.

[0094] The terms quantum information and quantum data refer to information or data carried, held, or stored by a quantum system, and the smallest non-trivial system is the qubit (i.e., the system that defines the unit of quantum information). It is understood that the term "qubit" encompasses all quantum systems that can be suitably approximated as two-level systems in the corresponding context. Such quantum systems can include, for example, multi-level systems having 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 considered to be the ground state and the first excited state, but it is understood that other settings are possible where the computational states are considered to be higher levels of excited states (e.g., qubits).

[0095] The term "data processing device" refers to digital and / or quantum data processing hardware, and includes, by way of example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, or multiple digital and quantum processors or computers, and combinations thereof, and all kinds of devices, apparatuses, and machines for processing digital and / or quantum data. The device can be, or further include, dedicated logic circuits, such as FPGAs (field programmable gate arrays), or ASICs (application specific integrated circuits), or quantum simulators, i.e., quantum data processing devices designed to simulate or generate information about a particular quantum system. In particular, a quantum simulator is a special-purpose quantum computer that does not have the ability to perform general quantum computing. The device can optionally include, in addition to the hardware, code that creates an execution environment for digital and / or quantum computer programs, such as processor firmware, protocol stacks, database management systems, operating systems, or code constituting one or more combinations thereof.

[0096] A digital or classical computer program, also called or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including a compiler-type language or an interpreter-type language, or a declarative language or a procedural language, and can be deployed in any form, either as a stand-alone program or as included as a module, component, subroutine, or other unit suitable for use in a digital computing environment. A quantum computer program, also called or described as a program, software, software application, module, software module, script, or code, can be written in any form of programming language, including a compiler-type language or an interpreter-type language, or a declarative language or a procedural language, can be translated into a suitable quantum programming language, or can be written in a quantum programming language, such as QCL, Quipper, or Cirq.

[0097] Digital and / or quantum computer programs, although not necessarily so, may correspond to files within a file system. The program may be stored within a part of a file that holds other programs or data, such as within one or more scripts stored within a markup language document, within a single file dedicated to the program in question, or within multiple coordinated files, such as files that store one or more modules, subprograms, or portions of code. Digital and / or quantum computer programs can be deployed to be executed on one digital or one quantum computer, or on multiple digital and / or quantum computers 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 can transmit quantum data using quantum systems, such as qubits. Generally, a digital data communication network cannot transmit quantum data, but a quantum data communication network can transmit both quantum data and digital data.

[0098] The processes and logical flows described herein, as appropriate, may be operated using one or more digital and / or quantum processors, perform operations on input digital and quantum data, and execute one or more digital and / or quantum computer programs to generate output, and can be executed by one or more programmable digital and / or quantum computers. The processes and logical flows can also be executed by dedicated logic circuits, such as FPGAs or ASICs, or quantum simulators, or by a combination of dedicated logic circuits or quantum simulators and one or more programmed digital and / or quantum computers, and the apparatus can be implemented as such.

[0099] For one or more digital and / or quantum computer systems or processors to be "configured" or "operable" to perform a particular operation or action means that the system has installed thereon software, firmware, hardware, or a combination thereof that causes the system to perform the operation or action during operation. For one or more digital and / or quantum computer programs to be configured to perform a particular operation or action means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform the operation or action. A quantum computer may receive from a digital computer instructions that, when executed by a quantum computing device, cause the device to perform an operation or action.

[0100] Digital and / or quantum computers suitable for the execution of digital and / or quantum computer programs can be based on general-purpose or special-purpose digital and / or quantum microprocessors, or both, or any other kind of central digital and / or quantum processing unit. Generally, the central digital and / or quantum processing unit receives instructions and digital and / or quantum data from read-only memory, random access memory, or a quantum system suitable for transmitting quantum data, such as photons, or a combination thereof.

[0101] Some exemplary elements of a digital and / or quantum computer are a central processing unit for executing or performing 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 complemented by, or incorporated into, dedicated logic circuitry or a quantum simulator. Generally, a digital and / or quantum computer also includes, or is operatively coupled to, one or more mass storage devices for storing digital and / or quantum data, such as magnetic disks, magneto-optical disks, optical disks, or a quantum system suitable for storing quantum information, so as to receive digital and / or quantum data from them, or to transmit digital and / or quantum data to them, or to do both. However, a digital and / or quantum computer need not have such devices.

[0102] Digital and / or quantum computer-readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include, by way of example, all forms of non-volatile digital and / or quantum memories, media, and memory devices, including semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, magnetic disks such as internal hard disks or removable disks, magneto-optical disks, CD-ROM and DVD-ROM disks, and quantum systems such as trapped atoms or electrons. A quantum memory is a device capable of storing quantum data with high fidelity and efficiency over a long period of time, and is understood, for example, to be an optical-matter interface in which light is used for transmission and matter is used to store and preserve quantum features of quantum data such as superposition or quantum coherence.

[0103] The control of the various systems or portions thereof described herein can be implemented in a digital and / or quantum computer program product that is stored on one or more tangible, non-transitory machine-readable storage media and includes instructions executable on one or more digital and / or quantum processing devices. The systems or portions thereof described herein can each be implemented as an apparatus, method, or electronic system that includes one or more digital and / or quantum processing devices and a memory storing executable instructions to perform the operations described herein.

[0104] This specification includes many details of specific implementations, which 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. The specific features described herein in the context of separate implementations may also be implemented in combination in a single implementation. Conversely, the various features described in the context of a single implementation may also be implemented separately in multiple implementations or in any suitable partial combination. Additionally, features may be described above as functioning in a particular combination and may even be initially claimed as such, but one or more features from the claimed combination may in some cases be removable from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0105] Similarly, the operations are depicted in the drawings in a particular order, but this should not be construed as requiring that such operations be performed in the particular order or sequence shown, or that all of the illustrated operations be performed, to achieve the desired result. Multitasking and parallel processing may be advantageous in certain circumstances. Further, the separation of various system modules and components in the implementation forms described above should not be construed as requiring such separation in all implementation forms, and it should be understood that the described program components and systems may generally be integrated in a single software product or packaged in multiple software products.

Explanation of Reference Numerals

[0106] 100 Parametric device 110 First (A) resonance mode, resonance mode, first resonance mode 110' First resonance mode 110" First resonance mode 111 First (A) port, first port 112 Passive coupling, coupling 112' Passive coupling, coupling 112" Passive coupling, coupling 120 Second (B) resonance mode, resonance mode, second resonance mode 120' Second resonance mode 120" Second resonance mode 121 Second (B) port, second port 122 Passive coupling, coupling 122' Passive coupling, coupling 122" Passive coupling, coupling 130 Third (B) resonance mode, resonance mode, third resonance mode 130' Third resonance mode 130" Third resonance mode 131 Third (C) port, third port 132 Passive coupling, coupling 132' Passive coupling, coupling 132" Passive coupling, coupling 140 Passive coupling 150 Parametric coupling 155 Pump tone signal 160 Parametric coupling 165 Pump tone signal 200 Parametric device 300 Parametric device 310 First (A) resonance mode, resonance mode, first resonance mode 310' First resonance mode 310" First resonance mode 311 First (A) port, first port 320 Second (A) resonance mode, resonance mode, second resonance mode 320' Second resonance mode 320" Second resonance mode 321 Second (B) port, second port 330 Third (A) resonance mode, resonance mode, third resonance mode 330' Third resonance mode 330" Third resonance mode 331 Third (C) port, third port 340 Passive coupling 350 First parametric coupling 355 First pump tone signal 360 Second parametric coupling 365 Second pump tone signal 400 Parametric device 500 Coupling circuit 510 First resonance mode 511 First capacitor 512 First inductor, inductor 515 First matching network 520 Second resonance mode 521 Second capacitor 522 Second inductor, inductor 525 Second matching network 530 Third resonance mode 531 Third capacitor 532 Third inductor, inductor 535 Third matching network 540 Passive coupling 542 DC source 543 Inductor 544 First magnetic flux portion 546 Second magnetic flux portion 550 First parametric coupling 551 First Josephson junction, Josephson junction, Josephson junction device 552 First pump tone source 553 First pump inductor 554 Third magnetic flux portion 560 Second parametric coupling 561 Second Josephson junction, Josephson junction, Josephson junction device 562 Second pump tone source 564 Fourth magnetic flux portion 600 Coupling circuit 610 First resonance mode 611 First capacitor 612 First inductor 615 First matching network 620 Second resonance mode 621 Second capacitor 622 Second inductor 625 Second matching network 630 Third resonance mode 631 Third capacitor 632 Third inductor 635 Third matching network 650 First parametric coupling, JJ array 651 JJ device 652 JJ device 653 JJ device 654 JJ device 660 Second parametric coupling, JJ array 661 JJ device 662 JJ device 663 JJ device 664 JJ device 700 Readout system 710 Readout device, first readout device 720 Readout device, second readout device 721 Low-noise amplifier (LNA), LNA 730 Readout device, third readout device 731 Receiver 740 Readout resonator 741 Control system 742 Qubit 743 Filter 744 Signal source 745 Circulator / Isolator 746 Directional amplifier 747 Pump source 748 Ferrite circulator 749 Phase shifter 800 Quantum computing system 802 Quantum hardware 804 Classical processor 806 Parameter 808 Measurement result 810 Quantum system 812 Control system 814 Readout system

Claims

1. A parametric device, comprising: a first resonator, a second resonator, and a third resonator, wherein both the first resonator and the third resonator are configured to operate at a first resonance frequency, and the second resonator is configured to operate at a second resonance frequency different from the first resonance frequency, the first resonator, the second resonator, and the third resonator; a passive coupling between the first resonator and the third resonator; a first parametric coupling between the first resonator and the second resonator; a second parametric coupling between the second resonator and the third resonator; an input port coupled to the first resonator of the parametric device; an output port coupled to the third resonator of the parametric device A parametric device comprising the above.

2. The parametric device according to claim 1, wherein the first parametric coupling comprises at least one Josephson junction configured to function as a modulation reactance and configured to receive a first pump tone signal characterized by a first pump frequency. The second parametric coupling, wherein the second parametric coupling comprises at least one Josephson junction configured to function as a modulation reactance and configured to receive a second pump tone signal characterized by a second pump frequency. The parametric device according to claim 1.

3. The parametric device according to claim 2, further comprising a single signal generator configured to provide both the first pump tone signal and the second pump tone signal.

4. The parametric device is configured to operate as a circulator, the first pump frequency and the second pump frequency are the same frequency, and are frequencies defined as the difference between the first resonance frequency and the second resonance frequency, and the phase of the first pump tone signal provided to the first parametric coupling is shifted relative to the phase of the second pump tone signal provided to the second parametric coupling. The parametric device according to claim 2.

5. The parametric device is configured to operate as a directional amplifier. The first pump frequency and the second pump frequency are the same frequency and are frequencies defined as the sum of the first resonance frequency and the second resonance frequency. The phase of the first pump tone signal provided to the first parametric coupling is shifted with respect to the phase of the second pump tone signal provided to the second parametric coupling. The parametric device according to claim 2.

6. The parametric device is coupled to the second resonator and includes an impedance that provides an internal termination for the second resonator. The parametric device is configured to operate as an isolator. The parametric device according to claim 2.

7. A matching circuit including one or more additional first resonators coupled between the first resonator and the input port, one or more additional second resonators coupled to the second resonator, and one or more additional third resonators coupled between the third resonator and the output port, the matching circuit providing impedance matching over a specified frequency band to the input port and the output port, the parametric device according to any one of claims 1 to 6.

8. Additional passive couplings are provided between the first resonator and the one or more additional first resonators, between the one or more additional first resonators and the input port, between the second resonator and the one or more additional second resonators, between the one or more additional second resonators and the internal termination, between the third resonator and the one or more additional third resonators, and between the one or more additional third resonators and the output port, the parametric device according to claim 7.

9. The parametric device according to claim 8, wherein one or more of the passive coupling and the additional passive coupling between the first resonator and the third resonator include capacitive coupling.

10. The parametric device according to claim 8, wherein one or more of the passive coupling and the additional passive coupling between the first resonator and the third resonator include inductive coupling.

11. The parametric device according to any one of claims 1 to 6, wherein the first resonator, the second resonator, and the third resonator include lumped element LC resonators.

12. A plurality of resonators configured to couple to respective plural qubits, A filter coupled to the plurality of resonators and configured to generate a bandpass response to a readout signal received by the plurality of resonators, A first Josephson parametric device configured to receive an output from the filter as an input signal and generate a first output signal, wherein the first Josephson parametric device includes A first resonator, a second resonator, and a third resonator, wherein the first resonator and the third resonator are both configured to operate at a first resonance frequency, and the second resonator is configured to operate at a second resonance frequency different from the first resonance frequency, A plurality of couplings including a passive coupling between the first resonator and the third resonator, a first parametric coupling between the first resonator and the second resonator, and a second parametric coupling between the second resonator and the third resonator Comprising a first Josephson parametric device A readout system for a quantum computing device.

13. Comprising a second Josephson parametric device configured to receive the first output signal from the first Josephson parametric device and generate a second output signal, wherein the second Josephson parametric device includes A fourth resonator, a fifth resonator, and a sixth resonator, wherein the fourth resonator and the sixth resonator are both configured to operate at a third resonance frequency, and the fifth resonator is configured to operate at a fourth resonance frequency different from the third resonance frequency, A plurality of couplings including a passive coupling between the fourth resonator and the sixth resonator, a first parametric coupling between the fourth resonator and the fifth resonator, and a second parametric coupling between the fifth resonator and the sixth resonator Comprising The readout system according to claim 12.

14. The first Josephson parametric device is configured to operate as a circulator, the first parametric coupling between the first resonator and the second resonator and the second parametric coupling between the second resonator and the third resonator are configured to receive a first pump tone signal characterized by a first pump frequency defined as the difference between the first resonance frequency and the second resonance frequency, the second Josephson parametric device is configured to operate as a directional amplifier, the first parametric coupling between the fourth resonator and the fifth resonator and the second parametric coupling between the fifth resonator and the sixth resonator are configured to receive a second pump tone signal characterized by a second pump frequency defined as the sum of the third resonance frequency and the fourth resonance frequency, The readout system according to claim 13.

15. The phase of the first pump tone signal provided to the first parametric coupling between the first resonator and the second resonator is shifted with respect to the phase of the first pump tone signal provided to the second parametric coupling between the second resonator and the third resonator, The phase of the second pump tone signal provided to the first parametric coupling between the third resonator and the fourth resonator is shifted with respect to the phase of the second pump tone signal provided to the second parametric coupling between the fifth resonator and the sixth resonator, The readout system according to claim 14.

16. A first signal generator for generating a first pump tone signal provided to the first parametric coupling and the second parametric coupling, a second signal generator for generating a second pump tone signal provided to the third parametric coupling and the fourth parametric coupling The readout system according to claim 14, comprising.

17. The first Josephson parametric device is One or more additional first resonators coupled between the first resonator and the input port, one or more additional second resonators coupled between the second resonator and the internal termination, and one or more additional third resonators coupled between the third resonator and the output port, the matching circuit providing impedance matching over a specified frequency band to the input port and the output port. The readout system according to claim 12.

18. Quantum hardware comprising a plurality of qubits, A readout system coupled to the plurality of qubits for receiving readout responses of the plurality of qubits, the readout system comprising one or more Josephson parametric devices, each Josephson parametric device A first resonator, a second resonator, and a third resonator, wherein the first resonator and the third resonator are both configured to operate at a first resonance frequency, and the second resonator is configured to operate at a second resonance frequency different from the first resonance frequency, the first resonator, the second resonator, and the third resonator A plurality of couplings including a passive coupling between the first resonator and the third resonator, a first parametric coupling between the first resonator and the second resonator, and a second parametric coupling between the second resonator and the third resonator A readout system comprising A quantum computing system comprising

19. A signal generator configured to generate a pump tone signal provided to both the first parametric coupling and the second parametric coupling, The phase of the pump tone signal provided to the first parametric coupling is shifted in phase relative to the pump tone signal provided to the second parametric coupling. The quantum computing system according to claim 18.

20. The quantum computing system according to claim 18, wherein the one or more Josephson parametric devices comprise a first Josephson parametric device configured to operate as a circulator or an isolator and a second Josephson parametric device configured to operate as a directional amplifier.

21. A method for measuring the state of an element of a quantum computing system, the method comprising measuring, by a readout system comprising the parametric device according to any one of claims 1 to 6, the amplitude and / or phase shift of a microwave pulse reflected from the parametric device.

22. A method for measuring the state of an element of a quantum computing system, the method comprising measuring, by a readout system according to any one of claims 12 to 17, the amplitude and / or phase shift of a microwave pulse reflected from a first parametric device.

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