Superconducting qubit and resonator system based on Josephson ring modulator

Abstract

A superconducting quantum mechanical device includes a first Josephson junction, a second Josephson junction, a third Josephson junction, and a fourth Josephson junction connected in a bridge circuit having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode. The device further includes a first capacitor pad and a second capacitor pad. The first capacitor pad, the second capacitor pad, and the bridge circuit form a superconducting qubit having a resonant frequency corresponding to the first resonant eigenmode. The device further includes a first resonator section and a second resonator section. The first resonator section, the second resonator section, and the bridge circuit form a resonator having a resonant frequency corresponding to the second resonant eigenmode. The device further includes a magnetic flux source disposed near the bridge circuit. The magnetic flux source is configured to provide a magnetic flux through the bridge circuit during operation to cause coupling between the first resonant eigenmode, the second resonant eigenmode, and the third resonant eigenmode when the third resonant eigenmode is excited.

Description

Technical Field

[0001] The presently claimed embodiments of the present invention relate to superconducting quantum mechanical devices, and more particularly to a superconducting quantum mechanical device having a superconducting qubit coupled to a superconducting resonator within the same device. Background Art

[0002] Circuit Quantum Electrodynamics (cQED) is a fundamental and common building block in quantum processor architectures. cQED includes superconducting qubits coupled to superconducting resonators. The resonance frequencies of the qubits and resonators are typically different. For example, the qubit frequency can be about 5 GHz, while the resonator frequency can be about 7 GHz. When the frequencies are different, the coupling is referred to as dispersive coupling. There are various types of qubits that can be used, including for example transmons, fluxonium, capacitively-shunted qubits, etc. There are also various geometries of superconducting resonators that can be used, including for example coplanar waveguide resonators, stripline resonators, microstrip resonators, three-dimensional cavities, etc. Examples of superconducting materials that can be used for the resonators include but are not limited to Nb, Al, TiN, NbTiN, NbN, etc. Various mechanisms can be employed to couple the qubits to the resonators, including capacitive coupling (e.g., through a capacitor) and inductive coupling (e.g., through mutual inductance).

[0003] cQED is used for many applications, including: 1) the resonator serves as a bandpass filter between the qubit and the external circuit to filter out noise entering through the line at the qubit frequency; 2) the qubit can be driven and controlled by injecting qubit pulses via the resonator port; and 3) the qubit state can be measured by detecting changes in the resonator frequency affected by the qubit state.

[0004] To measure the state of a qubit using the cQED architecture, a readout signal close to the readout resonator frequency is sent to the resonator. Due to the coupling (capacitive or inductive) between the qubit and the resonator, the resonator frequency depends on the qubit state. In other words, the resonance frequency of the readout resonator is different when the qubit is in the ground state compared to when the qubit is in the excited state. Due to the correlation between the readout resonator resonance frequency and the qubit state, the frequency of the readout signal is set to be in the middle between these two resonance frequencies. By monitoring or measuring the phase shift of the reflected readout signal, the qubit state can be determined because the phase shift will be different depending on the resonance frequency of the readout resonator, which depends on the qubit state.

[0005] Thus, in cQED, the readout resonator can protect the qubit from electromagnetic noise from the external environment. cQED also allows for relatively precise and sensitive measurement of the qubit state using the resonator. cQED allows for the implementation of quantum non-demolition measurements of the qubit state. In summary, the theory of cQED is well-developed, and the cQED architecture is relatively easy to implement and scale up.

[0006] However, in cQED, the coupling between the qubit and the readout resonator is always on. Thus, any noise photons (thermal or non-thermal) present in the readout resonator can cause the qubit state to dephase and lose its phase coherence. One way to avoid this problem is to increase the bandwidth of the resonator to reduce the time it takes to measure the qubit. However, increasing the bandwidth of the resonator to reduce the time it takes to measure the qubit can also lead to a reduction in the qubit lifetime (due to the Purcell effect). To counteract the Purcell effect and still provide relatively fast readout, a Purcell filter is typically added to the readout resonator. A Purcell filter is a microwave filter that has near unity transmission at the readout frequency but large attenuation at the qubit frequency. Thus, this solution adds hardware complexity to the quantum processor architecture.

[0007] For qubits coupled to a relatively slow (narrow bandwidth) readout resonator, the qubit dephasing caused by long-lived readout photons (which are part of the readout pulse) can be reduced by rapidly emptying the readout resonator of photons using a specific pulse sequence (such as the CLEAR method) applied to the readout resonator. This solution also adds software, pulse, and timing complexity to the quantum processor architecture.

[0008] In conventional devices, to reduce the photon population inside the readout resonator and thus reduce qubit dephasing, the coupling between the qubit and the readout resonator and the presence of noise photons place strict requirements on the qubit setup. For example, the readout resonator is well-thermalized to the base temperature level, the power of the applied pulses is kept as low as possible to prevent thermal effects, the thermal dissipation in the environment coupled to the readout resonator should also be minimized, and cryogenic isolators and circulators are added to the output line to protect against noise including electromagnetic noise such as amplified noise or thermal noise such as blackbody radiation at the readout frequency. These cryogenic circulators and isolators are large, difficult to thermalize, expensive, heavy, and use magnetic materials and strong magnetic fields that can have a negative impact on superconducting circuits. SUMMARY OF THE INVENTION

[0009] One aspect of the present invention is to provide a superconducting quantum mechanical device. The superconducting quantum mechanical device includes a first Josephson junction, a second Josephson junction electrically connected to the first Josephson junction, a third Josephson junction electrically connected to the second Josephson junction, and a fourth Josephson junction electrically connected to the third Josephson junction and the first Josephson junction, such that the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction are connected in a bridge circuit having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode. The superconducting quantum mechanical device further includes a first capacitor pad electrically connected to the first Josephson junction and the fourth Josephson junction at a node between the first Josephson junction and the fourth Josephson junction, and a second capacitor pad electrically connected to the second Josephson junction and the third Josephson junction at a node between the second Josephson junction and the third Josephson junction, such that the first capacitor pad, the second capacitor pad, and the bridge circuit form a superconducting qubit having a resonant frequency corresponding to the first resonant eigenmode of the bridge circuit. The superconducting quantum mechanical device further includes a first resonator portion and a second resonator portion. The first resonator portion is electrically connected to the first Josephson junction and the second Josephson junction at a node between the first Josephson junction and the second Josephson junction, and the second resonator portion is electrically connected to the third Josephson junction and the fourth Josephson junction at a node between the third Josephson junction and the fourth Josephson junction, such that the first resonator portion, the second resonator portion, and the bridge circuit form a resonator having a resonant frequency corresponding to the second resonant eigenmode. The superconducting quantum mechanical device further includes a magnetic flux source disposed near the bridge circuit. The magnetic flux source is configured to provide a magnetic flux through the bridge circuit during operation to cause coupling between the first resonant eigenmode, the second resonant eigenmode, and the third resonant eigenmode when the third resonant eigenmode is excited.

[0010] In one embodiment, the magnetic flux source is a current-carrying element to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit. In one embodiment, the magnetic flux source is a magnetic material to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit. In one embodiment, the magnetic flux source is controllable. In one embodiment, the magnetic flux source provides half of a flux quantum

[0011] In one embodiment, the superconducting qubit is a transmon-like qubit. In one embodiment, both the first resonator portion and the second resonator portion are resonator lines of substantially equal length. In one embodiment, the first resonator portion and the second resonator portion include resonator lines disposed between electrical ground pads.

[0012] In one embodiment, the superconducting quantum mechanical device further includes a resonator feeder configured to be electromagnetically coupled to the resonator to provide excitation of a second resonant eigenmode during operation. In one embodiment, the resonator feeder is separated from the resonator to define a capacitor between the resonator feeder and the resonator.

[0013] In one embodiment, the superconducting quantum mechanical device further includes a qubit feeder configured to be electromagnetically coupled to the superconducting qubit to provide excitation of a first resonant eigenmode during operation. In one embodiment, the qubit feeder is separated from the superconducting qubit to define a capacitor between the qubit feeder and the superconducting qubit. In one embodiment, the superconducting qubit and the resonator are formed on the same substrate, and the bridge circuit is substantially located at the common center of the superconducting qubit and the resonator.

[0014] In one embodiment, the first resonator portion, the second resonator portion, the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction include a superconducting material selected from the group consisting of Al, Nb, NbTiN, NbN, and TiN.

[0015] In one embodiment, a control drive applied to the superconducting qubit or the resonator is used to excite a third resonant eigenmode. In one embodiment, the frequency of the control drive is set to the difference between the qubit frequency of the superconducting qubit and the resonant frequency of the resonator. In one embodiment, the amplitude of the control drive is set to produce a full frequency conversion between the superconducting qubit and the resonator. In one embodiment, the amplitude of the control drive is set to produce a 50:50 beam splitter, where half of the qubit information is exchanged with half of the resonator information. In one embodiment, the frequency of the control drive is set to the sum of the qubit frequency of the superconducting qubit and the resonant frequency of the resonator, and the amplitude of the control drive is set to produce two-mode squeezing of the qubit mode and the resonator mode. In one embodiment, the frequency of the control drive is in the microwave frequency range.

[0016] This quantum mechanical device has many benefits, including protecting qubits from dephasing due to photons or photon noise in the resonator during qubit initialization, single-qubit gates, and / or multi-qubit gates. This is because the qubit mode (X mode) and the resonator mode (Y mode) are orthogonal. The X mode is orthogonal to the Y mode, and the two modes can only be coupled or interact via a third mode (Z mode) when the control drive signal is on. Therefore, this protection feature allows the device to reduce the number of cryogenic isolators and circulators required on the output line. Additionally, qubits may be vulnerable to photon noise in the common third mode (Z mode) of the circuit. However, because the Z mode is at a different frequency from the readout resonator frequency (Y mode), the input and output lines can be filtered within a frequency band near this unique frequency without using circulators and / or isolators. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The concepts of the present invention, as well as the functions of the relevant elements of the method and structure of operation, and the combination of components and the economy of manufacture, will become more apparent by considering the following description and the appended claims in conjunction with the accompanying drawings, all of which form a part of this specification, wherein like reference numerals refer to corresponding parts in the respective drawings. However, it should be clearly understood that the drawings are for illustrative and descriptive purposes only and are not intended as a definition of the limits of the present invention.

[0018] Figure 1 is a schematic diagram of a superconducting quantum mechanical device according to an embodiment of the present invention;

[0019] Figure 2 is a schematic diagram of a superconducting quantum mechanical device according to another embodiment of the present invention; and

[0020] Figures 3A - 3C shows a bridge circuit having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] Figure 1Schematic diagram of a superconducting quantum mechanical device 100 according to an embodiment of the present invention. The superconducting quantum mechanical device 100 includes a first Josephson junction 102, a second Josephson junction 104 electrically connected to the first Josephson junction 102, a third Josephson junction 106 electrically connected to the second Josephson junction 104, and a fourth Josephson junction 108 electrically connected to the third Josephson junction 106 and the first Josephson junction 102, such that the first Josephson junction 102, the second Josephson junction 104, the third Josephson junction 106, and the fourth Josephson junction 108 are connected in a bridge circuit 110. The bridge circuit 110 has a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode. The bridge circuit 110 is similar to a conventional Wheatstone bridge. However, instead of resistors in a conventional Wheatstone bridge, the bridge circuit 110 has at least four Josephson junctions arranged in a similar configuration.

[0022] Figures 3A - 3C Shows a bridge circuit 110 having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode according to an embodiment of the present invention. For example, Figures 3A - 3C Shows the rf voltage polarities corresponding to the first eigenmode, the second eigenmode, and the third eigenmode at the bridge nodes. Figure 3A Shows the bridge circuit 110 operating in the first eigenmode (X mode). Figure 3B Shows the bridge circuit 110 operating in the second eigenmode (Y mode). Figure 3C Shows the bridge circuit 110 operating in the third eigenmode (Z mode). In some embodiments, the first eigenmode, the second eigenmode, and the third eigenmode are orthogonal to each other. The bridge circuit 110, which can be a Josephson ring modulator (JRM) in some embodiments, is a nonlinear dispersive circuit based on Josephson tunnel junctions (e.g., four Josephson junctions), and this nonlinear dispersive circuit can perform three-wave mixing of electromagnetic signals (e.g., microwave signals) under quantum confinement. However, the general concept of the present invention is not limited to only four Josephson junctions. According to some embodiments, additional Josephson junctions can be included in one or more branches of the bridge circuit 110.

[0023] The superconducting quantum mechanical device 100 further includes a first capacitor pad 112 electrically connected to the first Josephson junction 102 and the fourth Josephson junction 108 at node 1 between the first Josephson junction 102 and the fourth Josephson junction 108. The superconducting quantum mechanical device 100 further includes a second capacitor pad 114 electrically connected to the second Josephson junction 104 and the third Josephson junction 106 at node 2 between the second Josephson junction 104 and the third Josephson junction 106. The first capacitor pad 112, the second capacitor pad 114, and the bridge circuit 110 form a superconducting qubit 116. The superconducting qubit 116 has a resonance frequency (f Q ) corresponding to the first resonance eigenmode (X-mode) of the bridge circuit 110.

[0024] The superconducting quantum mechanical device 100 further includes a first resonator portion 120 electrically connected to the first Josephson junction 102 and the second Josephson junction 104 at node 3 between the first Josephson junction 102 and the second Josephson junction 104. The superconducting quantum mechanical device 100 further includes a second resonator portion 122 electrically connected to the third Josephson junction 106 and the fourth Josephson junction 108 at node 4 between the third Josephson junction 106 and the fourth Josephson junction 108. The first resonator portion 120, the second resonator portion 122, and the bridge circuit 110 form a resonator 126 having a resonance frequency (f R ) corresponding to the second resonance eigenmode (Y-mode) of the bridge circuit 110.

[0025] The superconducting quantum mechanical device 100 further includes a magnetic flux source 128 disposed near the bridge circuit 110. The magnetic flux source 128 is configured to provide a magnetic flux through the bridge circuit 110 during operation to cause coupling between the first resonance eigenmode, the second resonance eigenmode, and the third resonance eigenmode (X-mode, Y-mode, and Z-mode) when the third resonance eigenmode (Z-mode) is externally driven and excited.

[0026] In one embodiment, the magnetic flux source 128 is a current-carrying element to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit (loop) 110. In another embodiment, the magnetic flux source 128 is a magnetic material to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit (loop) 110. The magnetic flux source 128 is not limited to these specific examples. It can be a combination of one or more current-carrying elements and / or one or more magnets formed of magnetic materials. In one embodiment, the magnetic flux source 128 can be controlled and can be set to provide zero flux. When no magnetic flux passes through the bridge circuit (loop) 110, the coupling constant between the three eigenmodes disappears. In another embodiment, the magnetic flux source 128 can be set to provide half of the flux quantum In this case, coupling is generated among three eigenmodes.

[0027] In one embodiment, the superconducting qubit 116 is a transmon-like qubit. For example, the superconducting qubit 116 can be a transmon-like qubit.

[0028] In one embodiment, the first resonator portion 120 includes a resonator line 120A, and the second resonator portion 122 includes a resonator line 122A. In one embodiment, the lines 120A and 122A have substantially equal lengths. In one embodiment, the first resonator portion 120 and the second resonator portion 122 are coplanar. In one embodiment, the first resonator portion 120 and the second resonator portion 122 include microstrip or stripline. In one embodiment, the first resonator portion 120 and the second resonator portion 122 include the resonator lines 120A and 122A disposed between electrical ground pads 130.

[0029] In one embodiment, the first resonator portion 120, the second resonator portion 122, the first Josephson junction 102, the second Josephson junction 104, the third Josephson junction 106, and the fourth Josephson junction 108 include superconducting materials such as, but not limited to, Al, Nb, NbTiN, NbN, and TiN.

[0030] In one embodiment, the superconducting qubit 116 and the resonator 126 are formed on the same substrate, and the bridge circuit 110 is substantially located at the common center of the superconducting qubit 116 and the resonator 126 and is incorporated into the superconducting qubit 116 and the resonator 126.

[0031] In one embodiment, the superconducting quantum mechanical device 100 further includes a resonator feeder 132 that is configured to be electromagnetically coupled to the resonator 126 and carry input and output readout signals at a readout frequency that excites a second eigenmode (Y mode). In one embodiment, the resonator feeder 132 is separated from the resonator 126 so as to define a capacitor 134 between the resonator feeder 132 and the resonator 126. In one embodiment, the capacitor 134 is defined by the spacing between the resonator feeder 132 and the first resonator portion 120 of the resonator 126. The capacitor 134 can electromagnetically couple the resonator feeder 132 to the resonator 126. The excitation of the second eigenmode (Y mode) can be achieved by sending a drive signal through the resonator feeder 132 to the resonator 126. For example, in one embodiment, the drive signal can have a frequency in the microwave range. However, the drive signal can also have a frequency in a higher frequency range or a lower frequency range.

[0032] In one embodiment, the superconducting quantum mechanical device 100 further includes a qubit feeder 136 configured to be electromagnetically coupled to the superconducting qubit 116 to provide excitation of a first resonant eigenmode (X-mode) during operation. In one embodiment, the qubit feeder 136 is separated from the superconducting qubit 116 to define a capacitor 138 between the qubit feeder 136 and the superconducting qubit 116. In one embodiment, the capacitor 138 is defined by the spacing between the qubit feeder 136 and the capacitor pad 114 of the qubit 116. The capacitor 138 can electromagnetically couple the qubit feeder 136 to the qubit 116. Excitation of the first resonant eigenmode (X-mode) can be accomplished by sending a drive signal through the qubit feeder 136 to the qubit 116. Excitation of the first, second, or third eigenmode can be achieved by applying a drive signal (e.g., a drive signal in the microwave frequency range) via the resonator feeder 132 or the qubit feeder 136.

[0033] In one embodiment, a control drive signal applied to the superconducting qubit 116 through the qubit feeder 136 or to the resonator 126 through the resonator feeder 132 is used to excite a third resonant eigenmode (Z-mode). In one embodiment, the frequency of the control drive is set to the difference between the qubit frequency (f Q ) of the superconducting qubit 116 and the resonator frequency (f R ) of the resonator 126. In one embodiment, the amplitude of the control drive is set to produce full frequency conversion between the superconducting qubit 116 and the resonator 126. In another embodiment, the amplitude of the control drive is set to produce a 50:50 beam splitter, where half of the qubit information is exchanged with half of the resonator information.

[0034] Figure 2 is a schematic circuit diagram of a superconducting quantum mechanical device 200 according to another embodiment of the present invention. The superconducting quantum mechanical device 200 is similar in many respects to the superconducting quantum mechanical device 100 described in the above paragraph. Therefore, in Figure 2 the same reference numerals are used to denote common components between the superconducting quantum mechanical devices 100 and 200, and only the different features are highlighted in the following paragraphs.

[0035] In one embodiment, the superconducting quantum mechanical device 200 further includes pads 202 connected to node 3 of the bridge circuit 110 and the first resonator section 120, and pads 204 connected to node 4 of the bridge circuit 110 and the second resonator section 122. For example, pad 202 may be provided and connected to the end of line 120A of the first resonator section 120 adjacent to node 3, and pad 204 may be connected to the end of line 122A of the second resonator section 122 adjacent to node 4. In another embodiment, instead of using pads 202 and 204, the widths of the ends of line 120A and the ends of line 122A may be made larger. Providing pads 202 and 204 or widening the ends of lines 120A and 122A allows for reducing charge dispersion at nodes 3 and 4 by increasing the shunt capacitors across Josephson junctions 102, 104, 106, and 108.

[0036] The superconducting quantum mechanical devices 100 and 200 have multiple benefits, including protecting the qubits 116 from dephasing due to photons or photon noise in the resonator 126 during qubit initialization, single qubit gates, and / or multiqubit gates. This is because the qubit mode (X mode) and the resonator mode (Y mode) are orthogonal. The X mode is orthogonal to the Y mode, and these two modes can only be coupled or can interact via the Z mode when the control drive signal is on. Therefore, this protection feature allows for reducing the number of cryogenic isolators and circulators on the output line. Additionally, the qubits 116 may be vulnerable to photon noise in the common mode (Z mode) of the circuit. However, since the Z mode is at a different frequency from the readout resonator frequency (Y mode), the input line and the output line can be filtered within a frequency band near this unique frequency without using a circulator and / or an isolator.

[0037] As described in the above paragraphs, in one embodiment, the frequency (f D ) of the control drive can be set to the difference between the qubit frequency (f Q ) of the superconducting qubit 116 and the resonator frequency (f R ) of the resonator 126, f D = |f Q - f R |, and the drive amplitude / power can be set to produce a full frequency conversion between the qubit and the resonator. This operating mode can be used to measure the qubit state. By applying a control drive (excitation or no excitation), the qubit state is exchanged with the resonator readout photons. By measuring the output readout photons, the qubit state can be inferred. Notably, the resonator 120 can be used as a storage resonator (i.e., a memory) instead of a readout resonator.

[0038] As described in the above paragraphs, in another embodiment, the amplitude of the control drive can be set to produce a 50:50 beam split, where half of the qubit information is exchanged with half of the resonator information. In this case, the control drive frequency remains f D =|f Q -f R |. However, the amplitude or power is set to produce a 50:50 beam splitter point, where half of the qubit information is exchanged with half of the resonator information, while the other half remains in the qubit and the resonator. By measuring the output readout photon, the qubit state can be entangled with the flying photon, i.e., the output readout photon. Therefore, by measuring the output readout photon, the qubit state can be inferred.

[0039] In another embodiment, the control drive frequency f D can alternatively be set to be equal to the sum of the qubit frequency f Q and the resonator frequency f R . f D =|f Q +f R | and the drive amplitude or power can be set to produce two-mode squeezing of the qubit mode and the resonator mode. Due to the longitudinal coupling between the resonator and the qubit, this operating mode can provide a very fast and high-fidelity readout of the qubit state (faster than cQED using transverse coupling). This operating mode can eliminate the need for a quantum-limited Josephson amplifier in the readout chain and the overhead and losses of the necessary intermediate stages.

[0040] In yet another embodiment, a full conversion mode can be achieved, followed by four-wave mixing operation (single-mode squeezing or amplification). In this mode, the qubit and resonator information are exchanged, and then by applying a relatively strong pump (relatively high power) to the resonator at the resonator frequency f R (or at twice the resonator frequency, 2f R ), the reflected readout signal can be squeezed or amplified, which can lead to an improvement in the measurement signal-to-noise ratio (SNR). This single-mode squeezing or amplification is useful in implementing certain error-correcting bosonic codes. In another embodiment, in the four-wave operation (single-mode squeezing), the vacuum noise inside the readout resonator is squeezed before the information exchange between the qubit and the resonator.

[0041] The description of the various embodiments of the present invention has been given for illustrative purposes, but it is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein are chosen to best explain the principles of the embodiments, the practical application, or the technical improvement of the technology existing in the market, or to enable other ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A superconducting quantum mechanical device, comprising: a first Josephson junction, a second Josephson junction electrically connected to the first Josephson junction, a third Josephson junction electrically connected to the second Josephson junction, and a fourth Josephson junction electrically connected to the third Josephson junction and the first Josephson junction, such that the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction are connected in a bridge circuit having a first resonant eigenmode, a second resonant eigenmode, and a third resonant eigenmode; a first capacitor pad and a second capacitor pad, the first capacitor pad being electrically connected to the first Josephson junction and the fourth Josephson junction at a node between the first Josephson junction and the fourth Josephson junction, the second capacitor pad being electrically connected to the second Josephson junction and the third Josephson junction at a node between the second Josephson junction and the third Josephson junction, such that the first capacitor pad, the second capacitor pad, and the bridge circuit form a superconducting qubit having a resonant frequency corresponding to the first resonant eigenmode of the bridge circuit; a first resonator section and a second resonator section, the first resonator section being electrically connected to the first Josephson junction and the second Josephson junction at a node between the first Josephson junction and the second Josephson junction, the second resonator section being electrically connected to the third Josephson junction and the fourth Josephson junction at a node between the third Josephson junction and the fourth Josephson junction, such that the first resonator section, the second resonator section, and the bridge circuit form a resonator having a resonant frequency corresponding to the second resonant eigenmode; and a magnetic flux source disposed near the bridge circuit, wherein the magnetic flux source is configured to provide a magnetic flux through the bridge circuit during operation to cause coupling between the first resonant eigenmode, the second resonant eigenmode, and the third resonant eigenmode when the third resonant eigenmode is excited.

2. The superconducting quantum mechanical device according to claim 1, wherein the magnetic flux source is a current-carrying element to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit.

3. The superconducting quantum mechanical device according to any one of the preceding claims, wherein the magnetic flux source is a magnetic material to provide an electromagnetic magnetic flux source for flux biasing the bridge circuit.

4. The superconducting quantum mechanical device according to any one of claims 1 to 2, wherein the magnetic flux source is controllable.

5. The superconducting quantum mechanical device according to any one of claims 1 to 2, wherein the magnetic flux source provides half of the flux quantum φ 0 / 2.

6. The superconducting quantum mechanical device according to any one of claims 1 to 2, wherein, the superconducting qubit is a transmon-like qubit.

7. The superconducting quantum mechanical device according to any one of claims 1 to 2, wherein the first resonator section and the second resonator section are both resonator lines of substantially equal length.

8. The superconducting quantum mechanical device according to any one of claims 1 to 2, wherein the first resonator portion and the second resonator portion include resonator lines disposed between electrically grounded pads.

9. The superconducting quantum mechanical device according to any one of claims 1 to 2, further comprising a resonator feeder configured to be electromagnetically coupled to the resonator to provide excitation of the second resonant eigenmode during operation.

10. The superconducting quantum mechanical device according to claim 9, wherein the resonator feeder is separated from the resonator to define a capacitor between the resonator feeder and the resonator.

11. The superconducting quantum mechanical device according to any one of claims 1 to 2, further comprising a qubit feeder configured to be electromagnetically coupled to the superconducting qubit to provide excitation of the first resonant eigenmode during operation.

12. The superconducting quantum mechanical device according to claim 11, wherein, the qubit feeder is separated from the superconducting qubit to define a capacitor between the qubit feeder and the superconducting qubit.

13. The superconducting quantum mechanical device according to any one of the preceding claims 1 to 2, wherein the superconducting qubit and the resonator are formed on the same substrate, and the bridge circuit is substantially located at the common center of the superconducting qubit and the resonator.

14. The superconducting quantum mechanical device according to any one of the preceding claims 1 to 2, wherein, the first resonator portion, the second resonator portion, the first Josephson junction, the second Josephson junction, the third Josephson junction, and the fourth Josephson junction include a superconducting material selected from the group consisting of Al, Nb, NbTiN, NbN, and TiN.

15. The superconducting quantum mechanical device according to any one of the preceding claims 1 to 2, wherein the third resonant eigenmode is excited using a control drive applied to the superconducting qubit or the resonator.

16. The superconducting quantum mechanical device according to claim 15, wherein the frequency of the control drive is set to the difference between the qubit frequency of the superconducting qubit and the resonant frequency of the resonator.

17. The superconducting quantum mechanical device according to claim 15, wherein the amplitude of the control drive is set to produce a full frequency conversion between the superconducting qubit and the resonator.

18. The superconducting quantum mechanical device according to claim 15, wherein, the amplitude of the control drive is set to produce a 50:50 beam splitter, where half of the qubit information is exchanged with half of the resonator information.

19. The superconducting quantum mechanical device according to claim 15, wherein the frequency of the control drive is set to the sum of the qubit frequency of the superconducting qubit and the resonant frequency of the resonator, and the amplitude of the control drive is set to produce two-mode squeezing of the qubit mode and the resonator mode.

20. The superconducting quantum mechanical device according to claim 15, wherein the frequency of the control drive is in the microwave frequency range.

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